Interpreting the Confidence Interval

Given that both confidence intervals are quite similar, let’s focus our interpretation to only the percentile-method confidence interval of (-0.238, 0.302). Recall from the Precise and Shorthand Interpretation lesson that the precise statistical interpretation of a 95% confidence interval is: If this construction procedure is repeated 100 times, then we expect about 95 of the confidence intervals to capture the true value of $\hat{p}$_seed − $\hat{p}$_control. In other words, if we gathered 100 samples of $n$= 50 participants from a similar pool of people and constructed 100 confidence intervals each based on each of the 100 samples, about 95 of them will contain the true value of $\hat{p}$_seed − $\hat{p}$_control, while about five won’t. Given that this is a little long-winded, we use the shorthand interpretation: We’re 95% confident that the true difference in proportions $\hat{p}$_seed − $\hat{p}$_control is between (-0.238, 0.302).

There’s one value of particular interest that this 95% confidence interval contains and that’s zero. If $\hat{p}_{seed}- \hat{p}_{control}$ were equal to 0, then there would be no difference in the proportion of yawning between the two groups. This would suggest that there’s no associated effect of being exposed to a yawning recruiter on whether we yawn ourselves.

In our case, because the 95% confidence interval includes 0, we can’t conclusively say if either proportion is larger. Of our 1,000 bootstrap resamples with replacement, sometimes $\hat{p}$_seed was higher and so those exposed to yawning yawned themselves more often, and other times, the reverse happened.