# 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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### 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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### 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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### 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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### 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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### 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 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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### 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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### 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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### 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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### How to choose between ANOVA and ANCOVA in a designed experiment?

I am conducting an experiment which has the following: DV: Slice consumption (continuous or could be categorical) IV: Healthy message, unhealthy message, no message (control) (3 groups in which ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### Unequal variance in randomized experiments to compare treatment with control?

Consider a randomized experiment to compare (one or more) treatment(s) with a control. Since groups are defined by random assignment, we should expect equal variances for a null-experiment (that is, ...
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### How can I get a significant overall ANOVA but no significant pairwise differences with Tukey's procedure?

I performed with R an ANOVA and I got significant differences. However when checking which pairs were significantly different using the Tukey's procedure I did not get any of them. How can this be ...
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### What's the difference between regression and analysis of variance?

Like, I don't get it. In regression, we say $$Y_i = a + bX_i + \epsilon$$ where $X_i$ is just a real number for each observation $i$, and in analysis of variance with two groups, we say Y_i = a + ...
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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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### 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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### What is the lme4::lmer equivalent of a three-way repeated measures ANOVA?

My question is based on this response which showed which lme4::lmer model corresponds to a two-way repeated measures ANOVA: ...
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### How is MANOVA related to LDA?

In several places I saw a claim that MANOVA is like ANOVA plus linear discriminant analysis (LDA), but it was always made in a hand-waving sort of way. I would like to know what exactly it is supposed ...
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### Why do we use a one-tailed test F-test in analysis of variance (ANOVA)?

Can you give the reason for using a one tailed test in the analysis of variance test? Why do we use a one-tail test - the F-test - in ANOVA?
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### Prove F test is equal to T test squared

I need to show that F test is equal to T test squared, when the T test is for 2 independent groups and assuming variances are equal. I know that $F=\frac{MSB}{MSW}=\frac{SSB/k-1}{SSW/N-K}$ and I know ...
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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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### 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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### 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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### 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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### In three-way ANOVA, how to interpret the three-way interaction?

I have a significant three-way interaction (with no significant two-way interactions and no significant main effects). To begin with I have followed this up with two two-way ANOVAs (one at each level ...
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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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### 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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### 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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### 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. MSR/MSE...
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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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### Repeated measures ANOVA vs. factorial ANOVA with subject factor: understanding "error strata" and Error() term in aov

Consider repeated measures ANOVA (RM-ANOVA) with one within-subject factor A and several measurements per subject for each level of ...
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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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### 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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