# 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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### 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 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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### How to interpret type I (sequential) 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 into ...
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### What an experimental design is this?

I collect blood from one human (donor), separate leukocytes and put $2\times10^6$ of them per each well of five: well 1: $2\times10^6$ Lk (leukocytes) well 2: $2\times10^6$ Lk well 3: ...
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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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### 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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### 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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### 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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### 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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### 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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### Using and interpreting type I SOS in three-way ANOVA

My research question is from education: To test whether groups (university, department, gender) differ based on their scores in a test, and whether there are any interaction effects, I'll do 3-way ...
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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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### The effect of the number of replicates in different cells on the results of ANOVA

I have written 3way-anova in c++. I have 3 factors, lets say a,b and c and my aim to check the strength of all possible interactions and main effects.The result of my code is the same as MATLAB when I ...
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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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### 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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### 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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### 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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### 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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### 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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### 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 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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### Should the difference between control and treatment be modelled explicitly or implicitly?

Given the following experimental setup: Multiple samples are taken from a subject and each sample is treated multiple ways (including a control treatment). What is mainly interesting is the ...
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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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### Why is ANOVA interaction no longer significant after including a covariate?

I have initially run a 2x2x2 Anova and found some significant interaction between the independent variables. I then ran a ANCOVA where I added a covariate. I am confused with how to interpret the ...
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### Justification for low/high or tertiary splits in ANOVA

I have two groups of participants and they all took the same measurements. When I perform a median split on one of the measurements to test my hypothesis about an interaction, the dependent ...
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### Wrong results using ANOVA with repeated measures

I am using ANOVA with repeated measures to test significance between males and females results of an experiment during which participants had to evaluate 7 stimuli in 2 conditions (EXP1 and EXP2). ...
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### Does random effects allow me to do repeated measures?

I am analysing some behaviour data from several participants in Matlab. I used to do "repeated measures" in SPSS. But is this the same as adding "subject" as a factor, and choosing it as a random ...
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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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### 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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### 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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### Type III sum of squares from SAS and R

I'm analyzing data from an unbalanced factorial experiment both with SAS and R. Both SAS and ...
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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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### 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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### 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 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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### 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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### 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 to setup and interpret ANOVA contrasts with the car package in R?

Let's say I have a simple 2x2 factorial experiment that I want to do ANOVA on. Like this, for example: ...
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### How can I explain the intuition behind ANOVA?

I need to explain the intuition behind what ANOVA is doing to a non-technical person. Is there a visual that explains the idea? A visual that illustrates the key idea in the context of a one-way ANOVA ...
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### What test do I use in order to analyze a within participants repeated measure experiment?

@RyanB thank you for your quick reply and your help! I conducted an experiment supporting that men are attracted by women in red. I recruited 30 men and 25 women who followed exactly the same ...
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### How to run two-way ANOVA on data with neither normality nor equality of variance in R?

I am working on my master thesis at the moment and planned on running the statistics with SigmaPlot. However, after spending some time with my data I came to the conclusion that SigmaPlot might not be ...
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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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### Estimating Lambda for Box Cox transformation for ANOVA

Assumptions: In an ANOVA where the normality assumptions are violated, the Box-Cox transformation can be applied to the response variable. The lambda can be ...
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### How to interpret these custom contrasts?

I am doing a one way ANOVA (per species) with custom contrasts. ...
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### Difference between CI of ANOVA level coefficients vs t-test CI - which one is “correct”?

How do I get the 95% confidence interval for ANOVA level coefficients? For comparison with a constant value, not multiple comparison (like MMC). I tried to take the coefficient's SE from the model: ...
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### Friedman's test and post-hoc analysis

I am carrying out a statistical analysis for my research. I am using a Friedman's test with post hoc analysis. At present I am using the function ...
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### How robust is ANOVA when group sizes are unequal and residuals are not normally distributed?

I understand that there are degrees of trust one can have in the output of ANOVA. However, naturally I want to maximize the amount I can trust my results. Question: If I have data that violate the ...