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Annotated Output | Mixed ANOVA

Computer Output

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

> Results <- aov(Outcome ~ Factor * Time + Error(Subject / Time))
> model.tables(Results, "means")
Tables of means
Grand mean
     
5.25 

 Factor 
Factor
Level1 Level2 
   4.0    6.5 

 Time 
Time
Time1 Time2 
  4.0   6.5 

 Factor:Time 
        Time
Factor   Time1 Time2
  Level1 2     6    
  Level2 6     7    
> 
> lapply(
+   split(Outcome, interaction(Factor, Time)),
+   function(x) c(n = length(x), mean = mean(x), sd = sd(x))
+ )
$Level1.Time1
      n    mean      sd 
4.00000 2.00000 2.44949 

$Level2.Time1
      n    mean      sd 
4.00000 6.00000 2.44949 

$Level1.Time2
      n    mean      sd 
4.00000 6.00000 2.44949 

$Level2.Time2
      n    mean      sd 
4.00000 7.00000 2.44949

The descriptive statistics are calculated separately for each group and time point. They are not equivalent to getting the statistics for the variable(s) as a whole.

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)
Factor     1     25  25.000   2.885   0.14
Residuals  6     52   8.667               

Error: Subject:Time
            Df Sum Sq Mean Sq F value Pr(>F)  
Time         1     25  25.000     7.5 0.0338 *
Factor:Time  1      9   9.000     2.7 0.1515  
Residuals    6     20   3.333                 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

For the Factor Main Effect, F = 2.885, p = .140. This would not be considered a statistically significant finding.

For the Time Main Effect, F = 7.500, p = .034. This would be considered a statistically significant finding.

For the Interaction, F = 2.700, p = .152. This would not be considered a statistically significant finding.

Effect size measures (partial eta-squared) are not in the output, but can be calculated from the available information.

For the Factor Main Effect, partial eta2 = 0.325. Thus, 32.5% of the variability among the scores is accounted for by Factor.

For the Time Main Effect, partial eta2 = 0.556. Thus, 55.6% of the variability among the scores is accounted for by Time.

For the Interaction, partial eta2 = 0.310. Thus, 31.0% of the variability among the scores is accounted for by the Factor × Time interaction.

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

APA Style

The mixed ANOVA provides statistics for the main effects and interaction in a mixed design. Each effect would be summarized in a style analogous to a Factorial ANOVA.

A 2 (Factor) × 2 (Time) mixed ANOVA showed that the small main effect of Factor was not statistically significant, F(1,6) = 2.89, p = .140, partial η2 = .33, nor was the moderately sized interaction, F(1,6) = 2.70, p = .152, partial η2 = .31. However, the large main effect of Time was statistically significant, F(1,6) = 7.50, p = .034, partial η2 = .56.

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