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Nonparametric Tests 63
KruskalWallisH (data(,), pairsig, h, p, diff(,))
KruskalWallisH gives the Kruskal-Wallis H-test for independent samples. Pass a
data(,) array that contains “treatments” in its columns; that is, each column is a
dataset. Short columns can be padded out with missing values. Also pass pairsig, the
significance level at which columns are considered to be different. The test returns:
h
p
diff(,)
the H-hat statistic from the Kruskal-Wallis test; note that if more
than 25% of all values are involved in ties, h is the corrected H-hat
statistic
significance probability of h (see Warning)
pairs (i,j) of rank indices that test significantly different
For example, you could pass pairsig = .05 to find all columns that are different at the
5% level. If there are no such columns, Size(diff,1) is zero. But if there are, say, three
such pairs of columns i-j, i-k, and k-l, then Size(diff,1) is 3; and diff(1,1) is i, diff(1,2) is
j; diff(2,1) is i; diff(2,2) is k, etc.
By default, pairwise significances are computed by via chi-square distributions, as
given in Applied Statistics, p. 305. To switch to Dunn’s procedure for pairwise comparisons
via normal distributions, call SetHtest(1) before calling this routine.
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x WARNING: For small samples, Size(data,1) < 5 or Size(data,2) < 4, p
may be incorrect. Use a critical value table instead.
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See Applied Statistics, pp. 303-306, for a critical value table.
Exception:
755 Too many identical values for Kruskal-Wallis H test.
See KRUSKAL, on your diskette, for an example.
Friedman (d(,), cr(), fs, p)
Friedman gives the Friedman rank-ANOVA test, a distribution-free two-way ANOVA
for correlated samples.
Input the data in d(,) where each column is a treatment. The output is:
cr() column rank sums
fs Friedman statistic
p significance probability of fs (see Warning)
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