
Chapter 18
806
Mann–Whitney U test:
Small sample U test
Unn
nn
R
112
11
1
1
=+
−
()
Unn
nn
R
212
22
2
1
=+
−
()
Un
11
Large sample U Test
z
U
U
U
=
σ
where mean m
U
=
μ
U
nn
is
and standard deviation s
U
=
nn nn
12 12
1
12
.
++
Wilcoxon matched-pairs signed rank test:
Wilcoxon test for large samples (n > 15)
Mean =
μ
T
nn
=
()
1
Standard deviation =
σ
T
nn n
=
()()
12 1
24
z
T
T
T
=
σ
where n is the number of pairs and T the Wilcoxon test statistic.
Kruskal–Wallis statistic (K)
K
nn
T
n
n
j
j
j
k
=
+
⎛
⎝
⎜
⎞
⎠
⎟
=
∑
12
1
2
1
()
where k is the number of groups, n the total number of observations (items), T
j
the sum of ranks in a group and n
j
the
number of observations (items) in a group.
Friedman ...