ANOVA Guide as a specific case of GLMs

Introduction

This unique statistical method called analysis of variance (ANOVA) is used to estimate the variability in the outcome caused by various factors. It is a special case of a GLM with discrete or categorical explanatory independent variables and outcomes that are normally?distributed. The alternative hypothesis of an ANOVA test takes into account mean differences, whereas the null hypothesis asserts that there are no mean differences between groups.

Types of ANOVA

1-????? One-way ANOVA: Compares means of one factor with multiple levels.

2-????? Two-way ANOVA: Compares means across two factors and interaction effects

3-????? Repeated measures ANOVA: Consider repeated measurements multiple times for the same subject.

Different types to calculate ANOVA:

The methods used by Types I, II, and III of ANOVA to quantify variability (particularly the sum of squares) vary. All three methods will yield the same findings if your data is balanced, which means that each group has an equal number of observations. Type II or Type III will be utilized if the data observations are not balanced between the groups.

Preparing your data:

Several assumptions must be met to perform ANOVA test.

First, observation must be independent.

Second, the outcome must be continuous and normally distributed

Third, the variances within each level of all explanatory variables must be equal ( homogeneity of variances) because a single residual variance is used to estimate uncertainty of all groups

• Tests like the Leven's test can be used to verify the assumption of homogeneity of variance.
• A normal distribution can be tested using histograms, skewness and kurtosis data, or tests like the Shapiro-Wilk test.
• The study's design can be used to determine independence.

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