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# THE UNIVARIATE CHI-SQUARE TEST

Finally, chi-square (often written x2) is an important part of univariate analysis. It is a test of whether the distribution of a series of counts is likely to be a chance event. The formula for x2 is:

where O represents the observed number of cases and E represents the number of cases you’d expect, ceteris paribus, or ‘‘all other things being equal.’’

Suppose that among 14 families there are a total of 42 children. If children were distributed equally among the 14 families, we’d expect each family to have three of them. Table 20.2 shows what we would expect and what we might find in an actual set of data. The x2 value for this distribution is 30.65.

Table 20.12 Chi-Square for a Univariate Distribution

 Expected number ofchildren per family Family # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total 3 3 3 3 3 3 3 3 3 3 3 3 3 3 42 Observed number ofchildren per family Family # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total 0 0 5 5 5 6 6 0 0 3 1 0 6 5 42 (observed - expected)2 9 9 4 4 4 9 9 9 9 0 4 9 9 4 (observed - expected)2 expected 3 3 1.33 1.33 1.33 3 3 3 3 0 1.33 3 3 1.33 E (observed - expected)2 3 + 3 + 1.33 + 1.33 + ...1.33 30.65 Expected

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