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

Krukal-Wallis by Bootstrap sampling

Follow-up
The 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 19,20,21,22,23,24
REM
FOR i = 1 TO 24: READ ri(i): totr = totr + ri(i): NEXT i
REM
N = 24: C = 12 / (N * (N + 1))
INPUT " HOW MANY TABLES "; many
REM
FOR tb = 1 TO many
REM
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