SOURCEBOOK

EASI Articles

Annotated Output | Mixed ANOVA

Computer Output

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

$Level1

Summary Statistics for the Data

               N       M      SD    Skew    Kurt
Outcome1   4.000   2.000   2.449   0.544  -2.944
Outcome2   4.000   6.000   2.449   0.544  -2.944


$Level2

Summary Statistics for the Data

               N       M      SD    Skew    Kurt
Outcome1   4.000   6.000   2.449   0.544  -2.944
Outcome2   4.000   7.000   2.449  -0.544  -2.944


$Level1

Correlations for the Data

         Outcome1 Outcome2
Outcome1   1.000    0.500 
Outcome2   0.500    1.000 


$Level2

Correlations for the Data

         Outcome1 Outcome2
Outcome1   1.000    0.389 
Outcome2   0.389    1.000

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

$`Between Subjects`

Source Table for the Model

              SS      df      MS
Blocks    25.000   1.000  25.000
Subjects  52.000   6.000   8.667


$`Within Subjects`

Source Table for the Model

                     SS      df      MS
Measures         25.000   1.000  25.000
Measures:Blocks   9.000   1.000   9.000
Residual         20.000   6.000   3.333

$`Between Subjects`

Hypothesis Tests for the Model

             F     df1     df2       p
Blocks   2.885   1.000   6.000   0.140


$`Within Subjects`

Hypothesis Tests for the Model

                      F     df1     df2       p
Measures          7.500   1.000   6.000   0.034
Measures:Blocks   2.700   1.000   6.000   0.151

$`Between Subjects`

Proportion of Variance Accounted For by the Model

           Est      LL      UL
Blocks   0.325   0.000   0.600


$`Within Subjects`

Proportion of Variance Accounted For by the Model

                    Est      LL      UL
Measures          0.556   0.031   0.737
Measures:Blocks   0.310   0.000   0.591

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.

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.