performs a oneway analysis of variance.


performs an analysis of variance for model as a function of the categorical variables vars.


  • To use ANOVA, you first need to load the Analysis of Variance Package using Needs["ANOVA`"].
  • The data can have the form {{x1,y1,,f1},{x2,y2,,f2},}, where the number of coordinates x,y, is equal to the number of variables in the list vars.
  • For data of the form {{x1,f1},{x2,f2},}, a oneway analysis of variance can be obtained without explicitly specifying the model and variable.
  • The model argument can be a list containing main effects and interactions. Main effects are elements of vars, and interactions are products of main effects.
  • A full factorial model including all interactions between variables x,y, can be specified as {x,y,,All}.
  • The following options can be given:
  • CellMeansTruewhether cell means should be included in the output
    WorkingPrecisionMachinePrecisionthe precision used in internal computations
    PostTests{}significance tests to perform
    SignificanceLevel0.05significance level for performed tests
  • Possible settings for PostTests include: Bonferroni, Duncan, Dunnett, StudentNewmanKeuls, and Tukey.


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Basic Examples  (2)

A oneway analysis of variance:

A twoway analysis of variance:

Options  (4)

CellMeans  (1)

Omit cell means from output:

WorkingPrecision  (1)

Computation at precision 20:

PostTests  (1)

Analysis of variance with Bonferroni test:

SignificanceLevel  (1)

Bonferroni test at significance level .01:

Wolfram Research (2007), ANOVA, Wolfram Language function,


Wolfram Research (2007), ANOVA, Wolfram Language function,


@misc{reference.wolfram_2020_anova, author="Wolfram Research", title="{ANOVA}", year="2007", howpublished="\url{}", note=[Accessed: 05-March-2021 ]}


@online{reference.wolfram_2020_anova, organization={Wolfram Research}, title={ANOVA}, year={2007}, url={}, note=[Accessed: 05-March-2021 ]}


Wolfram Language. 2007. "ANOVA." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2007). ANOVA. Wolfram Language & System Documentation Center. Retrieved from