In article <[EMAIL PROTECTED]>, "VOLTOLINI" <[EMAIL PROTECTED]> wrote:
> Hi, I am impressed because in less than 24h 112 people sent me messages > interested in to discuss the problem of teaching what is a P value. > > After all these messages, I see that people are using two definitions: > > The most frequent definition is: "P is the probability of getting a value > of a test statistic equal to or greater than the one observed in your data, > if it is a random pick from the distribution of the test statistic that > would be created if a specified null hypothesis were true". > > But also some people are using....."P-value is the probability of wrongly > rejecting the null hypothesis". The second of these is clearly wrong. If I observe a p-value p=0.05, for example, on a test of a point null hypothesis (thought of as approximating a small interval null in some sense, see Berger and Delampady cited below) then the probability that I wrongly reject the null hypothesis, CONDITIONAL ON MY HAVING OBSERVED p=0.05, is in general significantly larger than 0.05. It is correct to say that the probability of observing p<=0.05 is 0.05 (tautologously). That is the probability of committing a Type I error when you set the rejection level at 0.05. But this is very different from the conditional frequentist consequences after you observe a particular p-value. The problem is that the information gained by learning that p<=0.05 is not the same (and indeed is much less) than the information gained by learning that p=0.05 precisely; obviously these two different kinds of information need to be treated differently. See Berger and Delampady, "Testing Precise Hypotheses," _Statistical Science_ 2:317-352 (1987) (with comments) and Berger and Sellke, "Testing a Point Null Hypothesis," _JASA_ 82:112-139 (1987) (with comments). Both of these papers can be downloaded at http://www.jstor.org Jim Berger has a web page on this subject, which includes a Java applet that illustrates the above points, and a recent paper suggesting a solution to the problem: http://isds.duke.edu/~berger/p-values.html Bill -- Bill Jefferys/Department of Astronomy/University of Texas/Austin, TX 78712 Email: replace 'warthog' with 'clyde' | Homepage: quasar.as.utexas.edu I report spammers to [EMAIL PROTECTED] Finger for PGP Key: F7 11 FB 82 C6 21 D8 95 2E BD F7 6E 99 89 E1 82 Unlawful to use this email address for unsolicited ads: USC Title 47 Sec 227 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
