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ANOVA - Science method

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Results show that these tests are not significant in every personal and functional data even though logically there is difference!
I have gender (male, female)
Position (3 choices)
Experience (4 choices)
How to treat this and did i use the wrong anova test?
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It seems like you are trying to compare categorical variables (gender, position, and experience) using an ANOVA test. However, the ANOVA test is primarily used to compare means between groups in a continuous variable, given categorical variables.
For your dataset, which contains only categorical variables, you should use a Chi-square test of independence to examine whether there is an association between these variables. The Chi-square test assesses the statistical significance of differences between two or more independent groups with categorical variables.
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Wir haben folgendes Design:
  • AV: Akzeptanz von Algotithmen
  • Es gibt drei Gruppen: a) ohne Hinweistexte, b) mit sachlichen Hinweistexten c) mit emotionalen Hinweistexten
  • Die Probanden sollen die Akzeptanz von Algorithmen bei insgesamt zwanzig verschiedenen Szenarien angeben. Diese Szenarien haben jeweils eine Bewertung auf den Skalen Risiko (1=niedrig .. 5=hoch) und Kreativität (1=niedrig .. 5=hoch)
Gewünscht ist eine Auswertung, wie sich die Hinweistexte auf die Akzeptanz auswirken unter der Moderation von Risiko und Kreativität des Szenarios.
Der Faktor Hinweistext ist offenbar between subject mit drei Ausprägungen. Aber wie gehe ich mit den Faktoren Risiko und Kreativität um? Ist das eine Messwiederholung (ANOVA)? Wie berechet sich die benötigte Stichprobengröße?
Ich würde mich über sachdienliche Hinweise freuen.
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Achim Scheuss , you should rather thank ChatGPT. Chuck's answer has a 100% chance of being AI generated (according to https://www.scribbr.com/ai-detector/).
Further note that your question cannot be seriously answered until you describe in detail what your DV and your sample size is so that sufficient information is available to judge a sensible distributional model or if one may possibly rely on the central limit theorem.
An additional aspect not at all recognized by the AI is that your two predictors are ordinal. I think this is relevant and should be considered in the analysis. I don't know how to do this with ordinal data, but maybe it is already helpful to not analyze the data but to analyze their ranks instead and use a multiple regression model including an interaction term. In any case I'd suggest to think about a good visualization of the results like in a heatmap (2 dimensions for the predictors, DV value is color-coded) or something similar to recognize and interpret general patterns.
A serious statistical analysis will surely include extensive simulations that would need to be programmed. This will require a consultation of a statistician being experienced in such things. Here I do agree with the advice given by the AI.
PS: just for comparison, this text has a 5% chance of being generated by AI ;)
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I can't really wrap my head around this and maybe somebody can help me.
I conducted an experimental study with a 2x2 between-subjects design (n = 50 per condition). I have the following variables:
  • Fixed factor 1 (dichotomous, experimental manipulation of stimulus)
  • Fixed factor 2 (dichotomous, experimental manipulation of stimulus)
  • DV (metric, a scale from the questionnaire)
  • Covariate (metric, a scale from the questionnaire)
  • Moderator (metric, a scale from the questionnaire)
I first ran the base ANOVA model with the following terms:
  • Factor 1
  • Factor 2
  • Factor 1 * Factor 2
  • Covariate
Nothing was significant. Out of curiosity, I included the moderator by adding the following terms in addition to the above:
  • Moderator
  • Moderator * Factor 1
  • Moderator * Factor 2
  • Moderator * Factor 1 * Factor 2
What happened is that Factor 1 * Factor 2 became significant (after being non-significant in the base model) as well as the three-way interaction Moderator * Factor 1 * Factor 2.
So the 2 issues I am struggling with are the following:
  1. Why did the interaction of Factor 1 * Factor 2 become significant (p = .036) even though it was not even close (p = .581) in the base model without the moderator?
  2. How do I make sense of the three-way interaction and how can I best report it?
For the two-way interaction, I guess that I would report the marginal means of the DV in the 4 conditions and plot them with lines. This option is provided by SPSS.
But for the three-way interaction, if I understand correctly, the above two-way interaction between experimental conditions is not uniform, but differs across various levels of the metric moderator (e.g., the two-way interaction might be reinforced/attenuated/reversed/non-significant at certain values of the moderator). But SPSS doesn't seem to offer an option to plot this in the ANOVA menu.
I know that the PROCESS macro by Hayes features conditional effects at -1 SD, mean, and +1 SD values of the moderator as well as Johnson-Neyman areas of significance. So I guess I would need something in this direction. Or am I mixing up things here?
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Not only in regression, but also in ANOVA, it is crucial to center your continuous covariates (as in ‘A by B with covariate’). That is, when you also request interactions between such a covariate and a main effect in the ‘/design’-subcommand. Otherwise, it may indeed occur that a lower term interaction may become false significant through adding a higher term interaction, as you described. In fact, without centering, your results are nearly uninterpretable. The main purpose of centering is to make the main-effect terms and the interaction-effect terms independent of each other, so they can be evaluated separately. This is also crucial in ANOVA with covariates, and this has received far too little attention. Not centering will give you counterintuitive results, as you experienced already.
To see what a three-way interaction might look like in practice, I made an exaggerated example in Figure ‘Three-way interaction example.png’. To illustrate, the DV increases from A=1 to A=2 in the B=2 subgroup when the Moderator=1, but decreases in the B=2 subgroup when the Moderator=3. (The Moderator here is ‘continuous’, be it only with values 1, 2, and 3 for illustrative purposes). In other words, the interaction between A and B depends on a third factor, in this case the ‘Moderator’.
In ‘Annotated SPSS-syntax with three-way interaction.docx’ you may see how you can make a Figure at the values of Moderator = M-1SD and M+1SD (there is no need to study and use Hayes’ PROCESS to do this). The result is (again) that the DV in subgroup B2 increases from A=1 to A=2 when the Moderator is ‘low’ but decreases when the Moderator is ‘high’. The A*B interaction depends on the value of the Moderator (see: ‘Three-way interaction example with Moderator at M-1SD and M+1SD.png’).
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Hey,
I am wondering which tests I can do to analyze my results and if there is a better way to analyze my results. If I have multiple treatments in columns and I have just one donor in a row, should I use an unpaired ANOVA test with Tukey's post-hoc analysis to compare my treatments to one another or can I use an unpaired student t-test and then manually compare each treatment alone to my control group. Also, if I have multiple treatments but then I have two donors, can I perform a paired ANOVA or is it ok to do a student's t-test and compare each treatment individually to my untreated samples? Which test in both cases is more reliable, and should I assume normal distribution and sphericity? I have no idea about specific things and I am wondering which one is the best to present in my thesis. Besides, If I do a t-test and ANOVA on the same data, some treatments are significant in one test but not in the other, what is the reason behind that? Furthermore, why do we perform statistics on raw data not normalized data?
Thank you, your inputs are well appreciated
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Hey Abolfazl,
I went throught the guide and tried to understand but to be honest, it’s not easy and I didn’t come up with satisfactory answers to what is the best option. That’s why I asked a question here.
Thank you
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Software procedures:
Make ANOVA 1 Analysis data with R software.
Find out "P" and "F" with values during an ANOVA 1 Analysis of experimental data.
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You can get statistical analysis like ANOVA by using 'LibreOfficeCal'(Pre installed in the ubuntu system). 1) Put your data then> 2) Select 'data' from above> 3) Select ANOVA (According to your requirement one way/two way).
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I want to research on the moderating role of anxiety trait levels (continuous) in the effects of type of reinstatement (independent variable, categorical) on fear avoidance behaviors. I cannot seem to find how to work with a categorical independent variable in a moderation analysis on SPSS and I was wondering whether I need to create dummy variables and run the typical moderation analysis or whether I should conduct a factorial ANOVA.
Thank you!
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Conventionally, factorial ANOVA involves only categorical IVs and a continuous DV. ANCOVA (i.e., "analysis of covariance") includes a continuous moderator in the model.
If you predict fear-avoidance (your continuous DV) from (1) the reinstatement types (a set of dummies), along with (2) anxiety (the continuous "covariate") and (3) a set of interaction terms (each of which is the product of a reinstatement dummy times anxiety), then you have an ANCOVA model. The interaction terms capture the moderation.
The conventional terminology is at best imprecise, because even the simplest regression model, without interactions, is ultimately based on the variances and covariances of the variables. Nevertheless, the model you have in mind is usually called ANCOVA.
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Using a questionnaire, I analyse the affective well-being after three different dance lessons at three points in time (before, during, after) in the same subjects. Background: the social interaction is changed in each of the three dance lessons, while movements, sequences, etc. are kept the same.
On the one hand, I would like to investigate whether well-being generally increases as a result of dancing, as well as whether well-being changes differently depending on the dance lesson content (social interactions). For this I would use a repeated measures ANOVA.
I would also like to investigate whether the experience of competence surveyed has an influence on the change in well-being (co-variate). I have read that an ANCOVA obviously does not work with a repeated measures ANOVA. Which statistical analysis should I use instead to analyse the influence of a co-variate (or moderator)? Thank you very much for your help
Translated with DeepL.com (free version)
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Thank you very much!
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Hi everyone,
I have data available for 4 years. To Compare weight-loss outcomes between the four medication groups for whole years, I will apply one-way ANOVA.
but I will be asked to compare weight-loss outcomes between the four medication groups for each year of the study. My question is,
should I apply one-way ANOVA 4 times as I have four years?
Thanks
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To compare weight-loss outcomes between the four medication groups for the entire duration of the study (four years), you can use a one-way ANOVA. Here's how you can do it:
  1. Data Preparation:Organize your data into a spreadsheet or dataset where each row represents a participant, and each column represents a variable, including medication group and weight-loss outcome. Assign numerical codes to represent the four medication groups (e.g., 1, 2, 3, 4).
  2. Check Assumptions:Before conducting the ANOVA, check the assumptions of normality and homogeneity of variances. You can use statistical tests (e.g., Shapiro-Wilk test for normality, Levene's test for homogeneity of variances) or visual inspections (e.g., histograms, Q-Q plots) to assess these assumptions.
  3. Conduct One-way ANOVA:Use statistical software such as R, SPSS, or Python with libraries like scipy.stats or statsmodels to conduct the one-way ANOVA. Input the weight-loss outcome variable as the dependent variable and the medication group variable as the independent variable. The ANOVA will test whether there are statistically significant differences in weight-loss outcomes among the four medication groups.
  4. Post-hoc Analysis (if necessary):If the ANOVA results indicate significant differences among the medication groups, you may want to conduct post-hoc tests to identify which specific groups differ from each other. Common post-hoc tests include Tukey's Honestly Significant Difference (HSD) test, Bonferroni correction, or Dunnett's test.
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I wanted to ask for clarification on statistical approaches for a classic 2x2 pre-post design where I measure an outcome in a pre-intervention and post-intervention phase in two distinct groups.
Typically, what we want to investigate in these cases is the interaction, which tells us if the changes over time in a specific outcome differ between the two groups. To do this, we have three approaches available: Repeated Measures ANOVA (RM ANOVA), ANCOVA, and Linear Mixed Models (LMM).
RM ANOVA: It allows us to study the interaction, as well as the main effects of the between-subject factor (group) and the within-subject factor (time). So, besides telling us if there's a different change over time for the two groups, RM ANOVA also informs us if there's a general change over time (disregarding groups) and if there's a general difference between the two groups (disregarding time). However, the issue with RM ANOVA is that it doesn't allow us to covary the score of the outcome in the pre-intervention phase. This means that any significant pre-intervention difference between the two groups could influence the results and make their interpretation much less robust. The solution in this case would be to verify (with an independent samples t-test) that there are no pre-intervention differences between the two groups in the outcome.
ANCOVA with the pre-intervention outcome score as a covariate: It allows us to see if there are differences between the two groups post-intervention. It doesn't tell us if there's a different change over time between the two groups, if there's a general change over time, or if there's a general difference between the two groups. It doesn't evaluate the interaction, the main effect of time, or the main effect of group, unlike RM ANOVA. The advantage of ANCOVA is that it enables us to study the differences between the two groups ONLY in the post-intervention phase, accounting for pre-intervention differences in the outcome. This means that this model works well even in cases of large outcome differences between the two groups in the pre-intervention phase.
Therefore, RM ANOVA and ANCOVA provide quite different information. If there are differences in the outcome in the pre-intervention phase, it's advisable to use ANCOVA (less informative, as it considers fewer effects); otherwise, it's better to use RM ANOVA (more informative, as it considers more effects). Right?
The solution to all of this is LMM because, in addition to considering all the effects of RM ANOVA (interaction + the two main effects), it also models any differences in the outcome pre-intervention. So, is it always better to use an LMM, right? Is everything correct, or am I missing something?
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Yes, I'm referring to a true experiment where subjects are randomly allocated to groups
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If the Box's Test yields a significant p-value (p < .001), indicating unequal covariance matrices of (X) across (3 variables) between (2 groups), it raises concerns about the assumption of homogeneity of covariance matrices. (ratio between 2 groups 1.21) In such cases, should we still rely on the results of the multivariate test, or should we consider applying Mauchly's Sphericity Test?..
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Neither. If there are more than 2 levels on a repeated measures factor it's sensible to assume the sphericity assumption is violated. The question is the severity of the violation. Using a correction based on epsilon is a sensible choice and will result in no correction if epsilon = 1 and the assumption is met.
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I have performed a fairly standard kinetics experiment, in which I investigated the stability of various oligonucleotides in an enzyme solution, by incubating the oligonucleotides with the enzyme solution over the course of 1 hour. I took aliquots at 7 time points, added a stopping buffer and performed a denaturing urea PAGE electrophoresis.
I expressed stability as a general proportion of (top band)/(all fragments+top band).
I performed a two-way ANOVA (edit. RM ANOVA) test in GraphPad Prism (the factors being time and the different oligos) and a Dunnett multiple comparisons test (as the first (0) time point was being used as a control). Following the recommendations on the GraphPad website I used a Geisser-Greenhouse approximation, as the sphericity assumption was violated (the epsilon estimate was equal to 0,2855).
I have doubts that I have perfomed the analysis correctly as the statistical significance between the control and some of the points seems too small (*) between points that visually are miles apart and which don't have large SD's. Conversely it gives the same significance to points very close to a control (though in these cases the SD's are extremely minor, so this part makes sense to me).
I have read that the GG approximation can underestimate p-values. I can't just assume sphericity regardless, as it overestimates significance and puts (****) pretty much everywhere. Hence I assume performing a Mauchly test on some other software would be redundant at this point, its seems very clear that a correction is required.
Should I use some other p-value correction? The epsilon estimate seems too small for Huynh and Feldt, and, from what I can tell, noboby uses lower bound estimates anymore. Perhaps take I should take a different approach to analysis altogether (possibly not on GraphPad)?
Any suggestions will be appreciated.
Thanks in advance!
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Bruce Weaver RM ANOVA should use paired t tests and probably a multiplicity correction as this doesn't require sphericity and respects the correlated structure in the data.
The GG correction is conservative and the HF correction liberal so I have seen a suggestion that you could average the two epsilon estimates. However generally I think HF is OK when epsilon is close to 1 and GG better when its close to lower bound.
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1. Can I do one way ANOVA to know significant difference between my 3 groups on individual Likert items( each measured on 5 point scale). These Likert items are part of my unobserved latent variable. I have read that Likert items measured on atleast 5 point scale can be treated as interval / continuous data. Therefore I don't want to analyse it using non parametric Kruskal wallis test. 2. Am I correct in my approach?
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Traditionally, a statistician would advise against it as it would violate the assumptions of ANOVA, but there is evidence to show that despite the violation of certain assumptions, ANOVA is capable of helping one reach the right conclusion.
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In a clinical study, after applying the clustering method, several classes are identified. We perform ANOVA or Kruskal Wallis for between-class comparison. The class has a different sample size (unequal). I hope that is fine. For a post hoc test, it has been suggested that effect sizes are better than the p-value. Can you please suggest what type of effect size is expected? If there is any other method, please let us know.
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If you are opting for ANOVA, you need to calculate eta square. In case you have opted for the Kruskal-Wallis test, then you need to calculate Epislon's measure. I have a YouTube video on how to do this.
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1. Is Smartpls the only way to deal with formative constructs?
If we have formative constructs, cant we use SPSS and AMOS? If not, that means that all the studies done on SPSS and AMOS are having only reflective constructs (having similar meaning items)?
2. What to do if i have formative constructs, but want to do EFA & CFA?. Can I do ANOVA, MANOVA and other multivariate tests on formative constructs?
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Hi Karan
1. No. In SPSS you could run a principal component analysis which is a model for causal indictors. In AMOS you could set up a model with causal indictors, although there will some restrictions - have a look at some more brilliant work by Bollen on this issue doi: 10.1037/a0024448
2. Yes, you could use principal component analysis to do an 'EFA' although this would not strictly be a factor analysis, and a CFA could be set up with causal indictors.
Once you have a measurement model set up, the ANOVA or MANOVA are not too difficult to specify by using dummy coded variables (and maybe products if you want interactions). Have a look at some of Richard Bagozzi's work from back in the day - it's brilliant.
My usual suggestion when there are questions on formative/reflective constructs is to read everything Ken Bollen has written on this - start with the 'Conventional Wisdom' paper, it's one of the best papers on measurement that has ever been written.
Bollen, K., & Lennox, R. (1991). Conventional wisdom on measurement: A structural equation perspective. Psychological Bulletin, 110(2), 305–314. https://doi.org/10.1037/0033-2909.110.2.305
1991 was a good year for the nerds!
Mark
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Can I do ANOVA, MANOVA & Multiple regression with formative constructs?
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Mahesh Lal Maskey
Assumptions about the correlations among the predictors are only problematic in the presence of high multicollinearity, and I doubt that PLS can solve that problem.
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If I do ANOVA after calculating the MEAN (which will form my continuous dependent variable) of all 6 items ( MOT 1, MOT 2, MOT 3, MOT 4, MOT 5, MOT 6), then how can i find out difference between my three groups (independent categorical variable), on the basis of any specific motivation item out of these: ( MOT 1, MOT 2, MOT 3, MOT 4, MOT 5, MOT 6) ?
Please suggest the right way to do it. I know ANOVA can give me significant difference between the three groups with post hoc analysis, but how can I ascertain the difference on a specific item level, if I am transforming the 6items to a mean value? Is it better to do MANOVA or apply any other technique for this purpose??
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I am running a two-way mixed anova analysis with one IV is a between-subjects variable and another is a within-subjects variable (each participant was measured six times) and find a significant interaction effect. What should I do to interpret the interaction? I have find similar papers and it says that we should calculate the slope for each participant as shown in the picture, but how?...I am really confused...
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If you obtain an overall p value less than 0.05 for the total ANOVA, you then do pairwise comparisons between the variables to find out which have significant interactions. You don't need to do anything with slope values :)
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I have two groups (A and B) each going through 5 repeated measures. I want to know how I can determine eta squared so that I can use it to calculate an a-priori sample size.
Thanks in advance
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Hi,
Before your study, estimate the effect size for your mixed ANOVA by reviewing similar research or using Cohen's conventions if no prior studies exist. Then, determine your sample size using G*Power, considering your desired power and significance level.
Hope this helps.
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Dear experts,
Now I am writing my PhD research proposal, and I have a question regarding variables.
You see, I have two dependent variables in my research and one independent variable. My question is, is it ok to have two DVs in my research? If so, what kind of methodology should I use to justify it? (I think maybe AnoVa is cool?)
Thank you. I am looking forward to hearing from you.
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Mingyue Li Thank u very much for your response. Now, I get it noww.
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My research scenario is as follows:
I have ppts in three different intervention groups (independent variable one, between groups)
I have two time points (independent variable two, within groups) where scores on psychometrics will be recorded first at month 0 and month 12
My dependent variable is treatment change from month 0 to month 12
Am I right in thinking that the appropriate statistical analysis would be a mixed factorial ANOVA? As I have two IV's, one between, one within, and want to measure their effect both together and separately on my DV.
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It took me a while to work out that ppts = participants.
I have two questions (for now):
1) Were participants randomly allocated to the 3 groups?
2) Was the baseline score (at time 0) obtained prior to the interventions being administered?
If the answer is yes to both of those questions, then I think ANCOVA would be in order (with the 12-month score as the DV and the baseline score as the covariate). See this BMJ Stats Note, for example:
HTH.
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In my study, I have a within-subject independent variable (the DV was measured twice for each participant), and I am also interested in examining the effect of participants’ demographic characteristics (between-subject) on the dependent variable. Therefore, I am running a mixed model ANOVA using SPSS.
Here are my questions:
  1. I noticed that the SPSS output of the mixed model ANOVA is slightly different (in both the main effects of the two IVs and their interaction effect) when I (1) run the analyses for each demographic characteristic individually and (2) include all the demographic characteristics in the between-subjects factor column simultaneously. Why is this the case? (Is this related to multiple comparisons and type I error? and/or different missing data in the multiple analyses?) And which one is the correct way to do so?
  2. One of the demographic characteristics I am interested in examining is a continuous variable (e.g. age). However, since the IV must be categorical for ANOVA, can I include the continuous variable as a covariate in the analysis but interpret the results the same as if it is an independent variable? If not, then what analysis can I perform in SPSS to examine the effect of a continuous between-subject IV on a continuous DV, along with the categorical within-subject IV?
Thank you in advance for your advice.
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Hello,
Yes, you can interpret and report the results of a continuous covariate (e.g., age) as a main effect, similar to an independent variable. Phrases like 'when controlling for...' indicate that the effects of covariates have been accounted for in the analysis.
Hope this helps.
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For my research, I have to compare multiple groups (between) and some factors within those groups. I will try to explain it as good as possible.
Independent variable: group. There are two groups: experts (N =13) and non-experts (N=13). These two groups evaluated 6 different robot gestures, representing emotions. They evaluated these via 6 videos. The 6 emotions represented were: anger, surprise, happiness, fear, sadness and disgust.
They received this statement for every emotion: it is feasible for a child with the Autism Spectrum Disorder to recognize this emotion.
They answered via a 7-points Likert item (1 = strongly disagree to 7 = strongly agree).
I have to compare the feasibility of the gestures within the groups (within) and for every emotion between the groups (between). I was thinking about a mixed ANOVA. Unfortunately, some data is not normally distributed (I used Shapiro-Wilk in SPSS for this because of my sample size). The emotions anger, sadness, disgust (only for non-experts) and fear (only for non-experts) are not normally distributed. I tried to fix this with transforming (log) but this did not work.
I saw something about the Generalized Estimating Equations (GEE) and the Friedman test (non-parametric tests) but I am still not really sure what to do.
I hope someone can give me some tips.
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Did you by any chance find the solution to this problem?
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I have the survey among three groups of health professionals to answer the survey.
The survey is a Likert scale for seven different treatment options across different disease conditions (6 conditions).
The goal is to assess if there's a statistically significant difference between the mean scores of these different groups of health professionals for various treatment options.
I have 6 different disease condition (or 6 different question) each question with 7 different treatment option.
I am thinking to run ANOVA works here, but if I want to run ANOVA, then will need to run that 42 times. Because (6*7=42)
Then Applying corrections like the Bonferroni correction to adjust for the increased risk of Type I errors (false positives) when conducting multiple statistical tests, such as multiple ANOVAs. But still will need to apply ANOVA 42 times, is that correct method to do for this? Is there Any better method?
if I want to calculate the overall mean score for one specific treatment option across all disease conditions, then will run the ANOVA just seven times.
If I want to go with the first approach, what method do you suggest?
Am I correct to apply anova?
Thanks
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I agree with Hsin-Yuan Chen . MANOVA would be more suitable for your dataset and experimental design. It helps to control the Type I errors more effectively.
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Hello,
I conducted a lexical decision task using two distinct talkers (within subjects), to determine if three different types of particpants would respond differently (between subjects). Groups were counterbalanced as words 1-20 were spoken by a male talker, and words 21-40 were spoken by a female talker for half of participants (and vice versa).
I was guided to perform three separate ANOVAs on
-reaction time (ms)
-accuracy (0-1, means hovering around 93%)
-recall (0-20, means hovering around 2)
I have performed a log transformation on the reaction times for analysis. What transformations would be recommend for accuracy percentages and for the number of words recalled?
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I think one question we all have is if there is a reason you want to do an ANOVA?
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Hi everyone, I would appreciate to tell me you suggestion:
I’m going to compare just two independent group. The outcome variables are continuous -one of them has 5 subclass and another one has 4 subclass-
I am thinking to apply running separate t-test for each subclass of these outcome variables (to compare total score and subclass score).
Then will consider adjusting for multiple comparisons to control the Type I error rate by Bonferroni correction.
But as I have one confounding variable, so will ignore T-test and apply ANCOVA?
Am I correct, ANCOVA is the best for my goal?
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Excellent method. Thanks for sharing. I was unaware of this unique advantage of logistic regression.
Many Thanks,
Bahar.
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Dear Community,
I have recently used Aligned Rank Transform (ART) ANOVA for my dataset, due to its non-normal distribution and heteroscedasticity. As you might know, ART ANOVA is performed on aligned ranks rather than the original data.
I need to visually represent the main and significant effects of the factors studied. However, I am uncertain about the most appropriate method for plotting these effects. My question is:
Should I plot the differences in levels of a factor (e.g., showing mean values and error bars) using the aligned ranks generated from ART ANOVA? Is there a recommended best practice for visually summarizing the ART ANOVA results to illustrate the significant effects clearly and accurately?
I would greatly appreciate any insights or references to literature that could guide the appropriate visualization of ART ANOVA results.
Thank you
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As a further comment, if you are doing the analysis in R with ARTool, you can get output akin to emmeans with standard errors with, e.g.
art.con(model, "Location", method="eff")
However, it appears that the output is in the scale of the ranks, and relative to a zero effect point. So, it's probably not practically useful for a reader. But is kind of the right way to summarize the output of the model.
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I performed swelling experiments three times for each of five different samples, recording measurements every hour for 24 hours. How do I apply ANOVA to analyze this data?
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Why ANOVA? Sounds more like a regression problem (time-series).
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I can select one of these method:
  • Mann-Whitney/Kruskal-Wallis
  • T-test/ANOVA
  • metagenomeSeq (fitZIG)
  • metagenomeSeq (fitFeature)
  • EdgeR
  • DESeq2
Thank you in advance
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Your problem is going to be that nothing other than a barn-door difference is going to be significant. If you really want to distinguish between cancer and polyp tissue, this is too important a question to be decided on the basis of small numbers. The only thing that a small sample is useful for in a case like this is where there is a stunning difference between the groups – passes the Mark I Eyeball Test – indicating that the marker has possibly got clinical potential.
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Greetings, I am final year BSc.(H) Psychology. I used two-way, repeated measures ANOVA for a 2x2(time x intervention) pre and post-test model for my study. Now, within-subject effects of time and intervention are significant. However, the significance level of time*intervention is (0.67). How do I interpret these results?
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You have detected differences in the groups and a change in the outcome over time, but neither of these effects is related to the intervention. In a pre-post design the interaction is a test of the intervention because you'd expect the pre intervention scores to be similar (especially in a randomized design) and so the intervention effect should show up in the post scores only. This effect (the group difference on post minus the group difference on pre) is the intervention effect and what is tested by time*intervention.
One puzzle is that the groups differ at pre as well as post which suggests its not a randomized design (or you were unlucky).
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We are a group of students working on a grant poposal as part of our veterinary degree but are struggling with choosing the right statistical test.
Our project compares 2 premedication protocols in horses undergoing GA (60 horses in each group) where multiple parameters will be measured during the surgery (ie heart rate, blood pressure among other) every 10min. We are expecting the surgeries to last a maximum time of 120mins, which will create a lot of data to analyse.
Would a 2 way anova test be more accurate or should we consider running multiple T test (for each paramters measured) ? Our goal is to determine if one premedication protocol is better at safeguarding cardiovascular properties of enrolled animals vs the other premedication protocol.
Thank you any help !
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Jochen Wilhelm wrote: If the course over time is relevant, then I'd expect some time-course analysis, that is, some kind of regression models, not ANOVAs or t-tests.
I agree. In that case, I think you would want a multilevel model, with horses as level 2 variables and occasions of measurement at level 1 (i.e., clustered within horses). Here are a couple of places where you might find some helpful resources:
Q. How many cardiovascular features will be recorded? And are they all considered equally important? Or do you have a small number of primary outcomes (1 or 2) with the others being considered secondary?
What I am getting at with that question is the so-called multiplicity problem that arises when you have multiple outcomes. Two of my favourite articles on multiplicity are these 2005 Lancet articles by Schulz & Grimes:
Finally, your situation reminds me of the attached excerpt from Frank Harrell's well-known book on regression models. He described a two-group clinical trial with several DVs measured on just one occasion. And in that scenario, he suggested binary logistic regression with group (treatment vs control) as the outcome variable and the multiple DVs (as originally conceived) as the explanatory variables. In your case, given the repeated measurements every 10 minutes, you would have to use a multilevel logistic regression model to account for the clustering of the repeated observations within horses.
Please bear in mind that I have only been thinking about this for 10 minutes, and I never heard Harrell or anyone else extend his suggestion to this multilevel scenario. But on the face of it, it makes sense to me. ;-)
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Q1
We have animal behavior scores of 4 group, Normal+ctrl virus, Normal+down-regulation virus, Model+ctrl virus and Model+down-regulation virus. It has two factors(Independent Variable): Model and virus. Editors suggested we use two way ANOVA to analyze, and now we obtained main effects of Model (F(1, 56)=201.18, P<0.0001) and virus (F(1, 56)=11.17, P=0.00427), as well as Model × virus interactions (F(1, 56)=16.13, P=0.0007).
If we should continue to calculate? For example, Model+ctrl virus vs. Model+down-regulation virus. We want to confirm the role of virus in Model animals.
Q2
Next, we used chemical drug to treat the Model animals and Normal animal. It has 4 drug concentration. Should we still use two way ANOVA to analyze the behavior scores? We want to know the role of different drug concentration in Model animals. And what do we do after two way ANOVA?
Thanks very very much!!!
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Dear Esteemed Colleague,
Following the completion of a two-way ANOVA, which serves to ascertain the effects of two independent variables on a dependent variable, as well as any interaction between these independent variables, your subsequent steps should be methodically oriented towards a comprehensive interpretation and validation of the results obtained. Here is a structured approach to guide your post-ANOVA analysis:
  1. Examine ANOVA Assumptions: Prior to delving into further analysis, it is crucial to ensure that the assumptions underlying the two-way ANOVA have been met. These include the assumptions of normality, homogeneity of variances (homoscedasticity), and independence of observations. Tools such as the Shapiro-Wilk test for normality and Levene's test for equality of variances can be employed to assess these assumptions. Should any assumptions not be satisfied, corrective measures such as data transformation or the use of non-parametric tests may be considered.
  2. Interpret Main Effects and Interaction Effects: The core of your analysis will involve interpreting the main effects of each independent variable and any interaction effects between them. A significant main effect indicates that different levels of an independent variable have significantly different impacts on the dependent variable. A significant interaction effect, on the other hand, suggests that the effect of one independent variable on the dependent variable varies depending on the level of the other independent variable. It is essential to carefully interpret these effects in the context of your research question.
  3. Conduct Post Hoc Tests for Multiple Comparisons: In the event that your ANOVA results indicate significant effects, post hoc tests are necessary to determine which specific groups differ from each other. Techniques such as Tukey's HSD (Honestly Significant Difference) test, Bonferroni correction, or Sidak adjustment are commonly employed for pairwise comparisons while controlling for the family-wise error rate. The choice of post hoc test depends on the specific characteristics of your data and the comparisons of interest.
  4. Evaluate the Magnitude of Effects: Beyond statistical significance, assessing the practical significance of your findings is vital. This can be achieved by calculating effect sizes, such as partial eta squared (η²) or Cohen's d, which provide insight into the magnitude of the differences or relationships observed. These measures help to contextualize the importance of your findings in real-world terms.
  5. Graphical Representation of the Results: Visualizing your data and the results of the ANOVA can greatly aid in their interpretation. Interaction plots, for example, are particularly useful for visualizing how the levels of one independent variable affect the outcome across the levels of another independent variable. Box plots and bar charts can also be effective in displaying the central tendencies and variabilities within and across the groups.
  6. Report Your Findings: The final step involves a detailed and coherent reporting of your methodology, analysis, results, and interpretations. This should include a summary of the ANOVA results, post hoc tests, effect sizes, and any graphical representations. It is crucial to discuss the implications of your findings in the context of existing literature and your research objectives, including any limitations and suggestions for future research.
By following these steps, you will ensure not only the rigorous analysis of your two-way ANOVA results but also the meaningful interpretation and reporting of these results within the broader context of your research field.
Should you require further assistance or clarification on any of these steps, please do not hesitate to reach out.
Warm regards.
This protocol list might provide further insights to address this issue.
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As a Computer Science student inexperienced in statistics, I'm looking for some advice on selecting the appropriate statistical test for my dataset.
My data, derived from brain scans, is structured into columns: subject, channels, freqbands, measures, value, and group. It involves recording multiple channels (electrodes) per patient, dividing the signal into various frequency bands (freqbands), and calculating measures like Shannon entropy for each. So each signal gets broken down to one data point. This results in 1425 data points per subject (19 channels x 5 freqbands x 15 measures), totalling around 170 subjects.
I aim to determine if there's a significant difference in values (linked to specific channel, freqband, and measure combinations) between two groups. Additionally, I'm interested in identifying any significant differences at the channel, measure or freqband level.
What would be a suitable statistical test for this scenario?
Thanks in advance for any help!
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SPSS doesn't offer Aligned Rank sum test in version 17-21? If one were to report a multiple time data where continuous variable werent normal, would normalizing and using anova not amount to simple split plot anova? what of if the data is ranked originally, how can one handle it possible with these older SPSS versions?
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What are the possible ways of rectifying a lack of fit test showing up as significant. Context: Optimization of lignocellulosic biomass acid hydrolysis (dilute acid) mediated by nanoparticles
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I performed the mixed model ANOVA analyses and repeated measures analyses.
I need answer for this question:
What is considered small, medium or large effect size and cite reference as needed? Also explain, how should I calculate or examine effect size. I used SPSS.
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Common effect size measures for ANOVA are:
  • Eta Squared (η2): This is often used for between-subjects, one-way, or factorial ANOVA, as well as repeated measures ANOVA.
  • Cohen’s F1
  • Omega Squared (ω2)
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I am analysing a set of data which have both within-subject and between-subject variables. However, since my assigned task is just simply focusing on part of this data set, I am not interested in examining the within-subject variable.
To make you understand it easier, here is an example:
The original study is to examine how the branding of the product (independent variable) affects participants' happiness (dependent variable), and all participants are required to try both brand A and brand B product. However, extending from this original study, I was asked to examine how participants' demographic may actually affect their happiness instead.
My questions are:
  1. Can I run a mixed model ANOVA and only focus on the main effect of the between-subject variable while ignore the main effect of the within-subject variable and the interaction effect? Is this an acceptable way to analyse the data for academic publication?
  2. Since participants are required to try both brand A and brand B product, my dependent variable is recorded by two separated columns in the data set (one for brand A's dv and another for brand B's dv). So, what should I do if the analyses that I want to run does not allow me to specify the within-subject variable. Even if I use the "restructure" function in SPSS and make the dependent variable to be in one column only, I still cannot run the analyses as it violated the assumption of the test (e.g. independence of observation) and make the results less reliable. For example, I want to run the moderation analyses using PROCESS Marco in SPSS, but it only allow me to put one item in the dependent variable option. I can restructure the data, so that my dependent variable would only be in one column. However, I still cannot run the analyses as it violated the assumption of independence of observation. In this case, what should I do?
How can I solve these problems using SPSS? Can anyone help? Thank you
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If your research question(s) is/are completely addressed by the between-Ss factors, then I would say YES in response to your first question. But I imagine that even in that case, reviewers and editors will probably want you to report all of the usual results from your mixed design ANOVA. And I think that's fair enough, given that readers may have other questions beyond your research question(s).
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Hello, I am looking for an advice regarding my experimental design and what statistics I should do.
My experimental design:
I have 3 cell lines (A, B, C) and from each I do 3-4 differentiations into cardiac myocytes (A1-A4, B1-B4, C1-C3). Then each differentiation is treated with the same 3 concentrations of a chemical (T1, T2, T3). And for each treatment, I measure the calcium concentration (y). So I have one continuous dependent variable (y), two categorical independent variables (x1 for cell line and x2 for treatment) and a random error which I want to correct for (e for differentiation).
I want to investigate the impact of the cell line (x1, main effect) on the cell response to the treatment (x2).
  1. I understand that e is nested under x1 but what about x2 ?
  2. Then I am not sure how to translate this in a correct formula for the aov() function in R. I am tempted to use aov( y ~ x1*x2 + Error(e)) but this does not account for the fact that e is nested under x1. Does it matter ?
  3. I don't understand how to interpret the different p-values, which one should I look for to answer my research question?
  4. Can I run a normal Tukey test for post-hoc multiple comparisons by pooling the differentiations (getting rid of the error source) or is there a way to correct for it without including it as another variable ?
Many thanks in advance !
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Sal Mangiafico you are right, but this seems to be a dummy coded variable with 3 levels. Therefore, the differences/slopes are the same, but the first model uses uncorrected test statistics to compare slopes/differences, whereas the "post hoc" test uses Holm adjusted p-values. Camille Charriere maybe it is possible to change the correction option to "none"? Then it should be the same.
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One of the many assumptions in ANOVA is that our data follows a normal distribution. Usually in biology experiments are carried out in triplicates and the avalilable data is very small, not > 30 which I think is standard sample size for assessing normality. Any one who is familiar with use of statistics in phytochemistry, microbiology, pathology or any relavant field kindly answer the following questions.
1. Is it necessary to carry out tests of normality such as Shapiro-Wilk normality test to confirm if our data follows normal distribution?
2. With such a small sample size is it possible to carryout these tests?
3. Is it true that test for normality is unnecessary in biological experiments?
4. Can I safely assume that my data will follow normal distribution wiithout any of these tests?
5. Which statistical software is best for a beginner?
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Checking the normality of your data is important when using parametric statistical tests like t-tests and ANOVA. These tests make certain assumptions about the distribution of the data, and if those assumptions are violated, it can affect the validity of your results.
For t-tests and ANOVA, normality is particularly important when dealing with smaller sample sizes. However, these tests are somewhat robust against violations of normality, especially with larger sample sizes (typically, n > 30 is considered reasonably robust).
If normality is a concern, you might consider non-parametric tests like the Mann-Whitney U test (for two groups) or the Kruskal-Wallis test (for multiple groups) as alternatives.
In summary, while it's a good practice to check for normality, the impact of deviations from normality depends on your sample size and the specific assumptions of the statistical test you're using. If in doubt, consulting with a statistician or using non-parametric tests may be appropriate.
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I would like to utilise the correct regression equation for conducting Objective Optimisations using MATLAB's Optimisation Tool.
When using Design Expert, I'm presented with the Actual factors or Coded factors for the regression equation. However, with the Actual Factors, I'm presented with multiple regression equations since one of my input factors was a categoric value. In this categoric value, the factors were, Linear, Triangular, Hexagonal and Gyroid. As a result, I'm unsure which Regression equation to utilise from the actual factors image.
Otherwise, should I utilise the single regression equation which incorporates all of them? I feel like I'm answering my own question and I really should be using the Coded Factors for the regression equation, but I would like some confirmation.
I used one of the regression equations under "Actual Factors" where Linear is seen, but I fear that this did not incorporate all of the information from the experiment. So any advice would be most appreciated.
Most appreciated!
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Multiple objective is appropriate.
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I am working on plant breeding and need to compare many genotypes in the breeding process. What is the best post-hoc test to compare differences between 10, 20 or 30 genotypes?
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The most appropriate multiple comparison test in filed experiments is Tukey test, because in such as conditions the experimental design could be with factorial arrangement. For this reason, it is important to take into account the experimental design of the experiment and the experimental conditions in which that research is carried out. Duncan's test is only valid for one-factor experiments, while Tukey's test can be used in experiments with a factorial arrangement and of course has greater power according to Fonseca-Pantoja, unpublished, 1990.
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1. As I navigate through the complexities of miRNA expression analysis using qPCR, my study involves a panel of 20 plates, each containing 96 wells—18 dedicated to patient samples and 2 for controls.
In categorizing my samples into newly diagnosed lymphoma/leukemia, those in remission, and those exhibiting resistance to treatment, I aim to calculate essential parameters such as ΔCT, ΔΔCT, and fold change. Is it appropriate to determine the average CT values for each subgroup to obtain a representative measure of miRNA expression within these distinct clinical states? keep in mind each group contain 3 samples from different individuals. Also is't acceptable to take multiple reference genes and take average of them for normalization?
Additionally, I encounter undetermined CT values; what would be the most judicious approach to handle these values? Should I assign them as 35?
Similarly, CT values exceeding 35 pose a challenge. How can I establish thresholds for further analysis in order to maintain data accuracy? because I cant delete any thing from genes as they are panel of miRNA
Moving into the statistical analysis phase, which methods, like ANOVA or t-tests, would be most effective in discerning significant differences between the categories of my samples?
Finally, in presenting my findings, how can I ensure clarity and transparency, incorporating well-organized tables and figures to visually convey the intricate dynamics of miRNA expression?
Moreover, how should I adeptly discuss the biological implications of my results while addressing potential limitations in my study?"
It's worth noting that the source of my samples is plasma, and they are derived from patients with hematological malignancies at various stages of the disease. Furthermore, each sample has been processed only once without any technical repeats.
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Hello vectoria, firstly thank you for your response.
I dont make any replicate and many samples in my plates have undetermined ct values and values above 35, so from this I dont know how I can deal with this to complete my calculation ?
the other thing also I have 2 control , so here also take geomean or arithmatic mean ?
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Hi everyone! I tried to perform a classic One Way Anova with the package GAD in R, followed by a SNK test, which I always used, but it didn't work with this dataset, and I got the same error for both tests, which is the following:
"Error in if (colnames(tm.class)[j] == "fixed") tm.final[i, j] = 0 :
missing value where TRUE/FALSE needed"
I understand there is something that gives NA values in my datatset but I do not know how to fix it. There are no NA values in the dataset as itself. Here is the dataset:
temp Filtr_eff
gradi19 11.33
gradi19 15.90
gradi19 10.54
gradi26 11.01
gradi26 -1.33
gradi26 9.80
gradi30 -49.77
gradi30 -42.05
gradi30 -32.03
So, I have three different levels of the factor temp (gradi19, gradi26 and gradi30) and my variable is Filtr_eff. I also already set the factor as fixed.
Please help me, how do I fix the error? I could do the Anova with another package (library car worked for example with this dataset) and I could do tukey instead of SNK, but I want to understand why I got this error since it never happened to me..thanks!
PS: I attached the R and txt files
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no one aswered but I found the solution so I write it here just in case someone will need it in the future!
with GAD package you have to change the name of the factor , it cannot be the same as the variable so I changed it as in the script I leave here and now it works!
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Mean, median, Range, one way ANOVA, Pearson correlation, spatial distribution with scatter plot, species richness and Shannons index are applied to the data. Is there any other tools are to be included for the data?
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Diversity indices, such as Shannon or Beta, abundance of species, and presence-absence data :)
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I am trying to report the results of a study that employs a 2 (between subjects: tx vs ctrl) X 4 (within subject: time :T0,T1, T2 and T3) mixed factorial ANOVA. I have analyzed the data using both SPSS and JAMOVI.
Personally, I find the JAMOVI results cleaner and the graphs of estimated marginal means much better because SPSS is not graphing with error bars at all. and JAMOVI tables are much simpler.
Question is: why does SPSS provide a multivariate table here for an analysis that is essentially univariate (One continuous DV), then follows it up with separate tables for within and between subjects factors?
Second, from the JAMOVI output, I have been using the interaction term posthoc testing to breakdown the significant interaction- I wanted to verify this is essentially doing the same thing as a simple main effects analysis. conceptually this is testing each level of each factor within each level of the other factor- so this should be okay, right?
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It is not true that SPSS cannot graph error bars. It is possible to show confidence intervals as well as standard errors. Maybe you use an old, outdated SPSS version?
ad 1) I think you description is not correct. The results from the multivariate table and the univariate tables should differ and you do NOT have ONE continous variable but 4, since you have 4 repeated measures. Using an ANOVA approach ist only one method to analyze repeated measures using difference scores. Another approach would be to use MANOVA, where your 4 repeated measures are considered as four DVs. Please have a look at Tabachnick & Fidell (2007) for a detailed description of this approach (a third option would be a multilevel model, which has been recommended instead of an ANOVA apporach in the last couple of years).
ad 2) Is the question if simple main effects are ok? Which post hoc analyzes are "okay" depends on your hypotheses and cannot be answered without further information.
Tabachnick, B. G., Fidell, L. S. (2013). Using multivariate statistics (7th ed.). Boston, MA: pearson.
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I am doing a two way ANOVA in spss 27. However, the homogeneity of variances assumption is violated. Thus, I considered doing a Welch's factorial Anova but I cannot seem to find the way to do this in spss. How can I do this? And is there anything else I can do in spss, as it is the only program available to me, to solve this problem? I tried transforming my DV with the square root method, it did not work.
Thank you
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Hi Sal Mangiafico. Re your first question, a pretty good rule of thumb, IMO, is that if ratio of largest variance to smallest variance is no greater than 4 or 5 (when all sample sizes are equal), the model will be pretty good. See Table 2 in Glass et al. (1972), for example.
Glass, G. V., Peckham, P. D., & Sanders, J. R. (1972). Consequences of Failure to Meet Assumptions Underlying the Fixed Effects Analyses of Variance and Covariance. Review of Educational Research, 42(3), 237-288. https://doi.org/10.3102/00346543042003237
Re your second question, excellent point. It has been a while since I tinkered with the ROBUST option for UNIANOVA, but I just cobbled together a quick "toy" example to remind myself that the tables of EMMEANS are the same (including SEs and CIs) regardless of whether the ROBUST sub-command is included. The difference appears in the table of "parameter estimates" (i.e., coefficients). But some more tinkering tells me that when you include the ROBUST sub-command, contrasts carried out via LMATRIX use the robust covariance matrix.
But frankly, I find LMATRIX very fiddly and frustrating. So if I needed to do this sort of thing, I would do it via Stata instead of SPSS! ;-)
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Hello everyone,
I am performing multiple comparisons at the same time (post hoc tests), but among all the possible p value adjustments available (Bonferroni, Holm, Hochberg, Sidak, Bonferroni-Sidak, Benjamini-Hochberg, Benjamini-Yekutieli, Hommel, Tukey, etc.), I don't know which one to choose... And I want to be statistically correct for the comparisons that I am making in my experiment.
In my experiment, there are 4 groups (let say A, B, C, D), but I want to compare A vs B, and C vs D. That's all. So, after performing wilcoxon tests, the non-parametrical equivalent of a t test (because I have such a low amount of repeat per group (n=6) + non-normality for some groups), for A vs B, and C vs D, I don't know which p value adjustment should be performed here.
I would like to understand 1. which adjustment I should perform here. 2. how to decide which test I should perform for any other analysis (what is the reasoning).
Thanks in advance for your response,
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Hi! Was your query answered? I am confused about a similar set up of mine!
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Dear all,
I am currently exploring Latent Profile Analysis (LPA) and have noticed a trend in some of the papers I've read. After completing LPA to categorize subjects into groups, these studies often proceed directly to further analyses such as ANOVA, without conducting tests for normality or homogeneity of variance. I am curious if this approach is considered methodologically sound.
For context, in my own research, I have divided participants into three groups and performed the Shapiro-Wilk test, which indicated that none of the groups conform to a normal distribution. Despite this, I am interested in conducting an analysis of differences between groups. Consequently, I opted for the Kruskal-Wallis test. Is this approach justified in this context?
I appreciate any insights or advice on this matter.
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Related to Christian Geiser 's point, many of the statistics that you might apply (e.g., t-test) assume the groups have no measurement error. The structural after measurement approaches address this. That said, this assumption is often ignored. I would go with Christian's suggestion. How high are the probabilities? And do the classes make sense?
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Using GraphPad Prism, when I carry out a 2-way ANOVA with an interaction term, data between two groups is not significant. The post-hoc tests shows non significant interaction between my column and row data. So I did redid the analysis using a 2-way ANOVA without an interaction term, and now I get significance between two groups of data, which is more like what I think happens biologically speaking. But why does the p values change when I use an interaction term versus when I don't use an interaction term, given that the interaction term is not significant anyway? Which is the correct way to analyse the data?
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  • Probably the cause of the model terms being non-significant when the interaction is added is because the interaction terms takes degrees of freedom away from the residual degrees of freedom. This should all make sense if you look at the degrees of freedom in the output from each way you analyzed it, and the way that the F-test is calculated.
  • As to what to do, you'll find different suggestions. There is a philosophy that says that it's fine to drop out non-significant terms from a model. There's another philosophy that says you should conduct the analysis you planned to conduct before you saw the data.
  • You should also take a look at the residuals from the analysis and see if either of your models meets the assumptions of the analysis.
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Dear professors and readers,
I have data that is measured every day in two groups. The first group is shift workers (2 weeks data which divided into the first week is day shift and the second week is night shift). Then, the second group is non shift workers (1 week data which only do day shift).
Workers of the shift work and non shift work are different.
I want to know:
- if there is a group difference between shift work and non shift work
- what is the weakest working shift type condition (day shift or night shift or non shift)
My dependent variables are blood pressure, heart rate, etc (continuous data). I already checked the data distribution and most of them are not normal and also not homogen.
I tried repeated one way Anova for comparing between day shift and night shift. (Because the subjects are same people)
I also tried one way Anova for comparing between day shift - non shift and night shift - non shift. (Subjects between shift and non shift are different)
Other teacher said I can use GLMM (Generalized Linear Mixed Model), but I am still not understand the basic concept of it.
My questions are:
1. Was my statistical analysis correct?
2. Is there other statistical analysis that I can use for comparing those conditions in the same time? I wonder might be there is an interaction or interesting phenomenon between day shift, night shift and non shift.
3. Is GLMM suitable with those conditions?
Thank you very much for your kind help and support.
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Here are some resources and examples that might help you understand and implement longitudinal analysis with mixed-effects models:
Books:
"Data Analysis Using Regression and Multilevel/Hierarchical Models" by Andrew Gelman and Jennifer Hill.
"Mixed-Effects Models in S and S-PLUS" by José C. Pinheiro and Douglas M. Bates.
Longitudinal analysis using mixed-effects models is a statistical approach commonly used to analyze repeated measurements taken on the same subjects over time. Mixed-effects models are also known as hierarchical linear models or multilevel models. Here are some key notes on longitudinal analysis with mixed-effects models:
Definition:
Longitudinal Data: Data collected from the same subjects at multiple time points.
Mixed-Effects Models: Incorporate fixed effects (population-level effects) and random effects (subject-specific effects).
Key Components:
1.Fixed Effects: Correspond to population-level parameters that are assumed to be constant across all subjects.
Examples include treatment effects, time effects, and covariates.
2.Random Effects: Capture subject-specific variability. Modeled to account for individual differences and correlations within the same subject over time.
Random intercepts for subjects and, if needed, random slopes for time-related variables.
3.Time Variable: Represents the repeated nature of measurements over time.
Allows for modeling the change in outcomes over the course of the study.
Advantages:
1. Model Flexibility: Accounts for individual variability in trajectories over time.
Accommodates unbalanced and missing data.
2. Increased Power: More efficient than traditional repeated measures ANOVA when dealing with unbalanced designs.
3.Handling Correlation: Explicitly models and accounts for correlation among repeated measures within subjects.
Model Assumptions:
1.Normality: Assumes that the residuals are normally distributed.
2.Linearity: Assumes a linear relationship between predictors and the response variable.
3.Independence of Random Effects: Assumes that random effects are independent of predictors.
Interpretation:
Fixed Effects: Interpret similarly to standard regression coefficients.
Random Effects: Variability in intercepts (and slopes) reflects subject-specific deviations. Software:
Popular software for fitting mixed-effects models includes R (lme4 package), SAS (PROC MIXED), and Python (statsmodels, mixedlm).
Model Comparison:
Likelihood Ratio Test: Used for comparing models with and without specific fixed or random effects.
Model Diagnostics:
Residual Analysis: Assess the model fit by examining residuals.
Variance Inflation Factors (VIF): Check for multicollinearity among predictors. Considerations:
Sample Size: Adequate sample size is crucial, especially when estimating random effects.
Model Complexity: Avoid overfitting by carefully selecting fixed and random effects. Reporting:Clearly report fixed effects estimates, random effects variances, and any interactions.
Handling Time Trends:
Consider incorporating time-related variables (linear, quadratic) to capture trends over time.
Handling Missing Data:
Use appropriate methods for handling missing data, such as multiple imputation or maximum likelihood estimation.
Extension to Non-Normal Outcomes:
Mixed-effects models can be extended to handle non-normal outcomes through appropriate link functions (e.g., logistic for binary outcomes).
Longitudinal analysis with mixed-effects models is commonly used in various fields, such as psychology, medicine, and social sciences, to analyze repeated measurements taken on the same subjects over time. Mixed-effects models account for both fixed effects (population-level effects) and random effects (individual-specific effects). Here are a few examples illustrating the application of longitudinal analysis with mixed-effects models:
Medical Research: Drug Efficacy Study
Objective: Investigate the effectiveness of a new drug over time.
Data: Measure the health outcome (e.g., blood pressure) at multiple time points for each patient receiving either the new drug or a placebo.
Model: A mixed-effects model can be used to examine how the drug affects the overall trend in health outcomes while accounting for individual variability.
Educational Research: Learning Trajectories
Objective: Explore individual learning trajectories in a longitudinal study.
Data: Assess students' academic performance (e.g., test scores) at different time points throughout their educational journey.
Model: A mixed-effects model can be employed to model how students' learning trajectories vary across individuals and how they are influenced by fixed factors like teaching methods.
Psychological Research: Mood Changes Over Time
Objective: Investigate how mood changes over the course of a psychotherapy intervention.
Data: Collect mood ratings from participants at multiple time points before, during, and after a therapeutic intervention.
Model: A mixed-effects model can be used to examine the overall trend in mood changes across participants, while considering the individual variations in response to therapy.
Economic Research: Income Growth
Objective: Analyze income growth trajectories over a period of years for individuals in a population.
Data: Gather annual income data for a sample of individuals over several years.
Model: A mixed-effects model can help identify common trends in income growth while accounting for individual-specific factors that may influence income trajectories.
Environmental Science: Long-Term Ecological Monitoring
Objective: Study changes in biodiversity over time in a specific ecosystem.
Data: Collect ecological measurements (e.g., species abundance) at multiple time points in the same location.
Model: A mixed-effects model can be used to assess how ecological factors contribute to changes in biodiversity while accounting for site-specific variations.
Sports Science: Athlete Performance
Objective: Evaluate the performance improvement of athletes over a training period.
Data: Record performance metrics (e.g., running times, strength measurements) at regular intervals during a training program.
Model: A mixed-effects model can help identify overall trends in performance improvement while considering individual athlete variations.
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I set the eta square as my effect size.
There is only the standard of effect size regarding eta square for one-way ANOVA.
What about the two-way ANOVA and three-way ANOVA?
Is there any book or researcher paper I can refer?
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Thanks Bruce Weaver - I'd also add that there are at least three versions of eta-squared:
classical - SS effect divided by SS total
partial - SS effect divided by (SStotal minus some effects that depend on design)
generalized - SS effect divided by (SS total adjusted to equate everything to the same design).
partial eta squared is useless as an effect size measure per se (e.g., it can sum to more than 100% over an ANOVA model so it can't be easily interpreted as a varianced explained measure even if thats what you want. It is sometimes useful for power/sample size estimation (assuming the design hasn't changed etc.)
Classical eta squared is very simple to explain, but not comparable between designs. So if using eta-squared I'd look at generaized eta-squared. This is fiddly to calculate but there's a simplified formula in my book (Serious Stats) and a more detailed explanation in:
Olejnik, S., & Algina, J. (2003). Generalized Eta and Omega Squared Statistics: Measures of Effect Size for Some Common Research Designs. Psychological Methods, 8(4), 434–447. https://doi.org/10.1037/1082-989X.8.4.434
I'm not a huge fan of variance explained measures but I use generalized eta-squared if I do use any in ANOVA.
Note that the design (independent, repeated or mixed measures) and nature of the factors (measured or manipulated) influences calculation of generalized eta-squared.
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I will conduct experimental research with two independent variables and one moderation variable so that the factorial design is 2x2x2; with the ANOVA interaction test, the research topic is accounting. What steps should I take to test the moderation role?
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Testing the moderation role in an experimental factorial design involves examining whether the effect of an independent variable on a dependent variable is influenced by the level of a third variable (moderator).
Include the moderator variable in the analysis and check for a significant interaction between the moderator and the independent variable.
Conduct moderation analysis using appropriate statistical techniques (e.g., regression analysis, ANCOVA, PROCESS model).
And to choose appropriate statistical tests and software based on the nature of your data and the analysis required.
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I am hoping someone can advise on the use of the Bonferroni correction. I am struggling to understand how and when to use it.
I have been part of a pilot study evaluating balance in older adults. We used several balance measures (sway area, sway velocity) with different parameters (eyes open/closed, solid/compliant surface), plus a timed functional test, measured on three occasions with the same subjects. I have performed separate repeated measures ANOVAs for each measure and parameter combination (7 in total) using SPSS, alpha set at .05. I understand the need to use the Bonferroni correction with the pairwise comparisons and that SPSS does this. However, I am unsure whether the correction needs to be applied across all the ANOVAs, namely whether I should set the corrected alpha level to 0.05/7 = 0.0071 when determining statistical significance for each individual ANOVA.
I understand there are debates around minimising Type I errors at the expense of Type II errors, but is the approach of using alpha of 0.0071 for each individual ANOVA fundamentally correct?
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No worries, Matthew Holmes. Despite being published nearly 20 years ago, those two articles remain among the best and most thoughtful discussions of multiplicity that I have seen (so far). ;-)
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dear my fellow colleague. I have a question, I have 3 independent variables ( with 3 means) and 1 dependent outcome. I had conduct Anova and reveal significant differences in these 3 (p < 0.001) and also run post hoc for this 3 variables, and i find differences in 1><3 and 2><3. but I also have 3 nominal confounding variable that need to be clear for the effect on the outcome. what kind analyses I can run for?
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Given your scenario with three independent variables (IVs) and one dependent variable (DV), along with three nominal confounding variables, you can perform a more comprehensive analysis to account for the confounding effects. Here are the steps and analyses you can consider:
  1. Multiple Analysis of Covariance (MANCOVA): MANCOVA extends ANOVA by allowing you to include multiple dependent variables while controlling for the effects of covariates. In your case, the dependent variable would be the outcome of interest, and the three independent variables would be treated as factors. The three nominal confounding variables can be included as covariates.
  2. Regression Analysis: Multiple regression can be used to assess the relationship between the dependent variable and multiple independent variables, including the three nominal confounding variables. This can help determine the unique contribution of each variable while controlling for others.
  3. Interaction Effects: Explore interaction effects between the independent variables and the confounding variables. Interaction terms in regression models can help identify whether the effects of the independent variables vary based on different levels of the confounding variables.
  4. Stratified Analysis: Conduct separate analyses for different strata defined by the levels of your confounding variables. This can provide insights into how the relationships between your independent variables and the outcome vary across different subgroups.
  5. Sensitivity Analysis: Assess the robustness of your findings by conducting sensitivity analyses. This involves testing the impact of varying assumptions or model specifications to ensure that your results are reliable and not overly sensitive to specific choices.
Remember to carefully interpret the results and consider the assumptions of each analysis method. Additionally, consulting with a statistician or data analyst with expertise in your specific research domain can provide valuable insights tailored to your study.
The assumptions for the analysis methods mentioned earlier are as follows:
  1. ANOVA: Assumption of Independence: Observations are assumed to be independent. Homogeneity of Variances: The variances of the groups being compared are assumed to be equal. Normality: Residuals should be approximately normally distributed.
  2. Post-Hoc Tests (e.g., Tukey's HSD): Similar to ANOVA, post hoc tests assume independence, homogeneity of variances, and normality.
  3. MANCOVA: Multivariate Normality: The dependent variables within each group should be multivariate normally distributed. Homogeneity of Covariance Matrices: The covariance matrices of the dependent variables should be equal across groups. Linearity: Relationships between each dependent variable and the covariates are assumed to be linear.
  4. Regression Analysis:Linearity: There is a linear relationship between the independent variables and the dependent variable. Independence: Observations are independent. Homoscedasticity: The variance of the residuals is constant across all levels of the independent variables. Normality of Residuals: Residuals are assumed to be normally distributed.
  5. Interaction Effects: Interaction terms assume that the effect of one variable on the dependent variable is not constant across different levels of another variable.
  6. Stratified Analysis: Assumes that the relationship between variables is consistent within each stratum defined by the confounding variable.
  7. Sensitivity Analysis: The assumptions of sensitivity analysis depend on the specific method being used. Generally, it involves testing the impact of different assumptions or model specifications to assess the robustness of results.
It's crucial to check these assumptions before interpreting the results of any statistical analysis. Violations of assumptions can affect the validity of findings, and researchers may need to consider alternative methods or transformations if assumptions are not met. Additionally, when in doubt, seeking guidance from a statistician or data analyst can help ensure the proper application of analysis methods and interpretation of results.
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I have a setting of 4 groups of normally distributed data and unequal sample sizes. Alpha-level is set at 0,05 in all analyses.
To see if there are any differences between the groups I've run (with SPSS) an ANOVA and Tukey HSD post hoc test. SPSS provides also the Welch test for cases with unequal variances (= significant Levene's test with p < 0,05), and with these I've used Games-Howell as a post hoc test.
However, there a few cases in which the Levene's test p > 0,05 and Welch test p < 0,05 (with GH finding significant differences between groups). In some of these cases the omnibus ANOVA p is significant but the Tukey HSD doesn't yield significant differences between the groups.
Welch test can be certainly used instead of ANOVA when the variances are unequal, but can it (with GH post hoc) also be used when the variances are somewhat equal according to the Levene's test?
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s. Rama Gokula Krishnan can you please explain why? Non-parametric tests do not answer the same questions/have not the same hypotheses. Why should one switch to them, if there are good robust alternatives, if variances are unequal or other issues. Please demonstrate why your approach is more suitable?
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During work for my undergrad thesis, I've examined and compared gene expression of stress-induced genes in plants challenged with a fungal infection.
I have calculated the relative fold change and wondered: How high does my fold change have to be for it to actually make a difference?
For example:
The log2 RFC between Group A and Group C is 0.63.
According to ANOVA, this difference is significant.
I'm wondering if this difference is enough to change the plants' stress response.
Is there a certain value that I can see as a "threshold" or is mere statistical significance enough to confirm the change in the plant?
Thank you in advance .)
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There is no cut-off for judging a fold-change (btw: fold-change already is a relative measure; it is superfluous to stress that you your fold-change is relative) being biologically relevant, as this depends on too many factors (what gene, involved in what signally/metabolic processes, in what cells, what is the proportion of relevant cells in the sample, at what time, are the cells synchronized, is the mean change considered or are expression bursts relevant, what compensatory effects can exist, can it be an unspecific side-effect without practical relevance in the cell, it the gene expression change counter-balanced by post-transcriptional or post-translational regulation, etc etc etc). It's your job as expert biologists to make such a judgement.
As Can wrote, the significance test only judges the information from your sample data to compare the sample estimate (b) to a hypothetical population value (h): d = b-h. If the information is considered sufficient, then b can be believed to be "on the correct side" of h, so the test tells us if we may have confidence in the sign of d, or that we can statistically distinguish b from h. This hypothetical value if often zero (h=0, so d = b), it is about interpreting sign of b (here: the sign of the log fold-change calculated from your sample).
Note that the point estimate b is associated with uncertainty. Consider the typical case that h=0. A test tells then that you can have confidence that the sign of b is correct, but not that b itself is correct. It might be that b is rather large and the p-value is small, but a irrelevantly small hypothetical value close to zero would not be statistically distinguishable from this h. So the data may be compatible with irrelevant values of h. If relevance (not statistical significance) is of interest, it's more useful to interpret the confidence interval (CI), which is the range of all possible values of h that would be statistically distinguishable from b (giving low p-values in a test). Only if the limit closest to zero is large enough to be considered relevant, then the information from the sample is sufficient to exclude irrelevantly small values of h and claim a "relevant effect".
But these are all technicalities. How large a relevant effect has to be is an expert judgement and cannot be answered statistically. Very often, biologists don't have much of a clue, so the best one can do to claim that one identified the direction of regulation (and avoid to say that the amount of regulation may not be of any biological relevance).
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I am conducting a study where 4 groups are measured over 4 different time points (t0, t30, t60 and t90). I am mainly interested in what happens within groups. I am carrying out RM_ANOVA, I got the mean differences between the groups but I want to represent the differences in percentage.
Any idea what is the best method to do this?
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Hi Wim Kaijser. I think you understood the OP to say that the DV is a percentage, and if it is, then you could convert that to a proportion (p) and use logit(p). But I did not understand the DV to be a percentage. I understood that the OP wants to convert differences between groups on whatever the original scale is to percentage differences. And provided the original raw values are constrained to be positive, the method shown on that UCLA page ought to give the desired result, or something that can easily be converted to the desired result. But again, the OP needs to respond and indicate if any of us are understanding the question correctly. ;-)
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Is it the sum or average of all SDs?
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Pinting Bian Can the calculation done there for 'spooled SD' be incorrect? shouldn't it be this-
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Hello,
I am having problems on finding the right statistical test to use, hope you can help me. Essentially, I’m looking at the effect of a drug at reducing multiple sclerosis progression in a EAE mice model. I have two groups (treated and vehicle) and I have neurological scores for each mouse in each group for a period 16 days.
The neurological test are scored on a 5 point scale (0 to 5) where 0= normal and 5= paralysed (similar to a Likert scale), and are conducted daily (for the 16 days). compound is given to the animal daily, and so is the vehicle.
I am comparing the scores for the two groups (between subject design), but I also want to see how the scores change over time (within-subject design) i thought on using the Mixed ANOVA am I correct? However, since the neurological testing is scored as a Likert scale, the data should be non parametric, correct?
What equivalent test can I use on SPSS?
I appreciate your help in advance
Thanks
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Hi,
I have the same question, I would appreciate it if you share what test you found suitable for analysis?
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I have data for two seasons of tamarind genotypes, and I conducted the experiment trial using a Randomized Block Design (RBD). I need to analyze this data to estimate the variability. Can someone kindly provide an exact solution?
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Pradeep Paul George@ Thank you so much for responding to my question. Your answer on calculating CV was helpful. Now, I have a pooled ANOVA, and I need to calculate the Phenotypic coefficient of variation, Genotypic coefficient of variation, Heritability, and Genetic Advance. These are all components used to assess the variability of a trait present in the population.
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Counts data re-distribution.
I ran ANOVA however, the numbers don't make sense. My experiment was based on treating plant tissue culture explants with NaDCC and PPM. After a 30-day period, I had to count the number of aseptic and contaminated tubes from a batch of 10. So if 5 tubes were contaminated it means 50% were aseptic. On the other batches, I had O%-contaminated tubes and 100% clean tubes. Therefore, there's a huge variation between the numbers resulting in my data having a non-normal distribution or skewed distribution. For me to use ANOVA I assume my data must be normally distributed. The tubes were counted and values were converted to percentages. But when plotting graphs in Excel +/-SD extended passed zero to the negative quadrant. I am not familiar with statistics or ways to code, I am completely clueless on how to resolve this issue.
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yes for non normal data we use non parametric statistics, alternative to ANOVA is Kruskal Wallis, equally performance as ANOVA
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When i do regression analyze, in Model Summary Table, i found Rsquare is very weak like:0,001 or 0.052, and value of sig. in Anova table is greater than 0.05, how can i fix this?
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Unless you have an error in your data, this may just simply be the result of the analysis (i.e., that your predictor(s) is/are only weakly related to, and do not significantly predict, the dependent variable).
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Is there a need to check for Multi-collinearity before the ANOVA and ANCOVA?
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Another thought about multicollinearity in ANCOVA: what do you mean with it? The correlation between the IV and the CV? For ANCOVA to work best, IV and CV should be uncorrelated (what should be the case with random allocation to the IV groups). Otherwise, parts of the variance between the IV groups cannot be attributed to the IV, if it is correlated with the CV. That means that you may reduce the power to detect your IV effect (which is clearly not what is intended with an ANCOVA). Is that something you mean or have considered?
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Dear all,
as part of my Master thesis, I am conducting a two-way repeated measures ANOVA on data from a social evaluation paradigm. The purpose for running this analysis is to investigate whether social feedback prediction (like, dislike) moderates the impact of social feedback valence (negative, positive, neutral) on participants' self-rated state self-esteem (i.e. whether unexpected social feedback exerts a differential impact on state self-esteem depending on the feedback valence).
Participants undergo several trials in which they are instructed to make predictions as to the social feedback they will receive, after which they receive alleged social feedback on a personality profile. After a random number of trials, participants need to rate their state self-esteem with reference to the previous social evaluations.
The analysis revealed a significant interaction effect between social feedback valence and social feedback prediction on state self-esteem. I have already plotted this interaction effect using a bar chart, but I would like to quantify the mean differences in state self-esteem between levels of feedback prediction for each level of feedback valence such that I can clearly describe the underlying simple effects and, accordingly, interpret the cause of the interaction effect.
Which methods/procedures/strategies would you recommend using to probe the valence x prediction interaction effect?
I hope that I have provided sufficient information.
Thank you very much in advance.
With warm regards,
Marius
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Use the emmeans or lsmeans option in the software you are using. This is a post-hoc test after the anova, and accounts for the repeated-measures nature of the model. Often you can get confidence intervals for the e.m. means. Plotting or reporting these intervals with the e.m. means is useful for the reader.
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Hey everyone,
I have the following situation:
Two groups of mice wildtype (WT) and knockout (KO) in each group I have lets say 10 mice. I isolate cells and treat the cells from each mouse with a basal or insulin condition (these treatments are done on the same cell suspension) and I measure glucose uptake as an outcome.
From previous data, I know that with increasing glucose uptake, which is induced by the insulin treatment the mean of glucose uptake increases and with increase in mean my variance increases. I choose to log-transform the data and I get approximately normal distribution and equality of variances. Is this reasonable to do?
Then I would like to carry out a statistical analysis. From my n=10 sample I can say very little about the distribution and assumptions of the model I want to use and I would therefore base my assumption about this sample on my previously observed findings of about 200 observations. Is this okay to do? Assuming the assumptions of a parametric test are fulfilled, how would you analyse this data?
As basal and insulin are from the same cell suspion, I assumed these to be paired/dependent. While the other measurement, so between WT and KO should be independent. In each group, so WT Bas, WT Ins, KO Bas, KO Ins I have 10 biological replicates. I was thinking about a repeated measures ANOVA. Could someone help here?
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Sure. But the effect of insulin is already encoded in the differences of the log(uptakes). You can test these values against zero if you like (e.g. in a model without intercept term).
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Hello All,
So I am doing a two-way ANOVA. The within-subject factor is Ethnicity (3 levels). The between-subject factor is Gender (2 levels). I have been writing it interchangeably as either "3 x 2 mixed ANOVA" or "2 x 3 mixed ANOVA". Of course, it doesn't change the total number of conditions, but in terms of clarity and understanding, is there a standard way of writing the factors? Do you state the within-subject factor first (i.e. 3 x 2) or between-subject factor first (i.e. 2 x 3).
Thank you so much.
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Both the factors here, ethnicity and sex, are between subject factors. One person can't have different sex or ethnicity assigned to them. I'm unsure why and how are you marking one of them as within subject factor "as you wish".
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I know I can use a paired t-test or repeated measures ANOVA, but I want to run a series of paired t-tests--is it possible to do them all at the same time? I want to see if there is a greater difference for some pre/post tests than others.
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Abolfazl Ghoodjani, I am not a GraphPad user, so pardon my ignorance if I am just misunderstanding the documentation. After reading the page you pointed to, I am left thinking that the "multiple t-test" method returns exactly the same results one would get by using the (single) paired t-test command multiple times. If so, there is nothing resembling the test of interaction that Wendy Baker Smemoe appears to be thinking about.
PS- Are you still at the AECRP? I could not find you on its website (https://www.mcgill.ca/painresearch/).
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Hello, I want to determine how much statistical power my study has in finding a significant 4-way interaction. The study uses a 2x2x2x2 mixed ANOVA design (1 between and 3 within factors all containing 2 levels each). Is there a tool that could be useful with such a design? Mixed ANOVA with g*power and superpower seems to be limited to 2x2x2 interactions. Perhaps someone can give a guide on a R packages and how to figure out the power.
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These are results from Bard in your querry.query
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Hi there,
I have qPCR results from 6 target genes and a housekeeping gene. Each different gene had its expression measured after 3 different treatment conditions and a non treatment control.
I have log 2 transformed the fold changes that were the result of normalising the different treatments to the housekeeping gene and non treatment control.
My question is, how does one present this on a graph. Is it necessary to leave a space for the non treatment control, given that all its values will equal to zero (log2(1) = 0)?
Also, does a one way ANOVA work for statistical analysis? But am I correct in saying that performing an ANOVA will only show statistical difference between different treatments, but not whether the treatment decreases or increases the expression?
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Thank you for your answer Timothy. I want to compare the treatment both to the control and to each other. The thing is, some of my treatments are not statistically significant when compared to the untreated control. I originally thought it would be visually better to have just a column in the graph with the dots placed at zero for the untreated control. But from your answer I gather it is standard practice to just drop the control column and mention in the figure legend that it was not statistically significant.
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I'm hoping to get some advice for my thesis research. I am running an RCT and due to having a large number of outcome measures (18 in total), I have conducted 18 4 (time: T1-T4) x 2 (group: intervention vs. control) mixed ANOVAs. For those with significant interactions, I am now thinking about the best approach to use for follow-up analyses.
Due to the vast number of comparisons that would be needed for post-hoc testing, there is a high risk of Type 1 error, and the required bonferroni correction would lead to a high risk of Type 2 error. It has therefore been suggested to me by an academic colleague that I could choose to not carry out post-hoc tests and, instead of looking at measures of statistical significance, focus on measures of effect size to interpret my results. This is not an approach I am familiar with and I have not yet been able to find examples of this in the literature.
I wondered whether anyone is aware of research where post-hoc testing has not been carried out in studies of this nature? Would be helpful to hear views on whether this could be an acceptable approach to analysis in this context or whether it would be frowned upon!
Thank you in advance.
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Hello Sarah,
As you are apparently considering your outcome measures as distinct (hence, running 18 univariate comparisons rather than some smaller number of multivariate comparisons), one might argue that the sheer number of tests (across outcomes) is irrelevant.
I'm sure you recognize that, in the basic one-between, one-within anova, the interaction is frequently the most important test. Presence of the interaction implies different trajectories over time between groups, or varying group differences across time points. Detailing such differences is important to understanding what went on. One common approach is to use tests of simple effects.
At any rate, the guiding point should be the specific research question/s you are trying to address in your study.
Good luck with your work.
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Hello everyone,
I want to do a comparative analysis with an ANOVA, but my dependent variable is measured with a 5 point Likert scale. I am not sure if I can use ANOVA, as some people point out that it can be used because we treat the variable as continuous, but others recommend against it since it is ordinal.
Could you recommend me articles that justify the use of ANOVA with dependent variables measured with likert scales.
Thank you.
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Your response has been very helpful. I will think about the chi-square option also.
Thanks again.
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I have a question about what statistical tests I can do in R that would be most suited to analyse my enzymatic assay results.
My data
Dependent variable: Absorbance (its’ a colorimetric assay)
Factor 1: Protein (type of protein, wt and several mutants)
Factor 2: Substrate (several substrates)
For each assay, (e.g. Prot1 with Substr1) I have 3 – 6 data points (repeats), and it is not feasible to obtain more.
An example of my data would be something like fig1.
What I want to do:
1. Test if the different mutations have a different effect on the enzymes’ activity with the different substrates (basically test the dependence of Absorbance on the interaction between Protein and Substrate: Abs~Protein*Substrate)
Visually, if I plot my data on a bar chart (mean +/-SD), it appears to be the case, but I need to verify that what I see is significant.
Normally, I would do this with a two-way ANOVA, however:
my data is not normally distributed (according to Q-Q plot and skewness test, I have over-dispersed residuals (Laplace distribution), without any skew);
the variance is not homogenous (standardized residuals vs fitted values plot shows heteroskedasticity)
What sort of model could I use instead? Is there a way I can transform my data to allow a parametric test (the only transformations I found were against skewness, which I do not have)?
2. Test for each substrate, which mutations make the activity differ significantly from the wt (e.g. whether activity with Substr2 is significantly different for Prot2 and 3 from that for Prot1)
To avoid doing multiple pair-wise comparisons, I would normally do a pairwise.t.test with a Holm family-wise error rate correction.
For non-normally distributed data of non-equal variance, I saw it is recommended to do a Pairwise Wilcoxon rank sum test.
If I group my data by substrate, with one of the substrates (e.g. Substr2) it was normally distributed and of equal variance. I did the pairwise T test and it gave results consistent with what is seen on the graph. However, when I tried a Pairwise Wilcoxon rank sum test (holm correction) it showed no significant difference between any of the Proteins, which makes no sense (e.g. that there is no significant difference between Prot1 and 2, although one has an activity with the substrate and the other doesn’t). So it looks like the non-parametric test may not be powerful enough/ at all useful.
For the other substrates, either the distribution is not normal (again over-dispersed, Laplace distribution, with no skew), or the distribution is normal, but the variance is not equal (heteroskedasticity).
Just to note, one-way ANOVA or Kruskal-Wallis rank sum tests (where applicable) for Absorbance~Protein for each substrate individually, showed there is a significant variation in Absorbance depending on Protein.
What sort of pairwise comparison tests can I do in these cases? Or, again, how can I transform my data to be able to use a pairwise.t.test?
Thank you in advance!
I really appreciate any advice!
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glm(Protein*Substrate, Data, family=quasipoisson())
Or
lm(log(Protein)*Substrate, Data)
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I have 4 groups in my study and I want to analyse the effect of treatment in 4 groups at 20 time points. Which test should I chose?
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If I did understand your question correctly, I will suggest to you to use RCBD , at the
same time you still have the chance to analyze data for regression, for each 20 points and/or 80 collected together. Regards.
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What is the appropriate ANOVA model for the following experimental design: the effect of four different concentrations of compound X on microorganisms? Each X concentration has three jars and three replicates are collected from each pot. Samples are drawn weekly for 18 weeks.
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You would actually need a rather complex model.
One aspect is that you have repeated measures, in that you are taking samples from the same experimental units across 18 weeks.
Another aspect is that you have three samples from each jar, so usually you would use a model that includes sample within jar (nested effects).
You might be able to simply things depending on what you need to know.
It may be that the effect of jar isn't meaningful, so that you can treat three samples from three jars as nine simple samples.
It may be that you you don't need to account for the 18 weeks of samples, but only look at the final week for your statistics. In this case, you could still plot and present the data over 18 weeks, which may be of interest, but not have to run statistics over the 18 weeks. Again, it depends on what you want to know.
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Hello everyone, does anyone know how to calculate the simple size for a 2(gender: male, female)*2(culture: Asian, European)*2(age: children, adult)*2(direction: back, front)*2(position: left, right)*2( condition: confort, non-comfort) repeated ANOVA? We have 6 factors, among these, gender and culture are between-factors, while age, direction, position, and condition are within-factors. I'd appreciate it if someone can help me.
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Hi Hsin-Yuan Che, your are so nice, thanks again!
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I have two factors: time and intervention. Time has 4 levels (week 0, 4, 8, and 12), while the intervention consists of intervention group vs control group. The dependent variable is a test score. I have done two-way repeated measures ANOVA and found that there was significant time effect and interaction effect between time and intervention on the test score, but there was no significant main effect between intervention vs control. Now, I want to do a post-hoc analysis to see at which time point the score differences between intervention vs control group is significant. How should I perform the post-hoc test on SPSS? Please correct me if any of the steps that I have mentioned above are wrong. Thanks a lot.
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Sal Mangiafico is right, although he pointed to documentation for the MIXED command, whereas I think you may be using the GLM command. In any case, you need to add a sub-command like this:
/EMMEANS = TABLES(Group*Time) COMPARE(Group)
Replace Group and Time with the names you used if I did not guess them correctly. And if you wish, you can add ADJ(method) where method = LSD (no adjustment), BONFERRONI, or SIDAK.
This is the documentation for EMMEANS under GLM (univariate), but it is the same for GLM REPEATED MEASURES.
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I plan on creating a four-armed RCT investigating the effect of CBT vs. TAU (intervention: IV) on emotional reg scores (scores: DV).
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Dear Mya East
You are doing great research and an outstanding science experiment.
As a medical statistician, my advice to you
Firstly: Consider the repeated measures ANOVA test that requires more than two measurement times
At least one quantitative variable is needed to compare the mean between groups.
If you follow up with patients only before / after,
You do not need to use repeated-measures ANOVA
You can use T-test to check the effectiveness of the treatment by comparing the patient's condition before and after
Or its non-laboratory alternative, Wilcoxon, in case the data is not distributed normally
As for the comparison between the four multiple groups, you can during the same time (In the case of after, for example) the normal ANOVA procedure to compare the condition of patients in different groups, including the control group, if any, after taking the period for treatment
As well as for the case of the groups before the start of the experiment. Through the multiple binary comparisons, you can determine the source of the difference in favor of any of the drug groups.
This requires that the data be normally distributed or the sample size is greater than 30 individuals, If not, then use Kruskal-Wallis's alternative ANOVA test.
Second, don't go too far with more complex models because statistically things are gradual
Start with the basic tests, which will lead you if you do not reach your goal towards the higher-level models
If you’re considering using ANCOVA, it’s important to note that a covariate is a continuous independent variable that is added to an ANOVA model to produce an ANCOVA model. The inclusion of a categorical variable as a covariate in ANCOVA is possible and can be useful in certain situations. For example, if you have a categorical variable that you believe may be related to the dependent variable, you can include it as a covariate in your ANCOVA model.
However, it’s important to keep in mind that the inclusion of a categorical variable as a covariate in ANCOVA can lead to some issues. One issue is that the interpretation of the main effects and interactions in the ANCOVA model can become more complex when a categorical variable is included as a covariate 1. Another issue is that the inclusion of a categorical variable as a covariate in ANCOVA can lead to problems with multicollinearity, which occurs when two or more independent variables are highly correlated with each other.
I hope this helps!
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My ANOVA has total N of 457 and 7 groups within this. Equality of variances not met so I was going to use games howell. I've heard with large groups equality of variances is important, but normality isn't as important so a parametric test like the ANOVA should still be okay. Is this correct?
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Yes I'm using Games-Howell but normality is also not met. But I've read that if you have a large sample size this can be overlooked instead of using a non-parametric test. Is this correct?
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I have calculated a robust 2x3 mixed anova in R (with the package WRS2).
Now I wanted to calculate the effect sizes. However, I can't find anywhere how to calculate them for the robust anova. Does anyone know a function in R with which this is possible?
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Hello Nele,
Given that results likely depend on the degree of departure from the usual linear model assumptions manifest in the data set, I think the only way to be certain of sample size would be to run simulations with sample distributions corresponding to the likely or worst case scenarios you could envision. You might find this link to be helpful: https://aaroncaldwell.us/SuperpowerBook/
If that seems too daunting, then compute a priori sample sizes for ordinary mixed anova (assumptions met) and use these values as a lower bound.
Good luck with your work.
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There are 2 groups: one has an average of 305.15 and standard deviation of 241.83 while the second group has an average of 198.1 and a standard deviation of 98.1. Given the large standard deviation of the first group, its mean should not be significantly different from the second group. But when I conducted the independent sample t-test, it was which doesn't make sense. Is there any another test I can conduct to analyze the date (quantitative)?
The data is about solid waste generation on a monthly basis (averages). And I am comparing March and April data with that of other months. Also, the sample sizes are not equal i.e. less days in Feb as compared December for example.
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It is difficult to give a comprehensive answer without more details on 1) the data, 2) the experimental design, 3) your question and 4) what exactly you did to perform the Student's T-test.
Note however that usual Student's T-test assumes equal theoretical variances between the two populations, which is probably wrong considering your two values. You should use corrected T-tests for this case, like the Aspin-Welch test (default in R / t.test).
Note also that the T-test compares the means, that can be very precise even if the sample SD is very high if your sample size is big enough, so you cannot conclude just « by eye » based on means and sample SD. You should look at sample SEM to do that and better understand what's going on.
Never forget that T-test assumes Gaussian distributions, which may well be wrong also in your samples, and this all the more matter, than sample sizes are small and different (just like the hypothesis of variance equality is more important for unequal sized samples).
Last, don't confuse « statically significant » and « of practical interest », results of your test should be interpreted along with effect size / confidence intervals for the difference and so on.
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I am looking to conduct a study to address whether mindfulness has an effect on stroop inteference and spatial frames of reference. Therefore, I will conduct 2- two way Anova's. This will be 2(Mindfulness, Control) x 2(Pre, Post) Mixed anova as the groups are between subject but the measures will be repeated. How could I analyse this if parametric assumptions are not met?
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As far as I know, the non-parametric equivalent of the repeated measure ANOVA test is the Friedman test. However, since the Friedman test doesn't allow for posthoc analysis and comparison between groups, I don't know of any alternatives of RM ANOVA for the 2-way test. If your data is not normally distributed, you can normalize the data and use the ANOVA test.
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In my study, I have ten dependent variables (DVs) and three independent variables (A.B, and C)
*A (2 levels)
*B (3 levels)
*C (2 levels)
My research question is how the three-way interactions of A, B, and C impact changes in DVs.Which type of post hoc test would be best to analyze this data? Any suggestions will be highly appreciated.
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A slightly different aspect regarding your question "how the three-way interactions of A, B, and C impact changes in DVs".
The "how" is in the estimates, not in the tests/p-values. The tests answer the question if your sample data are sufficient to generalize the signs of these estimates to the sampled population. That's a different question. Large p-values indicate insufficient information (from the sample), not the absence of an effect (in the population).
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Kindly quote some reference
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ANOVA (Analysis of Variance) is a statistical test used to analyze the difference between the means of more than two groups. A one-way ANOVA uses one independent variable, while a two-way ANOVA uses two independent variables.
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I ran a 2x2 ANOVA. My interaction plots show full reversal (i.e., perfectly X-shaped plot) but statistics are non-significant. Am I missing anything?
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A significant interaction plot shows a statistically significant relationship between variables, indicating that their effects are not independent but depend on each other. Non-significant statistics suggest that there is no statistically significant relationship or effect between the variables being analyzed.
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I run repeated measure ANOVA with between subjects (gender) as independent variable to test its effect on the willingness to pay (WTP) for two conditions A and B (within-subjects) where the same participants provided their willingness to pay for each condition.
The result of ANOVA was as following:
WTP <.001
gender*WTP = 0.064
I run post hoc test using Tuky and benferroni, and among the interactions, I'm interested in:
1- Female WTP for A VS. Female WTP for B
2- Male WTP for A VS. Male WTP for B
both were significant with p<.001
The questions are:
1)- the interaction was not significant as shown above (P = 0.064), can we still report the post hoc test?
2)- I mainly interested in the post hoc result comparing males in condition A and B and females in condition A and B which both are significant, can I selectively report these post hoc result and ignore the remining?
An example of the remining post hoc test: Males WTP for A VS. Females WTP for B which was not significant, not related to my research questions and does not make sense to me (different genders and different conditions).
I used paired sample t-test at first, but was advised to use ANOVA as more robust, especially that we have other independent variables such as education level, income level and age groups which we intend to use sperate ANOVA model for each.
Note. I didn't include all independent variables in one ANOVA model because the samples become less than 2 in some cases and, therefore, test can't be run.
3)-Simple main effect provide the result of :
1- Female WTP for A VS. Female WTP for B
2- Male WTP for A VS. Male WTP for B
which both are significant. can I refrain form reporting post hoc test and report the simple main effect result instead?
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Hi,
I've been using growthcurver package for growth curves experiment. I have the output data per well- but now I want to group wells together according to my meta-data (for instance three biological replicates of a treatment). What is the best option for it? average the output variable for instance? perform ANOVA?
Thank you!
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Group replicates into one column in the input file. See example above.
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Hello Everyone, I have got data that is not normally distributed and I need to run the Mann-Whitney U test instead of the Independent Samples T-Test, as well as the Kruskal-Wallis Test instead of * ANOVA. The problem is my data consist of five-items Likert scales ( I have several items that test a particular aspect of the study, they are organized in terms of scales and every scale consists of a number of items which are all Five Point Liker-scales, and the Cronbach Alpha is fine). My questions is, do I compute these items based on the mean to create one variable? Or do I need to compute them based on something else (Sum, median...) because the non-parametric tests use rankings? I do hope you would be so kind as to help me. Thank you.
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The usual approach to creating scales from Likert-scored items is simply to add them together (or you can take an average, which is essentially the same thing because you are dividing by a constant). After that I would look at the distribution of your scales.
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Say we run a 3 (A: A1,A2,A3) x 3 (B: B1,B2,B3) repeated measures ANOVA. A significant p value for factor A, for example, indicates that there is at least one pair (A1-A2,A1-A3,A2-A3) in which the mean difference is statistically significant (let's assume there are no interaction effects).
Normally, to determine the specific pair(s) where a significant difference exists, post-hoc tests (multiple comparisons) are used, which will include some type of correction (e.g., Bonferroni, Tukey).
There is an alternative method, which is running the ANOVA first and then running follow-up pairwise t-tests comparing factor levels.
I'm wondering whether these two alternatives are equally valid from a statistical point of view.
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Hello Mikel Jimenez. Just a couple of quick comments.
  1. The design you described is 3x3, not 2x2. I.e., both A and B have 3 levels.
  2. I have not read them recently, but I think you might find these notes by the late David Howell useful. Note especially the standard multiple comparison methods like Tukey's HSD were designed for between-Ss factors, and it is not advisable to use them (without alterations) for repeated measures factors.
HTH.
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I have a two-factor experiment. We investigated the effect of the drug on the level of erythrocytes after surgery. One of the factors is the presence of the operation, the second is the presence of the drug, the third is the interaction of these factors. I have difficulty in interpreting the received data. We have one time point. Example: we obtained the influence of the operation factor (P <0.01) on the level of erythrocytes after the operation and the interaction of factors - operation * drug (P <0.05). But I didn't get the influence of the drug factor. Can I conclude that the drug affects the level of red blood cells after surgery?
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Interpreting data processed with two-way ANOVA can be difficult. However, there are some things you can do to make it easier. One thing you can do is to look at the interaction between the two factors. Another thing you can do is to look at the main effects of each factor.
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Hello!
I really hope anyone can help me out.
For my master thesis I am comparing cancer cell clones and their reaction to certain targeted inhibitors.
Now I would like to perform a two way ANOVA test for my data and I am struggling with the set up.
The null hypothesis is that the drug has no cytotoxic effect on the cells.
Here is the design of my data. I work with triplicates. The cells are seeded in a 96 well plate with the following set up.
Concentration: Clone Response (SRB intensity in %)
Control Control response
C1 R1
C2 R2
C3 R3
C4 R4
C5 R5
Since the two-way ANOVA test compares two data sets my first dataset is the one with the responses, correct?
Do I create a second data set where I simply put in all the responses for every concentration as 100%, artificially creating the set up that the drug has no effect?
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Hello Erika,
First, I'm inferring from your query that concentration level represents one IV. But, I'm unclear as to what the second IV might be. Is it drug? Replication (e.g., three trials of each concentration)? Something else?
Second, I'm not clear as to why you want to use GraphPad (perhaps, other than prior familiarity). The one time I looked at the user manual for this to address someone else's RG post, I was amazed at how non-standard one's data set-up needs to be for multi-factor designs (esp. mixed models). You might consider the freely available Jamovi package as a better alternative.
Good luck with your work.
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if i have two independent variables-mango peel liquid fertilizer group and commercial fertilizer group and dependent variables are: plants height, width and number of leaves.
There is a control group.
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Kandasamy Ravichandran, you may well be right about there being 3 groups. But until Alexander Alano comes back and clarifies, we won't know for sure! ;-)
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Hello, currently I am observing the increase of water activity and moisture content of 4 different formulas over the course of 6 months, with each formula having 3 replicates, meaning a total of 12 samples per month or 72 samples for 6 months. Ideally I would like to use two-way ANOVA as this looks like a factorial design with 2 factors, one factor has 4 levels and the other has 6 levels. All the replicates are normally distributed. However, upon using Levene's test for equality of variances, I found that some replicates are not homoscedastic.
The questions are:
- If Levene's mean test shows that some data do not have equal variances, but Levene's median test (Brown-Forsythe) shows that all data have equal variances, can I use BF's median test and move on using two-way ANOVA? If so, are there any changes regarding what post-hoc test I use?
- If it turns out I cannot use BF median test as replacement for Levene's mean test, thus the assumption of equal variances is violated, can I still use ANOVA? If yes, should I use the mean of the replicates for the ANOVA test and what post-hoc test is appropriate? If no, what other tests can I use and what post-hoc test is appropriate?
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If Levene's mean test shows unequal variances while Levene's median test (Brown-Forsythe) shows equal variances, it is generally recommended to use the median test as a more robust alternative. In this case, you can proceed with conducting a two-way ANOVA using the median test results. Regarding the post-hoc test, you can still use traditional post-hoc tests like Tukey's honestly significant difference (HSD) or Bonferroni correction, as they do not rely on the assumption of equal variances.
However, if the assumption of equal variances is violated and you cannot use the median test as a replacement, you can still consider using ANOVA. In this situation, you may apply transformations (e.g., log transformation) to the data to address heteroscedasticity. Alternatively, you can employ non-parametric tests such as Kruskal-Wallis test, which does not require the assumption of equal variances. For post-hoc analysis with non-parametric tests, you can use pairwise comparison tests such as Dunn's test or the Mann-Whitney U test with appropriate adjustments for multiple comparisons.
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Hi,
I conducted a replication of a study and need guidance on the data analysis. In my experiment, participants were exposed to two different stimuli consecutively, with 20 trials for each stimuli. I'm investigating the differences in participants' performance changes between the two stimuli. Here are the factors involved:
  • Stimuli type: Stimuli A, Stimuli B
  • Trial position: Early, late
  • Dependent variable: Response accuracy (continuous variable)
I also have a second group where the order of stimuli is counterbalanced (B, then A), and this will be analysed separately with the same type of analysis. Initially, I planned to run two separate ANOVAs. However, I first ran correlation analyses on participants' demographic characteristics and found that participants' native language (English, not English) and regular exposure to multiple languages (yes, no) were correlated with all four dependent variables. I initially included these characteristics as covariates in the 2 x 2 ANOVA, but I'm unsure if this is the correct approach since they are between-subjects factors. I also tried rerunning the ANOVA and treating the two characteristics as between-subjects factors instead, but again, I'm uncertain if this is the appropriate solution. I've searched online for information, but there is limited material available.
I would greatly appreciate your input on how to proceed. If you more clarification on my study is needed, I am happy to provide additional information. Thank you in advance for your assistance.
Best regards,
Joanne
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Hello Joanne,
Yes, the simple main effects tests would subsume the specific t-tests you ran (e.g., the t-tests are two of the four possible simple main effects for that interaction). The only possible distinction would be which error term spss applied for the simple main effects.
Good luck with your work.
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Hi everyone.
I am running an ANOVA analysis, and there is an interaction with a medium partial eta squared value (.06). Still, the p-value is insignificant ( .11). I have calculated the sample size based on previous studies, and it is ok for my experiment. So, what should I consider? How should I understand this data? Thanks.
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Hello Livia,
The brief answer is, the nonsignificant result means that the target effect can not be claimed to be different from zero.
If you conducted a thoughtful, a priori, power analysis and determined that your sample was sufficient to detect differences of at least your declared target effect size (however quantified), with an acceptable level of power, then the nonsigificant result implies that population differences do not reach the magnitude of your target ES.
However, if your sample size determination was based more on what other studies have used, rather than on detecting a variance-accounted-for (whether partial or full model) of six percent, then your nonsignificant result could have been due to: (a) too little power to detect such an effect (and, hence, insufficient N); or (b) a correct failure to reject Ho (the target ES does not exist in your target population).
Good luck with your work.
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Dear ResearchGate Community,
I am seeking guidance regarding the appropriate statistical analysis for my research study. In my study, I have two groups (Control and Experimental) and two states (Pre and Post). I conducted a Repeated Measures ANOVA with the factors of states, States*group interaction, and error(states) to analyze my data. However, I am unsure if this is the most suitable test for comparing the differences between the two groups.
Additionally, I am seeking advice on how to effectively present these findings in a result table following the guidelines of the APA (American Psychological Association) style. Should I create two separate tables, one for descriptive statistics and the other for the ANOVA table? I would appreciate any assistance in formatting the result table specifically for the factors of States, States*group interaction, and error(states).
Thank you in advance for your valuable insights and assistance
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When reporting the results of a repeated measures ANOVA (Analysis of Variance) in APA (American Psychological Association) style, you generally include a table and a concise narrative summary. Here's a step-by-step guide on how to present the results:
  1. Table: Create a table to present the key statistical information. The table should be labeled with a number (e.g., Table 1) and include a descriptive title. Here's an example format:
Table 1 Descriptive Statistics and Repeated Measures ANOVA Results
The table should include the following columns:
  • Descriptive Statistics: Present the means and standard deviations (SD) for each condition or time point.
  • Mauchly's Test of Sphericity: If you have more than two levels of the within-subjects factor, include the results of the Mauchly's test to assess the assumption of sphericity. Report the degrees of freedom (df) and the p-value.
  • Greenhouse-Geisser Correction: If the assumption of sphericity is violated, include the Greenhouse-Geisser correction results, which adjust the degrees of freedom and p-values.
  • Tests of Within-Subjects Effects: Present the main effects and interaction effects. Include the degrees of freedom (df), the F-value, the p-value, and effect size measures like partial eta-squared (ηp²) or epsilon-squared (ε²). Report the effect size values alongside the F-value and p-value.
  1. Narrative Summary: Alongside the table, provide a brief narrative summary of the key findings. The summary should include the following information:
  • Describe the purpose of the analysis and the variables involved.
  • State whether the assumption of sphericity was met. If it was violated, mention that the Greenhouse-Geisser correction was applied.
  • Report the main effects and interaction effects, including the relevant F-values, degrees of freedom, p-values, and effect size measures.
  • Interpret the significant effects and provide a concise summary of the findings. Focus on the direction and magnitude of the effects.
  • If appropriate, discuss any post hoc tests or planned comparisons conducted following the ANOVA. Highlight significant pairwise comparisons and any patterns observed.
Here's an example narrative summary:
"The repeated measures ANOVA revealed a significant main effect of time, F(2, 30) = 7.21, p < .001, ηp² = .32. Post hoc tests using the Bonferroni correction indicated that the mean scores at time point 3 (M = 8.56, SD = 1.21) were significantly higher than at time point 1 (M = 5.34, SD = 0.98, p < .01) and time point 2 (M = 6.12, SD = 1.05, p < .05). However, there was no significant main effect of condition, F(1, 15) = 1.89, p = .18, ηp² = .11. Additionally, the interaction between time and condition was not significant, F(2, 30) = 1.45, p = .25, ηp² = .09. These results suggest that time had a significant impact on the variable of interest, with scores increasing significantly from time point 1 to time point 3."
Remember to adapt the example to fit your specific study and its findings.
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I am doing a mixed ANOVA with one within-subjects factor and two between-subjects factors. To prevent order effects, the order in which participants received each level of the within-subjects factor has been randomized. Is it possible to include this order randomization in a repeated measures mixed ANOVA in SPSS? And if so, should it be included as a covariate?
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I have some questions.
  1. How many subjects are there?
  2. How many levels does the within-Ss factor have?
  3. How exactly was the order "randomized" to use your word?
  4. How many different orders were used?
Thanks for clarifying.
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Hi Everyone
I am Graduate student who isnt the greatest at statistics and I have a question regarding a 3 way ANOVA. I am trying to run a 3-way ANOVA for a data set in graphpad that is the following:
-3 diets (X,Y,Z)
-3 Genotypes (W, H, K)
-high fat vs low fat
In total, I have 9 groups (3x3 diet/gene interactions), between both high and low fat fed animals, and I set up the graphpad sheet exactly how it displays on the website, however, I get an error saying that the data is not correct to run a 3-way. Really my questions is that is this a limitation in graphpad, or can I only run a 3-way ANOVA with 4 groups? (PS if i trim my groups to 4 in graphpad I am able to run a 3-way.
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Hello James,
I'm not a Graphpad user, but a look at the statistics guide (https://www.graphpad.com/guides/prism/8/pdf/Prism-8-Statistics-Guide.pdf, pages 525 on) convinces me that the data entry format is anything but standard when compared with most statistical packages.
For this reason, you might not be entering your data in the way the program expects. You may want to consider a different software package, such as Jamovi, which is free, based on the open-source R system, and generally gets good ratings for ease of use.
Good luck with your work.
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OriginPro (https://www.originlab.com) is one of my favorite software, especially for graphing. It can also do many statistical analyses. However, I can't do one-way ANOVA with RCBD design (i.e. blocking is used as a factor to minimize error in the field experiment).
Does anyone have experience with the techniques for including blocking factors in this ANOVA model?
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Hello Kedir,
As both prior replies have directly addressed your concern, please allow me to offer a general observation.
In a real sense, the term "one-way anova with blocks" is a bit of a misnomer. You have, in reality, two independent variables. As a blocking factor frequently represents a restriction on randomization, it can be debatable as to whether the model should or should not include an IV x Block interaction term. But otherwise, this design will behave like a two-way anova (or the associated regression model).
As long as your preferred software program allows for either two-way anova or multiple linear regression, you can certainly obtain the results you seek, even if it does not claim to have a one-way anova for RCBD.
Good luck with your work.
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Please I am trying to test wether there is significant variation in the level of SR disclosure among 35 industries over 10 years. I learned one-way ANOVA is suitable, please how can I run the analysis (ANOVA)?
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Thanks for your valuable suggestions, I will do as recommended
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Is it possible to get non-significant results in post hoc test when we got the significant result in ANOVA? AND how can interpret it?
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Yes, it is possible to get non-significant results in post hoc test when we got the significant result in ANOVA. This can happen for several reasons, such as:
- The ANOVA is more sensitive to detect any differences among the groups, while the post hoc test is more conservative and adjusts for multiple comparisons. Therefore, the ANOVA may reject the null hypothesis of equal group means, but the post hoc test may fail to identify which specific pairs of groups are significantly different.
- The ANOVA is based on the assumption of normality and homogeneity of variance, while the post hoc test does not require these assumptions. Therefore, if the data violate these assumptions, the ANOVA may give a misleading result, while the post hoc test may be more robust and accurate.
- The ANOVA is affected by the sample size and the number of groups, while the post hoc test is not. Therefore, if the sample size is small or the number of groups is large, the ANOVA may have low power and high type II error rate, while the post hoc test may have higher power and lower type II error rate.
To interpret this situation, one can report that the ANOVA showed a significant effect of the factor on the outcome variable, but the post hoc test did not reveal any significant pairwise differences among the groups. This means that there is some evidence of heterogeneity among the group means, but it is not clear which groups are driving this effect. One can also discuss the possible reasons for this discrepancy and suggest further analysis or investigation to clarify the results.