Statistical Significance and the PHC Curve

<p>This book explains the importance of using the probability that the hypothesis is correct (PHC) an intuitive measure that anyone can understand as an alternative to the <em>p</em>-value. In order to overcome the ���reproducibility crisis��� caused by the misuse of significance tests this book provides a detailed explanation of the mechanism of <em>p</em>-hacking using significance tests and concretely shows the merits of PHC as an alternative to <em>p</em>-values.</p><p>In March 2019 two impactful papers on statistics were published. One paper Moving to a World Beyond ���<em>p</em> < 0.05������ was featured in the scholarly journal <em>The American Statistician</em> overseen by the American Statistical Association. The title of the first chapter is ���Don't Say ���Statistically Significant������ and it uses the imperative form to clearly forbid the use of significance testing. Another paper ���Retire statistical significance��� was published in the prestigious scientific journal <em>Nature</em>. This commentary was endorsed by more than 800 scientists advocating for the statement ���We agree and call for the entire concept of statistical significance to be abandoned.���</p><p>Consider a study comparing the duration of hospital stays between treatments A and B. Previously research conclusions were typically stated as: ���There was a statistically significant difference at the 5% level in the average duration of hospital stays.��� This phrasing is quite abstract. Instead we present the following conclusion as an example: (1) The average duration of hospital stays for Group A is at least half a day shorter than for Group B. (2) 71% of patients in Group A have shorter hospital stays than the average for Group B. (3) Group A has an average hospital stay that is on average no more than 94% of that of Group B. Then the probability that the expression is correct is shown. That is the PHC curve.</p>