Hi On 19 Mar 2003, VOLTOLINI wrote:
> What is a P value? Does anyone can give a simple explanation? > I am not using an easy explanation with my students and maybe > some of you are developing something interesting during > classes ! > For example, comparing the mean weight of male (M) and female > (F) fishes we have: Mean of M = 2,46kg (n = 59) and Mean of F > = 2,51kg (n = 59). Using a t test, the result is: df = 116, t > = 0,26 and P = 0,79. > Searching in books I have found different definitions. The > explanation for P = 0,79 could be..... Most of the definitions that you have listed are synonymous. > 2 - the probability of rejecting a correct null hypothesis. > 3 - the probability of incorrectly rejecting the null hypothesis. > 4 - the probability of rejecting a null hypothesis when in > fact it is true. These 3 are virtually equivalent. A "correct null hypothesis" (2) is a "true" null hypothesis (4), which means that rejecting it (i.e., concluding it is false) is the incorrect thing to do (3). The wording in 4 may be the preferred wording as it maps a little more directly onto the conditional probability that is the significance level, i.e., p(reject/outcome | Ho true). Some interpretations of 2 and 3 may entail more than we want. > 1 - the probability of Type I error. This is also synonymous, since a Type I error is defined as in 2, 3, and 4 above. That is, it is the incorrect rejection of a correct/true null hypothesis; p(Type I error) = p(reject Ho | Ho true). > 5 - the chance of getting statistic as extreme or more > extreme than this one [when null true] > 7 - the probability of the observed difference between groups > (or a larger difference) occurs [when null true] > 8 - the probability of obtaining a result equal to or more > extreme than what was actually observed [when null true]. These are also equivalent to one another, and equivalent to the earlier definitions once we add the implied "when null true" and recognize that the extremeness of the scores determines whether we reject Ho or conclude that the observed outcome is unlikely given the Ho. Using t as a sample statistic, the connection is something like: p(t > talpha | Ho true) = p(Reject Ho | Ho True) = p(Type I error) > 6 - the strength of evidence against an hypothesis This is more problematic as someone else noted, although it could perhaps be cast in acceptable terms if Ho were explicitly introduced and "strength of evidence against" were clearly defined. > What is the best way to explain this P = 0,79 ??? p(t > .26 | Ho true) = .79, where Ho represents Mu(female) = Mu(male) If you wanted a randomization test interpretation, you could say that if you randomly divided your set of 118 scores into two arbitrary groups, then the probability of getting an absolute difference between means as large as or larger than you did (i.e., 2.46 vs. 21.51) would be .79 (i.e., it would occur 79 times out of every 100 randomizations). This assumes the p-value is from a two-tailed test. Best wishes Jim ============================================================================ James M. Clark (204) 786-9757 Department of Psychology (204) 774-4134 Fax University of Winnipeg 4L05D Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED] CANADA http://www.uwinnipeg.ca/~clark ============================================================================ . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
