# PharmPK Discussion - Power analysis for a parametric test

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• On 11 Jan 2000 at 21:27:29, "Dr.Ibrahim Wasfi" (iawasfi.aaa.emirates.net.ae) sent the message
`Dear all:To calculate a power of a parametric statistical test we need todecide on a level of difference (delta), the desired probability(P'),the significance level ( alpha ) and we need to provide the SD (Snedecor and Cochran). How can we calculate it for a nonparametrictest? What replaces the SD?Regards,Dr. Ibrahim WasfiCamelracing Laboratory,P O Box 253, Abu Dhabi,UAEFax  00971  2 463409Tel   00971  2 4092522`
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• On 16 Jan 2000 at 18:08:54, ml11439.aaa.goodnet.com (Michael J. Leibold) sent the message
`Ibrahim,     Noncentrality parameters used for calculation of statisticalpower:     1) Noncentrality parameter of t test        phi= Minimum treatment effect/standard deviation     2) Noncentrality parameter for analysis of variance   phi= [minimum treatment effect to be detected/standard deviation]      x [sample size of each treatment group/2x(number of treatment groups]1/2     These noncentrality parameters are used with tables constructed for thechosen level of significance (eg alpha=.05) and sample size (or degrees offreedom) to determine statistical power.     There are noncentrality parameter calculations for Chi-square which usesimilar power charts. The power charts are based on degrees of freedom (samplesize) and alpha. Chi-sqare contingency tables are considered nonparametric.**The noncentrality parameter calculation for chi-square contains elementsof the chi-square contingency table, and does not involve standard deviation.     3) Noncentrality parameter calculation for chi-square contingency table   phi= [[N/((r-1)(c-1)+1)][sum(pij-RiCj)2/RiCj]]1/2       Where:         r= number of rows         c= number of columns         pij= proportion in row i, column j         Ri= Sum of row i         Cj= sum of column j     So, the difference between nonparametric and parametric estimations ofstatistical power seems to reside in the nature of the noncentralityparameter calculation. Standard deviation occurs in the parametric non-centrality parameter calculation, but not in the nonparametric version.           Mike Leibold, PharmD, RPh           ML11439.at.goodnet.comReference1) Glantz, S.A., Primer of Biostatistics 4th edition, McGraw-Hill,New York 1997`
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