The main output for this example is below. The confidence interval ranges from -4.073 to -0.614. It does not cross zero suggesting (if we assume that it is one of the 95% of confidence intervals that contain the true value) that the effect in the population is unlikely to be zero. Therefore, this confidence interval confirms our conclusion that there is a significant difference between the number of goats sacrificed when listening to the song containing the backward message compared to when listing to the song played normally. We can obtain the effect size as Cohen's d=−0.59 [−0.96,−0.21] (below). This represents a fairly large effect.
| 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 | |||||||||||||||
| message | - | nomessage | -2.764 | 31 | 0.010 | -2.344 | 0.848 | -4.073 | -0.614 | -0.585 | 0.229 | -0.957 | -0.205 | ||||||||||||||
| Note. Cohen's d corrected for correlation between observations. | |||||||||||||||||||||||||||
| Note. Student's t-test. | |||||||||||||||||||||||||||
| N | Mean | SD | SE | Coefficient of variation | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| message | 32 | 9.156 | 3.548 | 0.627 | 0.387 | ||||||
| nomessage | 32 | 11.500 | 4.385 | 0.775 | 0.381 | ||||||
Fewer goats were sacrificed after hearing the backward message (M = 9.16, SE = 0.627), than after hearing the normal version of the Britney song (M = 11.50, SE = 0.775). This difference, -2.34, 95% CI [-4.07, -0.61], was significant, t(31) = 2.764, p = 0.010, Cohen's d=−0.59 [−0.96,−0.21].