We have indicated that if you have two categorical variables and you want to check whether they are related, the best method is to create a crosstabs, possibly with the counts expressed as percentages. But suppose both categorical variables have only two categories and these variables are coded as dummy 0Ă˘â‚¬â€ś1 variables. Then there is nothing to prevent you from finding the correlation between them with the same Equation (3.2) from this section, that is, with ExcelĂ˘â‚¬â„˘s CORREL function. However, if we let C(i, j) be the count of observations where the first variable has value i and the second variable has value j, there are only four joint counts that can have any bearing on the relationship between the two variables: C(0,0), C(0,1), C(1,0), and C(1,1). Let C1(1) be the count of 1s for the first variable and let C2(1) be the count of 1s for the second variable. Then it is clear that C1(1) = C(1,0) + C(1,1) and C2(1) = C(0,1) + C(1,1), so C1(1) and C2(1) are determined by the joint counts. It can be shown algebraically that the correlation between the two 0Ă˘â‚¬â€ś1 variables is
To illustrate this, the file P03_32.xlsx contains two 0Ă˘â‚¬â€ś1 variables. (The values were generated randomly.) Create a crosstabs to find the required counts, and use the above formula to calculate the correlation. Then use Stat Tools (or ExcelĂ˘â‚¬â„˘s CORREL function) to find the correlation in the usual way. Do your two results match? (Again, we do not necessarily recommend finding correlations between 0Ă˘â‚¬â€ś1 variables. A crosstabs is more meaningful and easier to interpret.)
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