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Analysis of Variance and Covariance

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


anova1One-way analysis of variance
anova2Two-way analysis of variance
anovanN-way analysis of variance
aoctoolInteractive analysis of covariance
canoncorrCanonical correlation
dummyvarCreate dummy variables
friedmanFriedman’s test
kruskalwallisKruskal-Wallis test
multcompareMultiple 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.


  • 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.