If we use \( \hat{p_{T}} \) to denote the proportion from part (c) and use \( \hat{p_{N}} \) to denote the proportion from part (d), calculate the difference in roportion reporting sleep improvements, \( \hat{p_{T}}-\hat{p_{N}} \), between those getting therapy and those not getting therapy. ound your answer three decimal places. \( \hat{p}_{T}-\hat{p_{N}}= \) Ellis, JG, Cushing. T. Germain, A "Treating acute insomnia: a randomized controlled trial of a 'single-shot' of cognitive behavioral therapy for insomnia", SLEEP, 2015; \( 38(6): 971-978 \). eTextbook and Media

In the study you're referencing, \( \hat{p_{T}} \) and \( \hat{p_{N}} \) reflect the proportions of individuals reporting sleep improvements after undergoing therapy versus those who did not. The difference \( \hat{p_{T}} - \hat{p_{N}} \) is crucial as it helps quantify the effectiveness of therapy on sleep improvement. By analyzing the results from the randomized controlled trial, you can gain insight into how therapy influences sleep quality, providing a statistically-backed justification for treatment approaches. A common mistake researchers make when calculating this difference is not accounting for sample size disparities between the two groups. This can skew results and lead to misleading conclusions about therapy's efficacy. Always ensure that both proportions are derived from properly defined groups and consider employing confidence intervals to gauge the certainty of your findings—a little statistical rigor goes a long way in making claims!