On 24 Nov 2002 01:29:36 GMT, [EMAIL PROTECTED] (Radford Neal) wrote: > In article <[EMAIL PROTECTED]>, > Alan McLean <[EMAIL PROTECTED]> wrote: > > >In practice the population is almost always a model - at best it is ill > >defined. So the value of sigma is virtually never meaningfully 'known'. > >At the same time, a role of statistical analysis is to save one from > >jumping to unwarranted conclusions - so one should be conservative. On > >this basis, it is preferable to use t even when you might think z is > >reasonable. > > But what if the sample standard deviation that you computed to do your > t test is substantially less than what you think sigma is? Is it really > "conservative" to ignore this, and quote a result that is based on what > you have reason to believe is an optimistic estimate of the accuracy of > the observations?
Use the improved estimate and z -- That's what I do informally, and small variance is reason enough to dis-believe some data. I don't know that I have seen anyone publish using z that way. By the way, there is one usual context where exact sigma enters in - the definition of non-parametric tests. For a dichotomy or for (untied) ranks, the variance is perfectly known. That's why the 2x2 chisquared is chisquared and not t-computed-on-phi. That's why the extended tables for rank statistics use chisquared instead of F. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
