Biostatistics

SUMMARY OF FORMULAS FOR CHAPTER 13
SUMMARY OF FORMULAS FOR CHAPTER 13 731
Formula
Number Name Formula
13.3.1 Sign test statistic
Pk x X x
n; p ¼ n C k p k q n
k¼0
k
13.3.2 Large-sample
approximation of
the sign test
z ¼ þ 0:5 p Þþ0:5n
0:5 ffiffiffi ;
n
if k < n 2
z ¼ 0:5 p Þ 0:5n
0:5 ffiffiffi ;
n
if k n 2
13.6.1 Mann–Whitney test
statistic
T ¼ S
nnþ ð 1Þ
2
13.6.2 Large-sample
approximation of the
Mann–Whitney test
13.6.3 Equivalence of the Mann–
Whitney and Wilcoxon
two-sample statistics
13.7.1–13.7.2 Kolmogorov–Smirnov
test statistic
T mn=2
Z ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
nmðn þ m þ 1Þ=12
mmþ 2n þ 1
U þ W ¼ ð Þ
2
D ¼ sup jF s ðÞ x F T ðÞ x j
x
¼ max fmax½jF s ðx i Þ F T ðx i Þj; jF s ðx i 1 Þ
1ir
F T ðx i 1 ÞjŠg
13.8.1 Kruskal–Wallis test
statistic H ¼ 12
nnþ ð 1Þ
X k
j¼1
R 2 j
3ðn þ 1Þ
n j
13.8.2 Kruskal–Wallis test
statistic adjustment
for ties
13.9.2 Friedman test statistic
1
P T
n
n 3
x 2 r ¼ 12
nkðk þ 1Þ
X k
j¼1
2
R j 3nkþ ð 1Þ
13.10.1 Spearman rank correlation
test statistic
r s ¼ 1
6 P d 2 i
nn ð
2 1Þ