Biostatistics

REVIEW QUESTIONS AND EXERCISES 657
12.7.5 Expected frequency in the
Mantel–Haenszel statistic
12.7.6 Stratum expected frequency
in the Mantel–Haenszel
statistic
12.7.7 Mantel–Haenszel test statistic
12.7.8 Mantel–Haenszel estimator
of the common odds ratio
Symbol Key
ð
e i ¼ a i þ b i Þða i þ c i Þ
ð
v i ¼ a i þ b i
x 2 MH ¼
cOR MH ¼
n i
Þðc i þ d i Þða i þ c i
n 2 i ðn i 1Þ
P k P
a k
i e i
i¼1 i¼1
P k
v i
i¼1
P k
i¼1
P k
i¼1
ða i d i =n i Þ
ðb i c i =n i Þ
a; b; c; d ¼ cell frequencies in a 2 2 contingency table
A; B ¼ row totals in the 2 2 contingency table
b ¼ regression coefficient
x 2 or X 2 ¼ chi-square
e i ¼ expected frequency in the Mantel–Haenszel statistic
E i ¼ expected frequency
E ðyjxÞ
¼ expected value of y at x
k ¼ degrees of freedom in the chi-square distribution
m ¼ mean
O i ¼ observed frequency
cOR ¼ odds ratio estimate
s ¼ standard deviation
cRR ¼ relative risk estimate
v i ¼ stratum expected frequency in the Mantel–Haenszel statistic
y i ¼ data value at point i
z ¼ normal variate
Þðb i þ d i Þ
REVIEW QUESTIONS AND EXERCISES
1. Explain how the chi-square distribution may be derived.
2. What are the mean and variance of the chi-square distribution?
3. Explain how the degrees of freedom are computed for the chi-square goodness-of-fit tests.
4. State Cochran’s rule for small expected frequencies in goodness-of-fit tests.
5. How does one adjust for small expected frequencies?
6. What is a contingency table?
7. How are the degrees of freedom computed when an X 2 value is computed from a contingency
table?