At 05:56 PM 11/12/2002 -0500, you wrote: >Mike, could you expand on how it is that a p-value is >only meaningful if the Null is true? I understand the >second part of your statement (Replication only useful >is Null is rejected)... but would like more info on >the first... > >cheers! > >Jean-Marc >
The probability of events must be computed under the assumptions for some probability distribution. We can only make a Type I Error if the null hypothesis is in fact true. P-values (the probability of a Type I Error) are computed under the assumption that the null hypothesis is correct. Our decision point (or critical value for the test statistic) is determined by the point in the probability distribution that places 5% (for a p-value of .05) of the outcomes for the test statistic in the rejection region. Thus, we select a critical value so that we will reject the null hypothesis when it is true only 5% of the time. If the null hypothesis is, in fact, false, this distribution is irrelevant to the computation of probabilities for outcomes and some other distribution should be used (based on the distribution of values for the test statistic under the alternative hypothesis). This other distribution is the one we use when we try to compute the power of the statistic, which corresponds to the proportion of outcomes in the rejection region of the distribution defined by the alternative hypothesis. The big problem for the computation of power is that we don't know which of an infinite number of distributions, all consistent with the alternative hypothesis, is the correct one to use to calculate the value of power. We must assume (and this is a big assumption) the effect size, which defines one distribution for the computation of power. Hope this helps. Claudia Stanny ________________________________________________________ Claudia J. Stanny, Ph.D. e-mail: [EMAIL PROTECTED] Department of Psychology Phone: (850) 474 - 3163 University of West Florida FAX: (850) 857 - 6060 Pensacola, FL 32514 - 5751 Web: http://www.uwf.edu/psych/stanny.html --- You are currently subscribed to tips as: [EMAIL PROTECTED] To unsubscribe send a blank email to [EMAIL PROTECTED]
