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ANOVA[data]

performs a one‐way analysis of variance.

ANOVA[data,model,vars]

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

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Options  
CellMeans  
WorkingPrecision  
PostTests  
SignificanceLevel  
See Also
Tech Notes
Related Guides
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ANOVA`
ANOVA`

ANOVA

ANOVA[data]

performs a one‐way analysis of variance.

ANOVA[data,model,vars]

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

Details and Options

  • 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 one‐way 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:
  • CellMeans Truewhether cell means should be included in the output
    WorkingPrecision MachinePrecisionthe precision used in internal computations
    PostTests {}significance tests to perform
    SignificanceLevel 0.05significance level for performed tests
  • Possible settings for PostTests include: Bonferroni, Duncan, Dunnett, StudentNewmanKeuls, and Tukey.

Examples

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Basic Examples  (2)

A one‐way analysis of variance:

A two‐way 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, https://reference.wolfram.com/language/ANOVA/ref/ANOVA.html.

Text

Wolfram Research (2007), ANOVA, Wolfram Language function, https://reference.wolfram.com/language/ANOVA/ref/ANOVA.html.

CMS

Wolfram Language. 2007. "ANOVA." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ANOVA/ref/ANOVA.html.

APA

Wolfram Language. (2007). ANOVA. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ANOVA/ref/ANOVA.html

BibTeX

@misc{reference.wolfram_2025_anova, author="Wolfram Research", title="{ANOVA}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ANOVA/ref/ANOVA.html}", note=[Accessed: 13-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_anova, organization={Wolfram Research}, title={ANOVA}, year={2007}, url={https://reference.wolfram.com/language/ANOVA/ref/ANOVA.html}, note=[Accessed: 13-August-2025]}