<- file stat .html -> ************************* Power analyses ******************

... compute POWER?

This starts with a formula, before some questions are cited.

=====================Rich Ulrich, ???===========ssc Subject: Sample Size, logistic etc. More recently, Bob Wheeler suggested (for the general ANOVA-sort of cases, not Logistic in particular) a formula given in his own article in Technometrics (1974) Vol 16,#2:193-201, `Portable Power' (good article, worth looking up) : : Try N=(4rs/d)^2, : where N is the total sample size for all treatments, r is the : number of levels of a factor, s is the population standard : deviation, and d is the difference you desire to detect. : (1) 90% for a 5% test. It applies to all contrasts among r levels of a : factor -- not restricted to small numerator df. - Note, that difference is what he calls the `minimum detectable value', which is the difference for one group, to be detected when there is no difference for the others. : (2) Cohen's tables are bulky and a bit restrictive. One can find the : power for any sort of contrast with a simple formula and the Fox : or Pearson and Hartly graphs. You might like to look at a paper : I wrote in '74 (Technometrics). : (3) It is an interesting sidelight, that if one chooses power according : to the above, the power for interactions, regression coefficients, : etc. is also approximately what you want. : Bob Wheeler, ECHIP, Inc. * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

... compute power for Logistic regression? (several responses)

=======================Rich Ulrich, 01 Sep 1995==========ssc Subject: Re: odds ratio as effect size in meta-analysis Message-ID: <427s0c$44n@usenet.srv.cis.pitt.edu> : Is there a way to discuss the common odds ratio in terms of Cohen's 'small, : medium, large' effect nomenclature? Any help appreciated. Please reply Basically, no. [Yes, epidemiologists do use Odds ratios (ORs) and refer to different sizes of effects, but these are not helpful for power analyses, in the style of Cohen, until they are translated into the number of cases of diseased vs healthy. And regarding the Subject line: ORs *are* used for meta-analyses.] Cohen's nomenclature is suitable for `social science' studies with sample Ns between 10 and 200, say. Odds ratios come to us from health research where Effects, calculated in Cohen's terms, are minuscule. Rich Ulrich, wpilib@vms.cis.pitt.edu Several collected references: =============Jim Young, 17 Jan 1996==========ssc Message-ID: <3294208441E@whio.lincoln.ac.nz> From: "Young, Jim" <YOUNG2@WHIO.LINCOLN.AC.NZ> Subject: Re: power analysis for logistic regresssion > Is anyone familiar with a reference which deals with conducting a power > analysis for a logistic regression. I got interested in this last time the question came up, and so I collected the replies. I also found stuff in Cochran and Cox (1950, p23-29 of the second edition) that looks useful [none of these modern new fangled references for me]. Cheers Jim Young ============Stephen P. Baker//e-mail: stephen.baker@ummed.edu Hsieh, F. Y. (1989) "Sample Size Tables for Logistic Regression," Statistics in Medicine, 8, 795-802. He has it impemented in a nice little software package called SSize ============Frank Ivis//fivis@arf.org: Try 'Solo Power Analysis', distributed by BMDP. This software performs power analysis for a number of statisical techniques, including logistic regression. The manual will probably have some specific references on logistic regression. ============Bob Wheeler, ECHIP, Inc. : The logistic is simply a transformation of the response proportion scale, so you can use any procedure appropriate for regression on the transformed scale. The problem, as always, is in choosing detectable values. Your sample size will be in the ball-park if it is adequate for detecting differences of interest on the original proportion scale -- remember that sample size is different for different points on this scale. ===========Hans-Peter Piepho Whitehead J 1993 Sample size calculations for ordered categorial data. Statistics in Medicine 12, 2257-2271. ===========Jesse There's not much out there. What I've found quite useful is the Egret SIZ (Sample Size and Power for Nonlinear Regression) reference manual from the Statistics and Epidemiology Research Corporation (SERC). Bob Mauritsen, who develped Egret SIZ, is an expert (and excellent reference) in the field. You might want to give him a call (206) 632-3014 in Seattle or e-mail him at: rhm@ms.washington.edu. Another posting on power, logistic ===================Richard Mccleary, 16 Jan 1996==========ssc Message-ID: <Pine.SUN.3.91.960116164309.18831C-100000@orion.oac.uci.edu> From: Richard Mccleary <mccleary@ORION.OAC.UCI.EDU> The relevant citation is "Sample size for logistic regression with small response probability" by A.S. Whittemore, JASA, 1981, 76:27-32. This method is suitable for any outcome with p<.1. PASS 1.0 has a very good, easy-to-use implementation of this algorithm. The distributor is NCSS; phone number is 801-546-0445. > In particular, I'm interested in what measure of effect size is used and > how this measure is affected by various distributions of the DV. The appropriate measure of effect is the "odds ratio." Most logistic regression software packages (SPSS, SAS, Stata, etc.) print out the odds ratio (along with standard errors, etc.) for each independent variable. > I am planning to collect data for which I expect a very low rate of > positive cases on a dicothomous variable (approximately 5%) and want to > get an estimate of how this is going to effect the power of the analysis, > and if it is feasible to collect the number of subjects needed to obtain > sufficient power Loosely speaking, power increases with "balance." When p is small, say less than .1, nominal power requires very large Ns. ===================Richard Goldstein, 16 Jan 1996==========ssc Whittemore, A (1981), "Sample Size for logistic regression with small response probability," _JASA_, 76: 27-32 Hsieh, FY (1989), "Sample Size Tables for logistic Regression," _statistics in Medicine_, 8: 795-802 (includes an offer of software) Bull, SB (1993), "Sample size and power determination for a binary outcome and an ordinal exposure when logistic regression is planned," _Am. Journal of Epidemiology_, 137: 676-684 Also, the commercial packages PASS (from NCSS) includes a routine for logistic regression. Rich Goldstein * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

... find power for 2-way ANOVA?

====================Rich Ulrich, 09 May 1996======ssc From: wpilib+@pitt.edu (Richard F Ulrich) Subject: Re: Power of 2-way ANOVA Message-ID: <4mt0a2$6ts@usenet.srv.cis.pitt.edu> Andrew McLachlan (mclachla@tui.lincoln.ac.nz) wrote: : I have collected data and performed a two-way ANOVA. I want to : perform an _a posteriori_ measure of Power for the ANOVA and : investigate the effect of the low (n=3) sample size on detection : of differences between treatments. I have found information on : Power tests for one-way ANOVA and some software to do the tests, : but haven't been able to find any info about Power tests for : two-way ANOVA. I would appreciate any guidance that people can : give me. You are unlikely to find much that is specifically about two-way ANOVA because : an F-test in ANOVA has (basically) the same meaning whether there was one factor, or two, or ten. You *do* need to take into account the proper error term is looking at the effect size; a second, powerful, predicting factor acts like a covariate in reducing the error, that is, the residual, against which you judge your Effect. Beyond that, two-way analyses create the question of what to do about interactions; but you do not seem focused on that. * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

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