Biostatistics

12.8 SUMMARY 655
collected data on 297 families with a child in the Head Start nursery program in a rural area of Ohio
near Appalachia. The main outcome variable of the study was household status relative to food
security. Households that were not food secure are considered to be cases. The risk factor of interest
was the absence of a garden from which a household was able to supplement its food supply. In the
following table, the data are stratified by the head of household’s employment status outside the
home.
Stratum 1 (Employed Outside the Home)
Risk Factor Cases Noncases Total
No garden 40 37 77
Garden 13 38 51
Total 53 75 128
Stratum 2 (Not Employed Outside the Home)
Risk Factor Cases Noncases Total
No garden 75 38 113
Garden 15 33 48
Total 90 71 161
Source: Data provided courtesy of David H. Holben, Ph.D. and John P. Holcomb, Jr., Ph.D.
Compute the Mantel–Haenszel common odds ratio with stratification by employment status. Use the
Mantel–Haenszel chi-square test statistic to determine if we can conclude that there is an association
between the risk factor and food insecurity. Let a ¼ .05.
12.8 SUMMARY
In this chapter some uses of the versatile chi-square distribution are discussed. Chi-square
goodness-of-fit tests applied to the normal, binomial, and Poisson distributions are
presented. We see that the procedure consists of computing a statistic
X 2 ¼ X " #
ðO i E i Þ 2
that measures the discrepancy between the observed (O i ) and expected (E i ) frequencies of
occurrence of values in certain discrete categories. When the appropriate null hypothesis is
true, this quantity is distributed approximately as x 2 . When X 2 is greater than or equal to the
tabulated value of x 2 for some a, the null hypothesis is rejected at the a level of
significance.
Tests of independence and tests of homogeneity are also discussed in this chapter.
The tests are mathematically equivalent but conceptually different. Again, these tests
essentially test the goodness-of-fit of observed data to expectation under hypotheses,
respectively, of independence of two criteria of classifying the data and the homogeneity of
proportions among two or more groups.
E i