Statistical Analysis Stack Exchange
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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.

Although ANOVA stands for ANalysis Of VAriance, it is about comparing means of data from different groups. It is part of the general linear model which also includes linear regression and ANCOVA. In matrix algebra form, all three are:

$Y = XB + e$

Where $Y$ is a vector of values for the dependent variable (these must be numeric), $X$ is a matrix of values for the independent variables and $e$ is error.

The chief difference among ANOVA, ANCOVA and linear regression is that they arose in different fields. Also, ANOVA is usually restricted to cases where the independent variables are categorical, ANCOVA where some are numeric but most categorical. Regression (through dummy variables) can handle any type of independent variable.

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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 equivalence, is there any reason why ANOVA is used…
user28
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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 across the different samples are same or…
Victor
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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.
Tal Galili
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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 why do we need the global test first? If…
even
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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 into parts. First, if I am interested in the effect…
djhocking
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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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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 obvious options for analysing such data are: Test…
Jeromy Anglim
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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 residuals are normal. Equality (or "homogeneity")…
Roman Luštrik
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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 what needs to happen, but am still confused by few…
phosphorelated
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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 normality in the DATA. ANOVA is equivalent to linear…
Chris Beeley
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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-way ANOVA would definitely be the way to go,…
Rick L.
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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 test the models against one another? And why does the order matter? Here is an…
qed
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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 squared? Can they both be interpreted using the…
Short Elizabeth
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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 and a p-value. My null hypothesis ($H_0$) is that all group means are equal. There…
JanD
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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 anything procedurally different when working with such…
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