# Questions tagged [anova]

ANOVA stands for ANalysis Of VAriance, a statistical model and set of procedures for comparing multiple group means. The independent variables in an ANOVA model are categorical, but an ANOVA table can be used to test continuous variables as well.

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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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### Why is ANOVA equivalent to linear regression?

I read that ANOVA and linear regression are the same thing. How can that be, considering that the output of ANOVA is some $F$ value and some $p$-value based on which you conclude if the sample means ...
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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?...
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### How to interpret type I, type II, and type III ANOVA and MANOVA?

My primary question is how to interpret the output (coefficients, F, P) when conducting a Type I (sequential) ANOVA? My specific research problem is a bit more complex, so I will break my example ...
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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.
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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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### 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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### Using lmer for repeated-measures linear mixed-effect model

EDIT 2: I originally thought I needed to run a two-factor ANOVA with repeated measures on one factor, but I now think a linear mixed-effect model will work better for my data. I think I nearly know ...
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### Alternatives to one-way ANOVA for heteroskedastic data

I have data from 3 groups of algae biomass ($A$, $B$, $C$) which contain unequal sample sizes ($n_A=15$, $n_B=13$, $n_C=12$) and I would like compare if these groups are from the same population. One-...
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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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### 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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### Comparing two models using anova() function in R

From the documentation for anova(): When given a sequence of objects, ‘anova’ tests the models against one another in the order specified... What does it mean to ...
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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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### 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 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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### What does the anova() command do with a lmer model object?

Hopefully this is a question that someone here can answer for me on the nature of decomposing sums of squares from a mixed-effects model fit with lmer (from the ...
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### ANOVA on binomial data

I am analyzing an experimental data set. The data consists of a paired vector of treatment type and a binomial outcome: ...
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### Satterthwaite vs. Kenward-Roger approximations for the degrees of freedom in mixed models

The lmerTest package provides an anova() function for linear mixed models with optionally Satterthwaite's (default) or Kenward-...
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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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### 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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### Can ANOVA be significant when none of the pairwise t-tests is?

Is it possible for one-way (with $N>2$ groups, or "levels") ANOVA to report a significant difference when none of the $N(N-1)/2$ pairwise t-tests does? In this answer @whuber wrote: It is ...
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### How to get an "overall" p-value and effect size for a categorical factor in a mixed model (lme4)?

I would like to get a p-value and an effect size of an independent categorical variable (with several levels) -- that is "overall" and not for each level separately, as is the normal output from ...
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### Why do linear regression and ANOVA give different $p$-value in case of considering interaction between variable?

I was trying to fit one time-series data (without replicates) using regression model. The data looks like follows: ...
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### ANOVA vs multiple linear regression? Why is ANOVA so commonly used in experimental studies?

ANOVA vs multiple linear regression? I understand that both of these methods seem to use the same statistical model. However under what circumstances should I use which method? What are the ...
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### Difference Between ANOVA and Kruskal-Wallis test

I am learning R and have been experimenting with analysis of variance. I have been running both kruskal.test(depVar ~ indepVar, data=df) and ...
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### Choice between Type-I, Type-II, or Type-III ANOVA [duplicate]

We have a dataset with three variables (dV: self-reported measure on scale 1-5, assumed to be metric; iV1: factor with 4 levels; iV2: factor with 8 levels). We are interested whether the dV differs in ...
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### The order of variables in ANOVA matters, doesn't it?

Am I correct to understand that the order in which variables are specified in a multifactorial ANOVA makes a difference but that the order does not matter when doing a multiple linear regression? So ...
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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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### Practically speaking, how do people handle ANOVA when the data doesn't quite meet assumptions?

This isn't a strictly stats question--I can read all the textbooks about ANOVA assumptions--I'm trying to figure out how actual working analysts handle data that doesn't quite meet the assumptions. I'...
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### What is the non-parametric equivalent of a two-way ANOVA that can include interactions?

Hi I am trying to find the non-parametric equivalent of a two-way ANOVA (3x4 design) which is capable of including interactions. From my reading in Zar 1984 "Biostatistical analysis" this is possible ...
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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 the ...
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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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### 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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### Regression vs. ANOVA discrepancy (aov vs lm in R)

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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### Why Levene test of equality of variances rather than F ratio?

SPSS uses the Levene test to evaluate homogeneity of variances in the independent group t-test procedure. Why is the Levene test better than a simple F ratio of the ratio of the variances of the ...
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### Does it make sense for a fixed effect to be nested within a random one, or how to code repeated measures in R (aov and lmer)?

I have been looking through this overview of lm/lmer R formulas by @conjugateprior and got confused by the following entry: Now assume A is random, but B is fixed and B is nested within A. ...
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### Common statistical tests as linear models

(UPDATE: I dived deeper into this and and posted the results here) The list of named statistical tests is huge. Many of the common tests rely on inference from simple linear models, e.g. a one-sample ...
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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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### Bonferroni or Tukey? When does the number of comparisons 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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### Is Fisher's LSD as bad as they say it is?

When we perform experiments (on small sample sizes (usually the sample size per treatment group is about 7~8)) on two groups, we use a t-test to test for difference. However, when we perform an ANOVA (...
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### How do you "control" for a factor/variable?

To my understanding, "Control" can have two meanings in statistics. Control group: In an experiment, no treatment is given to the member of the control group. Ex: Placebo vs Drug: You give drugs to ...
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### When is a repeated measures ANOVA preferred over a mixed-effects model?

In response to this question, regarding whether my design where I randomly presented participants with pictures from different categories was an example where I should use a repeated measures ANOVA, I ...
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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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### Repeated measures ANOVA with lme/lmer in R for two within-subject factors

I'm trying to use lme from the nlme package to replicate results from aov for repeated ...
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### Why use ANOVA at all instead of jumping straight into post-hoc or planned comparisons tests?

Looking at a between-groups ANOVA situation, what do you get by actually doing such an ANOVA test first, and second do post-hoc (Bonferroni, Šidák, etc.) or planned comparisons tests? Why not skip the ...
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### Using ANOVA on percentages?

I have a table with four groups (4 BMI groups) as the independent variable (factor). I have a dependent variable that is "percent mother smoking in pregnancy". Is it permissible to use ANOVA for ...
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### Good resource to understand ANOVA and ANCOVA?

I am running experiments for a paper and I 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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### Why does lrtest() not match anova(test="LRT")

I was looking for ways to do a likelihood ratio test in R to compare model fits. I first coded it myself, then found both the default anova() function and also <...
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### Appropriateness of ANOVA after k-means cluster analysis

The notification after the ANOVA table after K-means analysis indicates that significance levels should not be looked at as the test of equal means, as the cluster solution has been derived based on ...
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