Stephen said "I appreciate Karl's expertise in helping me make sense of this apparently anomalous result. But I wonder whether his interpretation of the Fisher is unduly conservative. My copy of an old edition (the first, actually!) of Siegel's classic _Non-Parametric Statistics for the Behavioral Sciences_ says this about the requirements for use of the Fisher"
Well, Siegel is out-of-date. Believe it or not, we know more about statistics now that we did when Siegel wrote that classic. And it is the Fisher's test that is too conservative, not the Chi-square without correction for continuity -- as a case in point, the p for the proper Chi-square analysis on Stephen's data was LESS THAN that for the Fisher's test. The p = 1 result from the Fisher's test results from there being no way to construct a 2 x 2 table to give results more in accord with null hypothesis than those Stephen obtained, given the restriction that the marginal frequencies remain unchanged. Believing that the Pearson Chi-square is invalid with small sample sizes (small expected frequencies) is a very common delusion. Monte Carlo studies published in Psychological Bulletin over 20 years ago demonstrated quite clearly that the nominal alpha is preserved even when there are small expected frequencies, as long as you do not use the correction for continuity. The only problem with small expected frequencies is that power will be miserably low. If your results are significant, low power is, of course, not a threat to your statistical conclusion, although some ignorant reviewers misunderstand this too. Twice I have had manuscripts rejected because a reviewer found my analysis to have too little power, but in both cases the results were statistically significant. In other words, my effects were so large that I could detect them even with little power. Useful references for the Monte Carlo work on Pearson Chi-square include the Camilli and Hopkins article I cited earlier and also Overall, Psych. Bull 87: 132-135 and Bradley et al., Psych. Bull. 86: 1290-1297. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Karl L. Wuensch, Department of Psychology, East Carolina University, Greenville NC 27858-4353 Voice: 252-328-4102 Fax: 252-328-6283 mailto:[EMAIL PROTECTED] http://core.ecu.edu/psyc/wuenschk/klw.htm --- You are currently subscribed to tips as: [EMAIL PROTECTED] To unsubscribe send a blank email to [EMAIL PROTECTED]
