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