On 3 Dec 2002 16:20:03 -0800, [EMAIL PROTECTED] (Teresa from Oregon) wrote:
> I was doing a little mental calisthenics today and got myself confused > about how this test is calculated. My (perhaps naive) understanding is > that all potential sets of results from, say, a 2x2 table are > calculated and then the exact probability of the actual observed > result occurring simply by chance is determined. This is why there is > no associated test statistic, just p. > > My question is: If the test is distributionless, wouldn't the > probability of all unique results be equal? Or...put another way...Is > Fisher's exact one of those sneaky nonparametrics that really does > rely upon an underlying distribution? One the one hand, "nonparametric" is a misnomer, because the ones that are central to the idea are the ones that implicate an *infinite* number of parameters (for describing the mapping from scores, say, to ranks). Fisher's 2x2 only relies on the notion that one table can be described as "more extreme" which only requires adding the two off-diagonals. You take 1 away from each, adding to diagonal cells, to become "more extreme." If you dig deeper, you discover that the 2-tailed test is trickier, because in the abstract, there's more than a single criterion of what makes a table extreme. For 2x2 cases, do you compare Odds ratios? Difference in expectations? Something else? It gets even worse when you consider tables that are larger than 2x2. Just for one contrast: you could compute the Pearson chisquared, or compute the likelihood chisquared -- they do not agree 100% as to which tables are the most extreme. (Pearson's contingency test gives a greater weight to one *large* deviations in a single cell, where the likelihood test gives a relatively greater weight to multiple cells with moderate deviations.) (See the appendix in Agresti, for 'power family'.) -- 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/ . =================================================================
