Results

ANOVA

First, check that the predictor variable (pet) and the covariate (animal) are independent. To do this we can run a one-way ANOVA. The output shows that the main effect of wife is not significant, F(1, 18) = 0.06, p = 0.81, which shows that the average level of love of animals was roughly the same in the two type of animal wife groups. This result is good news for using this model to adjust for the effects of the love of animals.

ANOVA - animal
Cases Sum of Squares df Mean Square F p
pet 14.700 1 14.700 0.059 0.812
Residuals 4520.500 18 251.139  
Note.  Type III Sum of Squares

ANCOVA

The output below shows that love of animals significantly predicted life satisfaction, F(1, 17) = 10.32, p = 0.005. After adjusting for the effect of love of animals, the effect of pet is also significant. In other words, life satisfaction differed significantly in those with cats as pets compared to those with fish. The adjusted means tell us, specifically, that life satisfaction was significantly higher in those who owned a cat, F(1, 17) = 16.45, p = < .001.

ANCOVA - life_satisfaction
95% CI for ω²ₚ
Cases Sum of Squares df Mean Square F p ω²ₚ Lower Upper
pet 2112.099 1 2112.099 16.447 < .001 0.436 0.088 0.671
animal 1325.402 1 1325.402 10.321 0.005 0.318 0.020 0.591
Residuals 2183.140 17 128.420  
Note.  Type III Sum of Squares

Descriptives

To interpret the covariate create a plot of the outcome (life_satisfaction, y-axis) against the covariate ( animal, x-axis). The resulting plot (below) shows that there is a positive relationship between the two variables: the greater ones love of animals, the greater ones life satisfaction.

Descriptives - life_satisfaction
pet N Mean SD SE Coefficient of variation
Fish 12 38.167 15.509 4.477 0.406
Cat 8 60.125 11.103 3.925 0.185

Descriptives plots

animal - life_satisfaction


Linear Regression

Model Summary - life_satisfaction
Model R R² Adjusted R² RMSE
M₀ 0.000 0.000 0.000 17.506
M₁ 0.791 0.625 0.581 11.332
Note.  M₁ includes pet, animal
ANOVA
Model   Sum of Squares df Mean Square F p
M₁ Regression 3639.810 2 1819.905 14.172 < .001
  Residual 2183.140 17 128.420  
  Total 5822.950 19  
Note.  M₁ includes pet, animal
Note.  The intercept model is omitted, as no meaningful information can be shown.
Coefficients
Model   Unstandardized Standard Error Standardizedᵃ t p
M₀ (Intercept) 46.950 3.915 11.994 < .001
M₁ (Intercept) 18.944 6.819 2.778 0.013
  pet (Cat) 21.011 5.181 4.055 < .001
  animal 0.541 0.169 0.478 3.213 0.005
ᵃ Standardized coefficients can only be computed for continuous predictors.

From the output above we can see that both love of animals, t(17) = 3.21, p = 0.005, and type of pet, t(17) = 4.06, p < 0.001, significantly predicted life satisfaction. In other words, after adjusting for the effect of love of animals, type of pet significantly predicted life satisfaction.

Now, let’s look again at the output from the previous task, in which we conducted an ANCOVA predicting life satisfaction from the type of animal to which a person was married and their animal liking score (covariate).

The covariate, love of animals, was significantly related to life satisfaction, F(1, 17) = 10.32, p = 0.005. There was also a significant effect of the type of pet after adjusting for love of animals, F(1, 17) = 16.45, p < 0.001, indicating that life satisfaction was significantly higher for people who had cats as pets (M = 60.125, SE = 3.925) than for those with fish (M = 38.167, SE = 4.477).


The conclusions are the same as from the linear model, but more than that:

  1. The p-values for both effects are identical.
  2. This is because there is a direct relationship between t and F. In fact 𝐹=𝑡2
  3. Let’s compare the ts and Fs of our two effects:
  4. For love of animals, when we ran the analysis as ‘regression’ we got t = 3.213. If we square this value we get 𝑡2= 3.2132 =10.32
  5. . This is the value of F that we got when we ran the model as ‘ANCOVA’ .
  6. for the type of pet, when we ran the analysis as ‘regression’ we got t = 4.055. If we square this value we get 𝑡2=4.0552=16.45
  7. . This is the value of F that we got when we ran the model as ‘ANCOVA’.

Basically, this task is all about showing you that despite the menu structure in JASP creating false distinctions between models, when you do ‘ANCOVA’ and ‘regression’ you are, in both cases, using the general linear model and accessing it via different menus.