SOURCEBOOK

R Articles

Annotated Output | Repeated Measures ANOVA

Computer Output

The descriptive statistics can be used to determine the inferential statistics.

> Results <- aov(Outcome ~ Time + Error(Subject / Time))
> model.tables(Results, "means")
Tables of means
Grand mean
  
4 

 Time 
Time
Time1 Time2 
    2     6 
> lapply(
+   split(Outcome, Time),
+   function(x) c(n = length(x), mean = mean(x), sd = sd(x))
+ )
$Time1
      n    mean      sd 
4.00000 2.00000 2.44949 

$Time2
      n    mean      sd 
4.00000 6.00000 2.44949

The values of the statistics are calculated separately for each instance (which are shown as separate variables).

The grand mean and the marginal means for each factor are also presented.

The tables of inferential statistics show the key elements to be calculated.

> summary(Results)

Error: Subject
          Df Sum Sq Mean Sq F value Pr(>F)
Residuals  3     27       9               

Error: Subject:Time
          Df Sum Sq Mean Sq F value Pr(>F)  
Time       1     32      32   10.67 0.0469 *
Residuals  3      9       3                 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Here, F = 10.667 and p = .047. This would be considered a statistically significant finding.

Partial eta2 is not presented here but can be calculated from the available information (0.780). Thus, 78.0% of the variability among Outcome scores (after removing individual differences) is accounted for by repeated measures Factor.

For Repeated ANOVA, the confidence intervals around (centered on) each mean are appropropriate but not provided in the output.

APA Style

The RMD ANOVA tests for overall differences across the repeated measures. As such, its summary parallels that of the One Way ANOVA.

A repeated measures ANOVA showed that the difference in Outcome scores (N = 4) between the first time point (M = 2.00, SD = 2.45) and second time point (M = 6.00, SD = 2.45) was very large and statistically significant, F(1,3) = 10.67, p = .047, partial η2 = .78.

Alternatively, the means, standard deviations, and confidence intervals could be presented in a table or figure associated with this text.