Anova is just a special case of multiple regression.
There're many forms of ANOVA. It's a very common procedure in basic statistics.
Anova is more Appropriate when:
- there's true independent variable
It's most common application is to analyze data from randomized controlled experiments (ie experimental research) but it can be used in non-experimental context as well.
If we only generate two group means (only 2 means) then we can just do t-tests :
Anova is used more specifically for randomized experiments that generate more than 2 two group means (two means).
During an experimental research, if two group means are generated and that we want to compare those group means, then we'll engage in ANOVA.
- if the groups are all independent then we call that a “between groups ANOVA”.
- if the groups are all coming from the same subjects, then we call that “repeated measures ANOVA”.
During Independent t-test, there is multiple pairwise comparisons and this is a tedious task. There should be one procedure to do that in one step, and that's ANOVA.
ANOVA typically involves NHST, but it doesn't have to
An ANOVA will tell with the F-ratio if:
- there is an effect overall
- there is significant difference somewhere
The Post-hoc tests is used to figure out exactly where there are significant differences.
- a form of multiple regression where the predictors are not correlated
- an analysis used when the relationship between the independent variable and the dependent variable are linear and additive
Anova is an analysis used when the variables are correlated.