Results

ANOVA

First, check that the predictor variable (cloak) and the covariate (mischief1) are independent. To do this we can run a one-way ANOVA. The output below shows that the main effect of cloak is not significant, F(1, 78) = 0.14, p = 0.71, which shows that the average level of baseline mischief was roughly the same in the two cloak groups. This result is good news for using this model to adjust for the effects of baseline mischief.

ANOVA - mischief_pre
Cases Sum of Squares df Mean Square F p
cloak 0.654 1 0.654 0.135 0.714
Residuals 377.334 78 4.838  
Note.  Type III Sum of Squares

ANCOVA

The output below shows that baseline mischief significantly predicted post-intervention mischief, F(1, 77) = 7.40, p = 0.008. After adjusting for baseline mischief, the effect of cloak is also significant. In other words, mischief levels after the intervention differed significantly in those who had an invisibility cloak and those who did not. The adjusted means tell us, specifically, that mischief was significantly higher in those with invisibility cloaks, F(1, 77) = 11.33, p = 0.001. Additionally, we can look at the partial effect sizes and their 95% confidence intervals, which for both predictor variables do not include 0.

ANCOVA - mischief_post
95% CI for ω²ₚ
Cases Sum of Squares df Mean Square F p ω²ₚ Lower Upper
cloak 35.166 1 35.166 11.326 0.001 0.114 0.016 0.257
mischief_pre 22.972 1 22.972 7.398 0.008 0.074 0.002 0.206
Residuals 239.081 77 3.105  
Note.  Type III Sum of Squares

Descriptives

Descriptives - mischief_post
cloak N Mean SD SE Coefficient of variation
No cloak 34 8.765 1.724 0.296 0.197
Cloak 46 10.152 1.909 0.281 0.188

Descriptives plots

To interpret the covariate create a Descriptives plot of the outcome (mischief_post, y-axis) against the covariate ( mischief_pre, x-axis). The resulting plot shows that there is a positive relationship between the two variables: the greater ones mischief levels before the cloaks were assigned to participants, the greater ones mischief after the cloaks were assigned to participants

mischief_pre - mischief_post

The covariate, baseline number of mischievous acts, was significantly related to the number of mischievous acts after the cloak of invisibility manipulation, F(1, 77) = 7.40, p = 0.01,   = 0.074 (95% CI [0.002, 0.206]). There was also a significant effect of wearing a cloak of invisibility after adjusting for baseline number of mischievous acts, F(1, 77) = 11.33, p = 0.001, = 0.114 (95% CI [0.016, 0.257]), indicating that the number of mischievous acts was higher in those who were given a cloak of invisibility (M = 10.15, SE = 0.28) than in those who were not (M = 8.77, SE = 0.30).