Donald Burrill said on 11/19/02 5:13 PM: >It's not clear to me exactly what you mean by "a critical value >approach", nor what other approach(es) you might have in mind to >contrast it with. But the consequent of that sentence is correct. >(Although, if one is being pedantic, it is only true in the standardized >metric, not in the metric of the variable observed; in the latter >metric "a significant distance from the parameter" would be the c.v. >times the standard error of the observed statistic (the sample mean in >the cases we've been discussing).)
Another approach, as compared to a critical value approach, is a probability approach. The text I'm currently using (Triola) distinguishes between 'traditional' and 'P-value' approaches to hypothesis testing and teaches both. The author has subsections devoted to each approach for the hypothesis testing sections. The traditional approach is exactly what you expect it to be, use the sample data to calculate a value for a test statistic and compare it to a critical value, basing your rejection decision on that. The P-value approach takes advantage of what computer technology gives you, a probability associated with the calculated test statistic. The probability is compared directly to alpha and the rejection decision is based on that. Of course, these approaches yield identical answers on problems. I like it because it bridges the gap between the old style and the current prevelance in use of computers. The traditional approach has advantages because it is graphically easy to illustrate. The P-value approach has value because it is more like what students may encounter in using a computer to calculate a stat and is increasingly what is reported in journals (less and less are we seeing p<.05 in lieu of p=.028, for instance). The linkage to probability is also more emphasized compared to the traditional approach where the probabilities are getting somewhat hidden behind veils of alpha, t, and z. Now, if we can only get over the arbitrariness of the n<30 cut-off for use of t vs z and teach: use z when you know sigma and t when you don't. (Triola, as much as I like some of its choices, still retains this) <sigh> Paul . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
