Results

Repeated Measures ANOVA

To fit the model:

  1. In the Repeated Measures Factors box type a name (I typed Alcohol) for the first repeated measures factor
  2. Enter the 4 levels of the repeated measures variable below
  3. Repeat this for the second factor, which I named Lighting, and which has 2 levels
  4. Then, in the box called Repeated Measures Cells, drag the relevant variables to their matching cells


Within Subjects Effects
Cases Sphericity Correction Sum of Squares df Mean Square F p ω²ₚ
Alcohol None 38591.654 3.000 12863.885 104.385 < .001 0.746
  Greenhouse-Geisser 38591.654 2.619 14736.844 104.385 < .001 0.746
Residuals None 9242.596 75.000 123.235  
  Greenhouse-Geisser 9242.596 65.468 141.177  
Lighting None 1993.923 1.000 1993.923 23.421 < .001 0.253
Residuals None 2128.327 25.000 85.133  
Alcohol Lighting None 5765.423 3.000 1921.808 22.218 < .001 0.351
  Greenhouse-Geisser 5765.423 2.809 2052.286 22.218 < .001 0.351
Residuals None 6487.327 75.000 86.498  
  Greenhouse-Geisser 6487.327 70.232 92.370  
Note.  Sphericity corrections not available for factors with 2 levels.
Note.  Type III Sum of Squares

In your output Mauchley’s test will indicate a non-significant violation of sphericity for both variables, but I have argued that you should ignore this test and routinely apply the Greenhouse-Geisser correction, so that’s what we’ll do. Note that the correction does not exist for factors with only 2 variables (i.e., `Lighting`), so be sure to also keep None ticked under Assumption Checks. All effects are significant at p < .001. We’ll look at each effect in turn.


The main effect of lighting shows that the attractiveness ratings of photos was significantly lower when the lighting was dim compared to when it was bright, F(1, 25) = 23.42, p < .001,   = 0.25. The main effect of alcohol shows that the attractiveness ratings of photos of faces was significantly affected by how much alcohol was consumed, F(2.62, 65.47) = 104.39, p < 0.001,  = 0.75. However, both of these effects are superseded by the interaction, which shows that the effect that alcohol had on ratings of attractiveness was significantly moderated by the brightness of the lighting, F(2.81, 70.23) = 22.22, p < 0.001,   = 0.35. To interpret this effect let’s move onto the next task.

Between Subjects Effects
Cases Sum of Squares df Mean Square F p
Residuals 3281.827 25 131.273  
Note.  Type III Sum of Squares

Descriptives

Descriptives plots

Assumption Checks

Test of Sphericity
  Mauchly's W Approx. Χ² df p-value Greenhouse-Geisser ε Huynh-Feldt ε Lower Bound ε
Alcohol 0.820 4.700 5 0.454 0.873 0.984 0.333
Alcohol Lighting 0.898 2.557 5 0.768 0.936 1.000 0.333

Post Hoc Tests

Post Hoc Comparisons - Alcohol ✻ Lighting - Conditional on Alcohol
95% CI for Mean Difference 95% CI for Cohen's d
Alcohol Mean Difference Lower Upper SE df t Cohen's d Lower Upper pholm
0 Pints Dim Bright 3.423 -2.360 9.206 2.808 25 1.219 0.333 -0.636 1.302 0.234
2 Pints   Bright 4.808 0.171 9.444 2.251 25 2.136 0.468 -0.332 1.267 0.043 *
4 Pints   Bright -13.538 -18.887 -8.189 2.597 25 -5.213 -1.317 -2.414 -0.220 < .001 ***
6 Pints   Bright -19.462 -24.837 -14.086 2.610 25 -7.456 -1.893 -3.183 -0.603 < .001 ***
 * p < .05, *** p < .001

This is an example where it might be worth looking at the effect of lighting within each dose of alcohol. These effects are shown in the table above. and they are somewhat more useful because they show that lighting did not have a significant effect on attractiveness ratings after no alcohol, t(25) = 1.22, pholm = .234, had a slightly significant effect after 2 pints of lager, t(25) = 2.14, pholm = .043 (note that here the effect goes in the other direction compared to higher levels of alcohol - always check your Descriptives plots and don't just focus on p-values!), and more substantial effects after 4, t(25) = -5.21, pholm < .001, and 6 pints, t(25) = -7.46, pholm < .001. Basically the effect of lighting is getting stronger as the alcohol dose increases - you can also see this in the descriptives plot above by the black and white circles getting further apart.

Post Hoc Comparisons - Alcohol ✻ Lighting - Conditional on Lighting
95% CI for Mean Difference 95% CI for Cohen's d
Lighting Mean Difference Lower Upper SE df t Cohen's d Lower Upper pholm
Dim 0 Pints 2 Pints -0.462 -8.698 7.775 2.875 25 -0.161 -0.045 -1.023 0.933 0.874
    4 Pints 27.769 17.614 37.924 3.545 25 7.834 2.701 0.902 4.500 < .001 ***
    6 Pints 43.692 36.236 51.149 2.603 25 16.787 4.250 1.970 6.529 < .001 ***
  2 Pints 4 Pints 28.231 22.545 33.917 1.985 25 14.224 2.746 1.230 4.262 < .001 ***
    6 Pints 44.154 35.889 52.418 2.885 25 15.306 4.295 1.956 6.633 < .001 ***
  4 Pints 6 Pints 15.923 6.189 25.657 3.398 25 4.686 1.549 0.163 2.935 < .001 ***
Bright 0 Pints 2 Pints 0.923 -6.359 8.205 2.542 25 0.363 0.090 -0.776 0.955 0.720
    4 Pints 10.808 2.479 19.137 2.907 25 3.717 1.051 -0.066 2.168 0.004 **
    6 Pints 20.808 13.796 27.820 2.448 25 8.501 2.024 0.723 3.325 < .001 ***
  2 Pints 4 Pints 9.885 0.180 19.589 3.387 25 2.918 0.961 -0.284 2.207 0.015 *
    6 Pints 19.885 13.864 25.905 2.102 25 9.462 1.934 0.741 3.128 < .001 ***
  4 Pints 6 Pints 10.000 1.602 18.398 2.932 25 3.411 0.973 -0.134 2.079 0.007 **
 * p < .05, ** p < .01, *** p < .001
Note.  P-value and confidence intervals adjusted for comparing a family of 6 estimates (confidence intervals corrected using the bonferroni method).

Simple Main Effects

Simple Main Effects - Alcohol
Level of Lighting Sum of Squares df Mean Square F p
Dim 36922.885 3 12307.628 110.493 < .001
Bright 7434.192 3 2478.064 25.198 < .001
Note.  Type III Sum of Squares

Write it up:

The lighting by alcohol interaction was significant, F(2.81, 70.23) = 22.22, p < .001,  = 0.35, indicating that the effect of alcohol on the ratings of the attractiveness of faces differed when lighting was dim compared to when it was bright. The post-hoc tests of lighting within alcohol dose revealed that the effect of lighting on attractiveness ratings got stronger with alcohol dose. Specifically, lighting did not have a significant effect on attractiveness ratings after no alcohol, t(25) = 1.22, pholm = .234, had a slightly significant effect after 2 pints of lager, t(25) = 2.14, pholm = .043, and more substantial effects after 4, t(25) = -5.21, pholm < .001, and 6 pints, t(25) = -7.46, pholm < .001