The tables of descriptive statistics can be used to determine the inferential statistics.
Summary Statistics for the Data: B1
N M SD Skew Kurt
A1 4.000 2.000 2.449 0.544 -2.944
A2 4.000 7.000 2.449 -0.544 -2.944
Descriptive Statistics for the Data: B2
N M SD Skew Kurt
A1 4.000 6.000 2.449 0.544 -2.944
A2 4.000 5.000 2.449 0.544 -2.944
The descriptive statistics are calculated separately for each group or condition. They are not equivalent to getting the statistics for the variable as a whole.
The tables of inferential statistics show the key elements to be calculated.
Source Table for the Model
SS df MS
Factor 4.000 1.000 4.000
Blocks 16.000 1.000 16.000
Factor:Blocks 36.000 1.000 36.000
Residual 72.000 12.000 6.000
Hypothesis Tests for the Model
F df1 df2 p
Factor 0.667 1.000 12.000 0.430
Blocks 2.667 1.000 12.000 0.128
Factor:Blocks 6.000 1.000 12.000 0.031
Proportion of Variance Accounted For by the Model
Est LL UL
Factor 0.053 0.000 0.302
Blocks 0.182 0.000 0.442
Factor:Blocks 0.333 0.019 0.562
For the Factor A Main Effect, F = 0.667, p = .430. This would not be considered a statistically significant finding.
For the Factor B Main Effect, F = 2.667, p = .128. This would not be considered a statistically significant finding.
For the Interaction, F = 6.000, p = .031. This would be considered a statistically significant finding.
For the Factor A Main Effect, partial eta 2 = 0.053. Thus, 5.3% of the variability among the scores is accounted for by Factor A.
For the Factor B Main Effect, partial eta 2 = 0.182. Thus, 18.2% of the variability among the scores is accounted for by Factor B.
For the Interaction, partial eta 2 = 0.333. Thus, 33.3% of the variability among the scores is accounted for by interaction of Factor A and Factor B.
For Factorial ANOVA, the confidence intervals around (centered on) each mean are appropropriate but not provided in the output.
The Factorial ANOVA provides statistics for the main effects and interactions in a factorial design. Each effect would be summarized in a style analogous to a One Way ANOVA.
A 2 (Factor A) x 2 (Factor B) ANOVA indicated a small and non-statistically significant main effect for Factor A, F(1,12) = 0.67, p = .430, partial η2 = .05, and for Factor B, F(1,12) = 2.67, p = .128, partial η2 = .18. In contrast, the interaction was large in magnitude and statistically significant, F(1,12) = 6.00, p = .031, partial η2 = .33.
Typically, the means, standard deviations, and confidence intervals would be presented in a table or figure associated with this text.