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In this section, we explain how to calculate Cramer’s coefficient of association, which is an index expressing the strength of the relationship between two items on the front side and head of a cross-tabulation table.
Expected frequency
In the summary table (Table 1) of physician affiliation type and prescription of cardiovascular disease drugs, the value obtained by multiplying the horizontal and vertical totals of the number of respondents and dividing the result by the total number of respondents is called the “expected frequency.”
[Table 1] Case summary
Cramer’s coefficient of association
Calculate the horizontal % of the expected frequency as shown in Table 2.
[Table 2] Horizontal % of expected frequency
The horizontal percentage table of the expected frequency matches the overall management style of the facility to which the doctor belongs. In case of such aggregation results, it can be inferred that there is no relationship between physician affiliation type and prescription drugs, and Cramer’s coefficient of association is 0.
The number of respondents in the crosstabulation table obtained from the survey is called the “actual frequency.”
If the measured and expected frequency values match, Cramer’s coefficient of association is 0; it increases with the difference between the values. Based on this concept, the value of each cell was calculated using the formula listed in Table 3.
[Table 3] List of coefficient calculations
The value obtained by summing the cell values is called “the chi-square value.”
The Cramer’s coefficient of association, “r,” is calculated using the following formula, the chi-square value.
[Formula]
- k is the smaller value of the number of categories for two items in the cross-tabulation table.
(In this case, since the number of categories is 3 in both cases, k=3.)
The Cramer’s coefficient of association in this case can be calculated as follows.
No statistical standard exists for the number of Cramer’s coefficients of association required to be relevant. Generally, it is recommended to set the boundary at “0.1,” and if it is greater than that, then it is interpreted as related.
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