# Statistics - Analysis of variance (Anova)

### Table of Contents

## 1 - About

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
- the predictors (independent variable - IVs) are all categorical
- and the outcome (dependent variable - DV) is continuous

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.

## 2 - Articles Related

## 3 - Test

ANOVA typically involves NHST, but it doesn't have to

The NHST test statistic is an F-test or F-ratio.

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.

## 4 - Type

- Factorial: A ANOVA is factorial when we have multiple predictors. We can test for interaction effect

## 5 - True / False

### 5.1 - True

Anova is:

- used when the independent variables are categorical and the dependent variable is continuous
- 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

### 5.2 - False

Anova is an analysis used when the variables are correlated.