# Analysis of Variance and Covariance

Parametric and non-parametric analysis of variance, interactive and non-interactive analysis of covariance, multiple comparisons

## Functions

 `anova1` One-way analysis of variance `anova2` Two-way analysis of variance `anovan` N-way analysis of variance `aoctool` Interactive analysis of covariance `canoncorr` Canonical correlation `dummyvar` Create dummy variables `friedman` Friedman’s test `kruskalwallis` Kruskal-Wallis test `multcompare` Multiple comparison test

## Examples and How To

One-Way ANOVA

Use one-way ANOVA to determine whether data from several groups (levels) of a single factor have a common mean.

Two-Way ANOVA

In two-way ANOVA, the effects of two factors on a response variable are of interest.

N-Way ANOVA

In N-way ANOVA, the effects of N factors on a response variable are of interest.

ANOVA with Random Effects

ANOVA with random effects is used where a factor's levels represent a random selection from a larger (infinite) set of possible levels.

Other ANOVA Models

N-way ANOVA can also be used when factors are nested, or when some factors are to be treated as continuous variables.

Multiple Comparisons

Multiple comparison procedures can accurately determine the significance of differences between multiple group means.

Analysis of Covariance

Analysis of covariance is a technique for analyzing grouped data having a response (y, the variable to be predicted) and a predictor (x, the variable used to do the prediction).

Nonparametric Methods

Statistics and Machine Learning Toolbox™ functions include nonparametric versions of one-way and two-way analysis of variance.

## Concepts

Introduction to Analysis of Variance

Analysis of variance (ANOVA) is a procedure for assigning sample variance to different sources and deciding whether the variation arises within or among different population groups.