Question

Why is it better to use an ANOVA (Analysis of Variance) when you have more that 2 levels of an independent variable than to use multiple t-tests?

When should you use a Factorial ANOVA in stead of a simple ANOVA?

Answer 1

ANOVA is a better method to use compare to a multiple t test because when we take multiple t test we keep adding the error component with every additional variable

In ANOVA we are more interested in the variance from the mean hence the chance of error is small compared to multiple t test

Here when we talk about error we are refering to the Type 1 error also known as alpha value

A Factorial ANOVA should be used when we are comparing the means with 2 or more independent variables

In Factorial ANOVA the data is split into groups based on the number of independent variables hence the name factorial