- I am just taking a couple of questions in this note - On Thu, 29 Nov 2001 13:16:24 +0100, "Gaj Vidmar" <[EMAIL PROTECTED]> wrote: [ ... ]
I saw some decent comments about the table; the table was not very useful. z is used with large N as 'sufficiently good' approximation for t. z is used when "variance is known" -- which is, in particular, when statistics are computed that were based on dichotomies or on ranks (if there were no ties). That's basically when variances are known. With big samples and ties, you are probably better off doing your rank-transformation, then using the F-test or t-test. Depending on the outliers, ANOVA (t-tests) might be useless, regardless of how big the sample *might* get -- that happens more often than careless analysts expect, when they don't watch for outliers. -- If you can't opt for a parametric transform, you might need to test after rescoring as 'ranks' or into categories (two or more). > > Note 2: t-test is very robust (BTW, is Boneau, 1960, Psychological Bulletin - not in *my* opinion (see below) - > vol. 57, referenced and summarised in Quinn and McNemar, Psychological > Statistics, 4th ed. 1969, with the nice introduction "Boneau, with the > indispesable help of an electronic computer, ...", still an adequate > reference?), whereby: > - skewness, even extreme, is not a big problem > - two-tailed testing increases robusteness - I was annoyed when I learned that those old-line authors would decide that a test was 'robust with two-tails' when it rejected 9% in one tail in 1% in the other. It felt somewhat like having been lied-to. I still disagree with that opinion. Fortunately, the *problem* of really-bad-p-values (in both directions) does not exist for equal N. Unfortunately, even for equal N, there *can* be a great loss in statistical power. So, you should be unhappy to see great skewness. But for either equal or unequal N, I am much happier if I can trust that the variable has been transformed to its proper metric; and if that metric does not have skewness, or heterogeneity of variance. If a variable *needs* to be transformed, please transform it. (But the 'need' issue is worth its own discussion.) > - unequal variances are a serious problem with unequal N's with larger > variance of smaller sample Oh, a problem with larger variance in EITHER sample. A different problem, one way or the other. Outliers cause loss of power for ANOVA, just as much as outliers screw up a mean -- If you see outliers, ask, Are you sure ANOVA is the right tool? > > Now, what to do if t is inadequate? - This is a whole complex issue in > itself, so just a few thoughts: > - in case of extreme skewness, Mann-Whitney is not a good alternative > (assumes symmetric distrib.), right? [ ... ] It assumes *same* distributions in two samples, not necessarily symmetric. What is your hypothesis going to be? What can you fairly conclude, if one sample occupies both ends of the distribution? -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
