# Tagged Questions

ANOVA stands for ANalysis Of VAriance, a statistical model and set of procedures for comparing the means of groups of related data. Generally the independent variables in an ANOVA analysis are categorical, not continuous.

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### Why is ANOVA taught / used as if it is a different research methodology compared to linear regression?

ANOVA is equivalent to linear regression with the use of suitable dummy variables. The conclusions remain the same irrespective of whether you use ANOVA or linear regression. In light of their ...
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### How to visualize what ANOVA does?

What way (ways?) is there to visually explain what is ANOVA? Any references, link(s) (R packages?) will be welcomed. Thanks.
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### Best practice when analysing pre-post treatment-control designs

Imagine the following common design: 100 participants are randomly allocated to either a treatment or a control group the dependent variable is numeric and measured pre- and post- treatment Three ...
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### If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent?

I'm sure I've got this completely wrapped round my head, but I just can't figure it out. The t-test compares two normal distributions using the Z distribution. That's why there's an assumption of ...
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### What is compound symmetry in plain english?

I recently realized that a mixed-model with only subject as a random factor and the other factors as fixed factors is equivalent to an ANOVA when setting the correlational structure of the mixed model ...
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### Do we need a global test before post hoc tests?

I often hear that post hoc tests after an ANOVA can only be used if the ANOVA itself was significant. However, post hoc tests adjust p values to keep the global type I error rate at 5%, don't they? So ...
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### Have I computed these likelihood ratios correctly?

I'm the author of the ez package for R, and I'm working on an update to include automatic computation of likelihood ratios (LRs) in the output of ANOVAs. The idea is to provide a LR for each effect ...
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### ANOVA assumption normality/normal distribution of residuals

The Wikipedia page on ANOVA lists three assumptions, namely: Independence of cases – this is an assumption of the model that simplifies the statistical analysis. Normality – the distributions of the ...
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### How to interpret and report eta squared / partial eta squared in statistically significant and non-significant analyses?

I have data that has eta squared values and partial eta squared values calculated as a measure of effect size for group mean differences. What is the difference between eta squared and partial eta ...
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### Good resource to understand anova and ancova?

I am running experiments for a paper and am looking for an interesting book/website to understand properly how anova and ancova work. I have a good math background so I don't necessarily need a ...
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### Checking ANOVA assumptions

A few months ago I posted a question about homoscedascity tests in R on SO, and Ian Fellows answered that (I'll paraphrase his answer very loosely) "homoscedascity tests are not a good tool when ...
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### Differences between MANOVA and Repeated Measures ANOVA?

What is the difference between a repeated measures ANOVA over some factor (say experimental condition) and a MANOVA? In particular one website I stumbled across suggested that MANOVA does not make ...
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### Follow up: In a mixed within-between ANOVA plot estimated SEs or actual SEs?

I am currently finishing a paper and stumbled upon this question from yesterday which led me to pose the same question to myself. Is it better to provide my graph with the actual standard error from ...
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### Removing factors from a 3-way ANOVA table

In a recent paper, I fitted a three-way fixed effects models. Since one of the factors wasn't significant (p > 0.1), I removed it and refitted the model with two fixed effects and an interaction. ...
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### How does one do a Type-III SS ANOVA in R with contrast codes?

Please provide R code which allows one to conduct a between-subjects ANOVA with -3, -1, 1, 3 contrasts. I understand there is a debate regarding the appropriate Sum of Squares (SS) type for such an ...
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### Multiple comparisons on a mixed effects model

I am trying to analyse some data using a mixed effect model. The data I collected represent the weight of some young animals of different genotype over time. I am using the approach proposed here: ...
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### How are regression, the t-test, and the ANOVA all versions of the general linear model?

How are they all versions of the same basic statistical method?
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### Regression vs. ANOVA discrepancy

I was always under the impression that regression is just a more general form of ANOVA and that the results would be identical. Recently, however, I have run both a regression and an ANOVA on the same ...
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### How to determine the sample size needed for repeated measurement ANOVA?

I need some help about repeated measurement ANOVA. We are investigating the effect of some intervention on reducing blood stream infection (BSI) rate in some wards. We plan to capture the BSI rate ...
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### Should I include an argument to request type-III sums of squares in ezANOVA?

I developed the ez package for R as a means to help folks transition from stats packages like SPSS to R. This is (hopefully) achieved by simplifying the specification of various flavours of ANOVA, and ...
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### Bonferroni or Tukey? When does the number of group means become large?

Reading Field's Discovering Statistics Using SPSS 3rd Edition I was struck by a bit about post hoc tests in ANOVA. For those wanting to control the Type I error rate he suggests Bonferroni or Tukey ...
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### Sample size required to determine which of a set of advertisements has the highest click through rate

I am a software designer by trade and I am working on a project for a client, and I would like to make sure that my analysis is statistically sound. Consider the following: We have n advertisements ...
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### Why do lme and aov return different results for repeated measures ANOVA in R?

I am trying to move from using the ez package to lme for repeated measures ANOVA (as I hope I will be able to use custom ...
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### Split-Plot ANOVA: model comparison tests in R

How can I test effects in a Split-Plot ANOVA using suitable model comparisons for use with the X and M arguments of ...
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### How to justify the error term in ANOVA?

A probably very basic question about multi-factorial ANOVA. Assume a two-way design where we test both main effects A, B, and the interaction A:B. When testing the main effect for A with type I SS, ...
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### Is there an equivalent to Kruskal Wallis one-way test for a two-way model?

If the model does not satisfy ANOVA assumptions (normality in particular), if one-way, Kruskal-Wallis non-parametric test is recommended. But, what if you have multiple factors?
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### What is the NULL hypothesis for interaction in a two-way ANOVA?

Let's say we have two factors (A and B), each with two levels (A1, A2 and B1, B2) and a response variable (y). The when performing a two way ANOVA of the type: ...
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### Logic behind the ANOVA F-test in simple linear regression

I'm trying to understand the logic behind the ANOVA F-test in Simple Linear Regression Analysis. The question I have is like follows. When the F value, i.e. ...
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### Analysis with complex data, anything different?

Say for example you are doing a linear model, but the data $y$ is complex. $y = x \beta + \epsilon$ My data set is complex, as in all the numbers in $y$ are of the form $(a + bi)$. Is there ...
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### A non-parametric repeated-measures multi-way Anova in R?

The following question is one of those holy grails for me for some time now, I hope someone might be able to offer a good advice. I wish to perform a non-parametric repeated measures multiway anova ...
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### Can I trust ANOVA results for a non-normally distributed DV?

I have analyzed an experiment with a repeated measures ANOVA. The ANOVA is a 3x2x2x2x3 with 2 between-subject factors and 3 within (N = 189). Error rate is the dependent variable. The distribution of ...
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### ANOVA with non-independent observations

Sorry for the verbose background to this question: Occasionally in investigations of animal behaviour, an experimenter is interested in the amount of time that a subject spends in different, ...
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### MANOVA and correlations between dependent variables: how strong is too strong?

The dependent variables in a MANOVA should not be "too strongly correlated." But how strong a correlation is too strong? It would be interesting to get people's opinions on this issue. For instance, ...
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### Is there any difference between the terms “paired t-test” and “pairwise t-test”?

What is paired t-test, and under which circumstances should I use paired t-test? Is there any difference between paired t-test and pairwise t-test?
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### How can I adapt ANOVA for binary data?

I have four competing models which I use to predict a binary outcome variable (say, employment status after graduating, 1 = employed, 0 = not-employed) for n subjects. A natural metric of model ...
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### How to estimate variance components with lmer for models with random effects and compare them with lme results

I performed an experiment where I raised different families coming from two different source populations, where each family was split up into a different treatments. After the experiment I measured ...
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### How to perform a 4 by 4 mixed ANOVA with between- and within-subjects contrasts using R?

Beginner user of R here struggling with a repeated measures ANOVA. I have a dataset that consists of one between subjects factor with 4 levels (coded in a single variable called 'groups'), and one ...
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### Post hoc tests in ANCOVA

Question: What is a good method for conducting post hoc tests of differences between group means after adjusting for the effect of a covariate? Prototypical example: Four groups, 30 participants ...
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### Post hoc test after ANOVA with repeated measures using R

I have performed a repeated measures ANOVA in R, as follows: aov_velocity = aov(Velocity ~ Material + Error(Subject/(Material)), data=scrd) summary(aov_velocity) ...
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### How to specify specific contrasts for repeated measures ANOVA using car?

I am trying to run a repeated measures Anova in R followed by some specific contrasts on that dataset. I think the correct approach would be to use Anova() from the ...
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### Type III sums of squares

I have a linear regression model with one categorical variable $A$ (male & female) and one continuous variable $B$. I set up contrasts codes in R with ...
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### Phylogenetic dependent variables: ANOVA?

I understand deriving a covariance matrix from phylogenetic data to make $cov(X,Y) = 0$ for two variables you're making a regression on. But what happens if you have one continuous variable, that ...
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### How to analyse repeated measure ANOVA with three or more conditions presented in randomised order?

Context: My question concerns a typical design in my area – a researcher takes a group of subjects (say 10) and then applies three different conditions to them to measure the change in a response ...
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### R implementation of coefficient of partial determination

Does anyone have suggestions or packages that will calculate the coefficient of partial determination? The coefficient of partial determination can be defined as the percent of variation that cannot ...
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### What are the ANOVA's benefits over a normal linear model?

I'm experimenting with R and found that an anova() needs an object of type lm. But why should I continue with an anova after this: ...
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### Interpretation of the p-values produced by Levene's or Bartlett's test for homogeneity of variances

I have run Levene's and Bartlett's test on groups of data from one of my experiments to validate that I am not violating ANOVA's assumption of homogeneity of variances. I'd like to check with you guys ...
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### ANCOVA in R suggests different intercepts, but the 95% CIs overlap… how is this possible?

We have a data set with two covariates and a categorical grouping variable and want to know if there are significant differences between the slope or intercept among the covariates associated with the ...
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### Understanding repeated measure ANOVA assumptions for correct interpretation of SPSS output

I am investigating whether different reward conditions may affect task performance. I have data from a small study with two groups, each with n=20. I collected data on a task that involved performance ...
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### How to interpret F- and p-value in ANOVA?

I am new to statistics and I currently deal with ANOVA. I carry out an ANOVA test in R using aov(dependendVar ~ IndependendVar) I get – among others – an F-value ...
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### What's the minimum number of individuals in a group for repeated-measures ANOVA?

I'm in the process of running a repeated-measures ANOVA on two groups of participants from an experiment. In one group, there are 10 participants, and in the other group, there is only 1 participant. ...