Anova & Post-hoc
ANOVA
Basics
- ANOVA is a special case of Linear mixed models: it assumes the data are idd and continuous, while generalized linear mixed models do not.
- F-distribution & F-Test
Choosing ANOVA types
- How many independent variables do you have?
n variables => n-way ANONA - Whether you are replicating (i.e. duplicating) your tests with multiple groups?
Yes, e.g. two groups of students from two colleges taking two tests => ANOVA with replication - Whether you are comparing within subject?
Yes, e.g. changes in mean scores of same item over three or more time points=> Repeated Measures ANOVA (it is one-way here)
Prerequisite
- the group sizes are same
- the population is normal
<= can be tested using Normality Tests - the groups have equal variance
<= can be tested by Levene's Test for Equality of Variances - for a repeated-measures ANOVA, you have to be careful about the sphericity
- Sphericity is an important assumption of a repeated-measures ANOVA. It is the condition where the variances of the differences between all possible pairs of within-subject conditions (i.e., levels of the independent variable) are equal.
- It can be tested by the Mauchly's sphericity test (Mauchly's W), which is a statistical test used to validate a repeated measures ANOVA.
Post-hoc
A post hoc test is used only after we find a statistically significant result and need to determine where our differences truly came from.
It usually follows an ANOVA test.