The main output for this example is below, and we can obtain the effect size as Cohen's d=0.121 [0.033, 0.209]. Therefore, although this effect is highly statistically significant, the size of the effect is very small and represents a trivial finding. In this example, it would be tempting for Twaddle and Sons to conclude that their book produced significantly greater relationship happiness than our book. However, to reach such a conclusion is to confuse statistical significance with the importance of the effect. By calculating the effect size we’ve discovered that although the difference in happiness after reading the two books is statistically different, the size of effect that this represents is very small. Of course, this latter interpretation would be unpopular with Twaddle and Sons who would like to believe that their book had a huge effect on relationship happiness.
| 95% CI for Mean Difference | 95% CI for Cohen's d | ||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Measure 1 | Measure 2 | t | df | p | Mean Difference | SE Difference | Lower | Upper | Cohen's d | SE Cohen's d | Lower | Upper | |||||||||||||||
| women | - | statbook | 2.706 | 499 | 0.007 | 1.528 | 0.565 | 0.418 | 2.638 | 0.121 | 0.060 | 0.033 | 0.209 | ||||||||||||||
| Note. Student's t-test. | |||||||||||||||||||||||||||
On average, the reported relationship happiness after reading Field and Hole (2003) (M = 18.49, SE = 0.402), was significantly higher than after reading Women are from bras and men are from penis (M = 20.02, SE = 0.446), t(499) = 2.706, p = 0.007, Cohen's d=0.121 [0.033, 0.209]. However, the effect size was small, revealing that this finding was not substantial in real terms.
| N | Mean | SD | SE | Coefficient of variation | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| women | 500 | 20.018 | 9.981 | 0.446 | 0.499 | ||||||
| statbook | 500 | 18.490 | 8.992 | 0.402 | 0.486 | ||||||