The x2 value, as a measure of association, compares observed cell frequencies with expected cell frequencies in a contingency table. There are several ways to compute expected frequencies depending on the researcher's hypothesis. One hypothesis that might be of interest for most researchers is the
e.. v with n¡. as observed cell frequencies, e.j as expected cell frequencies, and 1 and J denoting the number of categories. For the independence model, for example, the expected cell frequencies are computed n. n+.
by e.. = 1 , whereby n.+ and n+. represent the marginal of category i of the first rating and j of the second rating. The degrees of freedom of the X2 value can be computed by df = (I - l)2 for quadratic contingency tables.
The higher the %2 value, the less the observed cell frequencies match the expected cell frequencies. Under the assumption of independence, a significant x2 value indicates that there is an association between both variables, which goes beyond the association expected by chance. If the expected cell frequencies are those of experts' ratings, a nonsignificant x2 value means that the novices generated a pattern of ratings that is similar to the experts' pattern. In this case the novices provided ratings of comparable quality.
Under the assumption of independence, the data in Table 17.1a yield the following %2 value:
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