Repeated-measures ANOVA (Greenhouse-Geisser)

Shown in the app as rm_anova. Part of the method reference, under Comparing groups.

When to use

Continuous outcome measured on the SAME subjects across the levels of a within-subject factor (e.g. pre / post / follow-up). Classic repeated-measures ANOVA with a sphericity correction; for unbalanced or missing data prefer the linear mixed model.

What you provide

• Outcome: one numeric column.
• Within-subject factor (the repeated measure): one categorical column.
• Subject id (the unit measured repeatedly): one column identifying the cluster.

Options

Missing data

• Complete case (listwise deletion)

Multiple comparisons

• Not adjustable for this method. Where it makes post-hoc comparisons, the procedure applies its own correction.

Confidence level

Every interval in the result is reported at the level you choose:

• 90%
• 95%
• 99%

Related methods

Other methods under Comparing groups:

• Welch's t-test
• Student's t-test
• Paired t-test
• Mann-Whitney U test
• Wilcoxon signed-rank test
• One-way ANOVA
• Welch's ANOVA
• Kruskal-Wallis test
• ANCOVA (analysis of covariance)
• Two-way ANOVA (factorial)

Guides that discuss this method

• How to choose a statistical test for your data
• Repeated-measures ANOVA or a linear mixed model?

Worked examples

Celeus's result on a published or illustrative dataset, next to an independent computation and, where one exists, a published value. The data themselves are not reproduced here.

nlme::ergoStool

• Source: Published dataset distributed with an R package
• Licence: nlme (GPL)
• Reference: Pinheiro & Bates (2000), Mixed-Effects Models in S and S-PLUS, Section 1.2 (A Randomized Block Design): F = 22.36 on 3 and 24 df for Type, as printed by the nlme package's own run of that section's code; the corrected p-value and the generalized eta-squared are independent computations

Quantity	Celeus	Independent computation	Published value	Agrees
Test statistic	22.3556	22.3556	22.36	Yes
Degrees of freedom	1.94,15.5	1.94,15.5	-	Yes
p-value	3.00556e-05	3.00556e-05	-	Yes
Estimate	0.459375	0.459375	-	Yes
Number of observations	36	36	-	Yes
Partial eta-squared for each model term	0.736458	0.736458	-	Yes
Partial eta-squared lower confidence limit	0.50518	0.50518	-	Yes
Partial eta-squared upper confidence limit	0.836507	0.836507	-	Yes

lme4::sleepstudy (reaction time on each of 10 days, 18 subjects)

• Source: Published dataset distributed with an R package
• Licence: lme4 (GPL)
• Reference: Belenky et al. (2003), Journal of Sleep Research 12:1-12 (the data); independent computation

Quantity	Celeus	Independent computation	Published value	Agrees
Test statistic	18.7027	18.7027	-	Yes
Degrees of freedom	3.32,56.46	3.32,56.46	-	Yes
p-value	5.46309e-09	5.46309e-09	-	Yes
Estimate	0.292691	0.292691	-	Yes
Number of observations	180	180	-	Yes
Partial eta-squared for each model term	0.523846	0.523846	-	Yes
Partial eta-squared lower confidence limit	0.421465	0.421465	-	Yes
Partial eta-squared upper confidence limit	0.586201	0.586201	-	Yes
Confidence level of the effect size interval	0.9	0.9	-	Yes

nlme::ergoStool with one effort value removed (subject 1, stool T3)

• Source: Published dataset distributed with an R package
• Licence: nlme (GPL)
• Reference: Pinheiro & Bates (2000), Mixed-Effects Models in S and S-PLUS (the data); independent computation

Quantity	Celeus	Independent computation	Published value	Agrees
Test statistic	21.4375	21.4375	-	Yes
Degrees of freedom	2.05,14.35	2.05,14.35	-	Yes
p-value	4.54722e-05	4.54722e-05	-	Yes
Estimate	0.503425	0.503425	-	Yes
Number of observations	32	32	-	Yes
Partial eta-squared for each model term	0.753846	0.753846	-	Yes
Partial eta-squared lower confidence limit	0.51131	0.51131	-	Yes
Partial eta-squared upper confidence limit	0.851881	0.851881	-	Yes

Validation report

References

1. Greenhouse, S. W., Geisser, S. (1959). On methods in the analysis of profile data. Psychometrika 24: 95-112. doi:10.1007/BF02289823 doi:10.1007/BF02289823