```Date: Mar 18, 2013 6:00 PM
Author: Luis A. Afonso
Subject: Re: Krukal-Wallis by Fisher´s random shuffling

Krukal-Wallis by Bootstrap samplingFollow-upThe same data is treated as follows as it is required by the Bootstrap sampling: the three 8 sized samples to achieve H are obtained from the source data items by choosing at random no matter the times a generic item is drawn, once, twice, etc., could even be absent. Comparing with the former method I found that the procedure is rather unworthy. In fact the p-values, the H´ fraction larger than 2.721, is as much as larger than 39% or so. I guess that for no symmetrical sample statistics, Bootstrap should be avoided or we risk not rejecting absurd large values. Luis A. Afonso        REM "GRAHB"        CLS        DEFDBL A-Z        DIM ri(24)        DATA    1,2,3,4        DATA    5.5,5.5        DATA    7,8,9,10,11,12        DATA    14,14,14        DATA    16        DATA    17.5,17.5        DATA    19,20,21,22,23,24REM        FOR i = 1 TO 24: READ ri(i): totr = totr + ri(i): NEXT iREM        N = 24: C = 12 / (N * (N + 1))        INPUT " HOW MANY TABLES   "; manyREM        FOR tb = 1 TO manyREM        LOCATE 10, 50: PRINT USING "########"; many - tb        RANDOMIZE TIMER        SUM(1) = 0: SUM(2) = 0: SUM(3) = 0        FOR ix = 1 TO 8        gg = INT(24 * RND) + 1        SUM(1) = SUM(1) + ri(gg)        NEXT ix        FOR iy = 1 TO 8        gg = INT(24 * RND) + 1        SUM(2) = SUM(2) + ri(gg)        NEXT iy        FOR iz = 1 TO 8        gg = INT(24 * RND) + 1        SUM(3) = SUM(3) + ri(gg)        NEXT iz        aa = SUM(1) * SUM(1) / 8        bb = SUM(2) * SUM(2) / 8        cc = SUM(3) * SUM(3) / 8        tsum = aa + bb + cc        hh = C * tsum - 3 * (N + 1)        IF hh > 7.271 THEN sgni = sgni + 1 / many        NEXT tb        LOCATE 10, 50        PRINT USING "sgnif.% = ##.##  "; sgni * 100        END
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