Bugs: Mixed Design 2 (Between Subjects) x 2 (Within Subject) x 2 (Within Subject) ANOVA

Description:

This data set, "Bugs", provides the extent to which men and women want to kill arthropods that vary in freighteningness (low, high) and disgustingness (low, high). Each participant rates their attitudes towards all anthropods. Subset of the data reported by Ryan et al. (2013).

Variables:

  1. Gender - Participant's gender (Woman, Man).
  2. Lo D, Lo F - Desire to kill an artrhopod with low freighteningness and low disgustingness.
  3. Lo D, Hi F - Desire to kill an artrhopod with low freighteningness and high disgustingness.
  4. Hi D, Lo F - Desire to kill an artrhopod with high freighteningness and low disgustingness.
  5. Hi D, Hi F - Desire to kill an artrhopod with high freighteningness and high disgustingness.
  6. For a description of the remaining variables see Ryan et al. (2013).

The desire to kill an arthropod was indicated on a scale from 0 to 10.

This example JASP file demonstrates the use of mixed design ANOVA. We will test the relation between hostility towards insects and their disgustingness and frighteningness for males and females separately.

References:

Ryan, R. S., Wilde, M., & Crist, S. (2013). Compared to a small, supervised lab experiment, a large, unsupervised web-based experiment on a previously unknown effect has benefits that outweigh its potential costs. Computers in Human Behavior, 29, 1295-1301.

Repeated Measures ANOVA

To conduct the mixed design ANOVA, select the ANOVA menu and click on Repeated Measures ANOVA. Add Disgustingness (Low/High) and Frighteningness (Low/High) as Repeated Measures Factors (just start typing to change names of factors and levels) and drag the disgustingness ratings into the right Repeated Measures Cells. Drag Gender into the Between Subject Factors box. Select the Estimates of effect size option from the Additional Options menu to display effect sizes.

Within Subjects Effects
Cases Sum of Squares df Mean Square F p ω²ₚ
Disgustingness 49.174 1 49.174 12.061 < .001 0.023
Disgustingness ✻ Gender 1.760 1 1.760 0.432 0.513 0.000
Residuals 346.552 85 4.077  
Frighteningness 138.075 1 138.075 32.122 < .001 0.064
Frighteningness ✻ Gender 5.523 1 5.523 1.285 0.260 6.263×10-4
Residuals 365.366 85 4.298  
Disgustingness ✻ Frighteningness 13.799 1 13.799 4.688 0.033 0.006
Disgustingness ✻ Frighteningness ✻ Gender 13.799 1 13.799 4.688 0.033 0.006
Residuals 250.177 85 2.943  
Note.  Type III Sum of Squares

The Within Subjects Effects table shows the results for the repeated measures factors. Disgustingness and Frighteningness both have a significant effect on Hostility (p < 0.001). There is also a significant two-way interaction between Disgustingness and Frighteningness, F(1,85) = 4.688, p = 0.033, and a significant three-way interaction between Disgustingness, Frighteningness, and Gender, F(1,85) = 4.688, p = 0.033. Effect sizes for the interaction effects are relatively modest (i.e., eta^2 = 0.05).

Between Subjects Effects
Cases Sum of Squares df Mean Square F p ω²ₚ
Gender 18.346 1 18.346 0.996 0.321 0.000
Residuals 1565.879 85 18.422  
Note.  Type III Sum of Squares

The Between Subjects Effects table shows the results for the between-subjects factor Gender. There is no statistically significant main effect of Gender, F(1,85) = 0.996, p = 0.321. 

Descriptives

The plots below can be created in the Descriptive Plots menu by dragging Disgustingness to the horizontal axis, Frighteningness to Separate lines, and Gender to Separate plots. The plot shows the nature of the three-way interaction that was indicated by the hypothesis test. 

Descriptives plots

Gender: Woman
Gender: Man

Assumption Checks

Select Homogeneity tests from the Assumption Checks menu to test the assumption of equal variances between women and men on all 4 repeated measures. To assess normality, we can look at the Q-Q plot of residuals.

Test for Equality of Variances (Levene's)
  F df1 df2 p
Lo D, Lo F 0.453 1 85 0.503
Lo D, Hi F 0.598 1 85 0.441
Hi D, Lo F 0.527 1 85 0.470
Hi D, Hi F 0.042 1 85 0.839

Q-Q Plot