The main output for this example is below, and we can obtain the effect size as Cohen's d =−1.628 [−2.651,−0.571]. As well as being statistically significant, this effect is very large and so represents a substantive finding. Note that I report the results of the Welch version of the t-test, as I recommended in the book, to have more robustness against possible unequal variances.
| 95% CI for Mean Difference | 95% CI for Cohen's d | ||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| t | df | p | Mean Difference | SE Difference | Lower | Upper | Cohen's d | SE Cohen's d | Lower | Upper | |||||||||||||
| life_satisfaction | -3.688 | 17.843 | 0.002 | -21.958 | 5.954 | -34.475 | -9.441 | -1.628 | 0.565 | -2.651 | -0.571 | ||||||||||||
| Note. Welch's t-test. | |||||||||||||||||||||||
| Group | N | Mean | SD | SE | Coefficient of variation | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| life_satisfaction | Fish | 12 | 38.167 | 15.509 | 4.477 | 0.406 | |||||||
| Cat | 8 | 60.125 | 11.103 | 3.925 | 0.185 | ||||||||
On average, the life satisfaction of cat owners (M = 60.13, SE = 3.93) was significantly higher than that people who had fish as pets (M = 38.17, SE = 4.48), t(17.84) = −3.688, p = 0.002, Cohen's d =−1.628 [−2.651,−0.571].
The output from the linear model is below. Compare this output with the one from the previous task (above) the values of t and p are almost the same. If we would have used the Student t-test, the results would be identical (Technically, t is different because for the linear model it is a positive value and for the t -test it is negative However, the sign of t merely reflects which way around you coded the fish and cat groups. The linear model, by default, has coded the groups the opposite way around to the t-test.) The main point I wanted to make here is that whether you run these data through the regression or t-test menus, the results are identical (if you give up the robustness to unequal variances, which does not exist in normal regression).