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\begin{document}

\title{A new definition of statistical significance}



\author[1]{Thomas F Heston}%
\affil[1]{Elson S Floyd College of Medicine, Washington State University, Spokane, Washington USA}%


\vspace{-1em}



  
  \date{May 21, 2024}


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\begin{abstract}
The classical definition of statistical significance is p \textless{}=
0.05, meaning a 1/20 chance the test statistic found is due to normal
variation of the null hypothesis. This definition of statistical
significance does not represent the likelihood that the alternative
hypothesis is true. Hypothesis testing can be evaluated using a 2x2
table (shown below). Box ``a'' = true positives: p \textless{}= 0.05 and
the alternative hypothesis is true. This is the study's power. A rule of
thumb is that study power should be at least 80\% (80\% of the time the
statistical test is positive when the alternative hypothesis is true).
Therefore a = 0.80. Box ``b'' = false-positives: p \textless{}= 0.05 but
the alternative hypothesis is false. By definition, when p = 0.05 the
test statistic has a 5\% probability of occurring by chance when the
null hypothesis is true. Therefore, b = 0.05. Box ``c'' =
false-negatives: p \textgreater{}= 0.05 but the alternative hypothesis
is true. This occurs 20\% of the time when the study's power is 80\%.
Therefore, c = 0.20. Box ``d'' = true-negatives: p \textgreater{}= 0.05
and the null hypothesis is true. This occurs 95\% of the time when p
\textless{}= 0.05. Therefore, d = 0.95. From this table we derive:
Sensitivity = power = a/(a+c) = 80\%. Specificity = (1-p) = d/(b+d) =
95\%. Positive predictive value = power/(power + p-value) = a/(a+b) =
94\%. Negative predictive value = d/(c+d) = 83\%. The classical
definition of statistical significance is (1-specificity) and does not
take power into consideration. The proposed new definition of
statistical significance is when the positive predictive value of a test
statistic is 95\% or greater. To arrive at this, the cut-off p-value
representing statistical significance needs to be corrected for study
power so that 0.05 \textgreater{} (p-value)/(p-value + power). To
achieve a 95\% predictive confidence,it can be derived that statistical
significance is a p-value \textless{}= power / 19.%
\end{abstract}%



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\emph{This abstract was presented at the 2013 Annual Meeting of the
Society of Nuclear Medicine and Molecular Imaging in Vancouver, Canada.}

Citation: Heston T. A new definition of statistical significance.
\href{http://jnm.snmjournals.org/content/54/supplement_2/1262}{J Nucl
Med~May 2013 vol. 54 no. supplement 2~1370}~~ ~

\par\null

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