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 to
decide 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 nonparametric
test? What replaces the SD?

Regards,

Dr. Ibrahim Wasfi
Camelracing Laboratory,
P O Box 253, Abu Dhabi,
UAE

Fax  00971  2 463409
Tel   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 statistical
power:

     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 the
chosen level of significance (eg alpha=.05) and sample size (or degrees of
freedom) to determine statistical power.

     There are noncentrality parameter calculations for Chi-square which use
similar power charts. The power charts are based on degrees of freedom (sample
size) and alpha. Chi-sqare contingency tables are considered nonparametric.
**The noncentrality parameter calculation for chi-square contains elements
of 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 of
statistical power seems to reside in the nature of the noncentrality
parameter calculation. Standard deviation occurs in the parametric non-
centrality parameter calculation, but not in the nonparametric version.

           Mike Leibold, PharmD, RPh
           ML11439.at.goodnet.com

Reference
1) Glantz, S.A., Primer of Biostatistics 4th edition, McGraw-Hill,
New York 1997

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