Yates's Correction

2×2 Contingency Tables, Expected Frequencies, and Chi-Square

Yates's correction is applicable to 2×2 contingency tables, which reflect the association between two dichotomous variables. Common in many areas of research, a dichotomous variable has only two possible values—for example, the variable “biological sex” is generally treated as having only two values (i.e., male vs. female), and a particular study might treat “personality pathology status” as having only two values (i.e., pathology present vs. pathology absent). Yates's correction can be used to evaluate, for example, the degree to which the presence or absence of personality pathology is contingent on one's biological sex.

Table 1 presents the frequencies of co-occurrences between values of two dichotomous variables—biological sex and personality pathology status. For example, this table shows that, from a total of 40 hypothetical participants, 15 are females without personality pathology and 1 is a female with personality pathology.

The frequencies in this contingency table indicate some degree of association between biological sex and personality pathology. Specifically, personality pathology is present in fully 33% of the males in the sample (8/24 =: 333) but in only 6% of the females (1/16 =: 063). These results suggest that personality pathology is contingent, to some degree, on biological sex in this sample—pathology is more likely to be observed in a male in the sample than in a female. Although these data provide clear information about the sample of participants being studied, they provide less direct information about a broader population.

To address the link between the sample's data and the broader population, a Pearson chi-square value is often used to evaluate the statistical significance of the association expressed in a contingency table. That is, the Pearson chi-square is an inferential statistic used to gauge whether the two variables are associated with each other in the population from which the sample was randomly drawn. A chi-square value is calculated from the deviations between (a) the frequencies actually observed in the sample and (b) a set of frequencies expected under the null hypothesis that the two variables are not associated with each other in the population (i.e., that the variables are independent). An expected frequency is determined for each cell in a contingency table, computed

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