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Visual Guides/ANOVA: Comparing Many Groups
STATISTICSUNIT 8: COMPARING GROUPS

ANOVA: Comparing Many Groups

Analyze whether means differ across groups. Decompose variance into between-group and within-group components. Run Bonferroni-corrected post-hoc pairwise comparisons.

ANOVA run
Decomposition completed
Post-hoc viewed
Repeated measures toggled
Interpretation viewed

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Dataset

GroupNMeanSD
Method A
2072.505.26
Method B
2076.054.77
Method C
2078.205.49
Method D
2074.753.48

Each group has 20 observations. Select a preset to change the dataset.

Distribution by Group

616773798591x̄Method Ax̄=72.5Method Bx̄=76.0Method Cx̄=78.2Method Dx̄=74.8
Grand mean
IQR box
Median

One-way ANOVA assumes independent observations, approximately normal residuals within each group, and roughly equal group variances. Check the box plots above for badly skewed groups or very unequal spreads before trusting the F-test.

Variance Decomposition

SS

ANOVA decomposes total variability into between-group and within-group components. Press Next to begin the variance decomposition.

SSTotal = SSBetween + SSWithin

Step 0 / 5

Post-hoc comparisons appear when ANOVA is significant (p < 0.05).

Repeated-Measures ANOVA

Currently showing between-subjects ANOVA: each participant is in exactly one group. Toggle to see how the design changes with repeated measures.

Between-subjects design:
SSTotal = SSBetween + SSWithin
80 participants × 1 group each = 80 independent observations

Results Summary

Run ANOVA to see a summary of results.

← t-Tests & Proportion TestsNonparametric Tests →