Results

ANOVA

First, let’s check that the predictor variable (elephant) and the covariate (experience) are independent. To do this we can run a one-way ANOVA. The output below shows that the main effect of elephant is not significant, F(1, 118) = 1.384, p = 0.244, which shows that the average level of prior football experience was roughly the same in the two elephant groups. This result is good news for using this model to adjust for the effects of experience.

ANOVA - experience
Cases Sum of Squares df Mean Square F p
elephant 4.033 1 4.033 1.384 0.242
Residuals 343.933 118 2.915  
Note.  Type III Sum of Squares

ANCOVA

The output below shows that the experience of the elephant significantly predicted how many goals they scored, F(1, 117) = 9.931, p = 0.002. After adjusting for the effect of experience, the effect of elephant is also significant. In other words, African and Asian elephants differed significantly in the number of goals they scored. The adjusted means tell us, specifically, that African elephants scored significantly more goals than Asian elephants after adjusting for prior experience, F(1, 117) = 8.589, p = 0.004.

ANCOVA - goals
95% CI for ω²ₚ
Cases Sum of Squares df Mean Square F p ω²ₚ Lower Upper
elephant 27.953 1 27.953 8.589 0.004 0.059 0.004 0.159
experience 32.321 1 32.321 9.931 0.002 0.069 0.008 0.173
Residuals 380.796 117 3.255  
Note.  Type III Sum of Squares

Descriptives

Descriptives - goals
elephant N Mean SD SE Coefficient of variation
Asian 60 3.533 1.900 0.245 0.538
African 60 4.617 1.842 0.238 0.399

Descriptives plots

To interpret the covariate we can create a Descriptives plot of the outcome (goals, y-axis) against the covariate ( experience, x-axis), including an error region to reflect our uncertainty. The resulting plot (below) shows that there is a (loose) positive relationship between the two variables that if you use your imagination looks like an elephant: the more prior football experience the elephant had, the more goals they scored in the season.

experience - goals

The covariate, football experience, was significantly related to the how many goals were scored, F(1, 117) = 9.93, p = 0.002,  = 0.069 (95% CI [0.008, 0.173]). The more prior football experience the elephant had, the more goals they scored in the season. African elephants scored significantly more goals than Indian elephants after adjusting for their experience, F(1, 117) = 8.59, p = 0.004,  = 0.059 (95% CI [0.004, 0.159]).