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Statistical significance—meaningful or not?

Statistical tests with large sample sizes can have large power. Power is the ability to detect an effect. Detection is indicated by a result which is statistically significant. A test with large power will detect a very small effect. This very small effect may not be meaningful in the context of the analysis being conducted. The courts have the perception that for an effect to be meaningful it is necessary for the effect to be statistically significant. However, statistical significance is not a sufficient condition for an effect to be meaningful. This can lead to a difficulty where testimony of no meaningful effect is interpreted by counsel as one with no statistically significant effect. Should the difference between a meaningful effect and a statistically significant effect be explained in reports and if so how? Some
possible answers are proposed.

 

C. G. G. AITKEN
 A. WILSON
School of Mathematics, the Maxwell Institute and the Joseph Bell Centre for Forensic Statistics
and Legal Reasoning, The University of Edinburgh,
Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
AND
R. SLEEMAN
Mass Spec Analytical Ltd., Building 20F, Golf Course Lane, Bristol BS34 7RP, UK



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