55x60 500 500
with df = 1 and p < .001. This means that the observed cell frequencies deviate greatly from the expected cell frequencies.
To apply the %2 test, three conditions have to be met to achieve an approximation of the sampling x2 distribution to the theoretical one (e.g., Kennedy, 1983). First, the observations have to be independent. Thus, all members of the population of interest must have the same probability of inclusion in the sample. In the ideal case, the sample represents a perfect representation of this population. Second, the classifications have to be independent, mutually exclusive, and exhaustive. Third, as a rule of thumb, the %2 test requires expected cell frequencies of at least five observations per cell (for a more detailed discussion, see Clogg & Eliason, 1987; Hagenaars, 1990; Read & Cressie, 1988). Hence, the %2 test cannot be applied to contingency tables with a large number of categories and only a few observations. On the other hand, large sample sizes increase the power of the %2 statistic. Contingency tables with identical cell proportions yield higher x2 values for those with larger samples, thus the same proportional deviations from the expected cell frequencies can lead to significant and nonsignificant %2 values, depending on the sample size.
The x2 value is not restricted to a special range of values. Its distribution is larger than zero but infinite. To standardize its values and to make it more comparable, the corrected contingency coefficient Ccorr and Cramer's V can be computed (see Liebetrau, 1983). Both coefficients transform the empirical %2 value to obtain values ranging from zero to one. In these transformations the empirical X2 value is compared to a maximal %2 value. Unfortunately Ccorr cannot reach 1 in nonquadratic contingency tables (where I ^ J), whereas V, on the other hand, does. Both coefficients are hard to interpret because there is no operational standard forjudging their magnitudes (Reynolds, 1977a).
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