# What Months and Payment Types Have Unusual Affinities for Which Types of Products?

This question is similar to the question in the previous section, except that it uses three columns instead of two columns. Answering this question introduces the multidimensional chi-square calculation. This is very similar to the two-dimensional version, the only differences being some adjustments to the formulas.

## Multidimensional Chi-Square

Adding additional dimensions does not change how the chi-square value is calculated. It is still the sum of the squares of the differences between a count and the expected count divided by the expected count.

What changes is the formula for the expected value. For two-dimensions, this is the product of the counts along each of two dimensions divided by the total count. This formula generalizes to more dimensions. For three, it is the product of the counts along each of the three dimensions divided by the total count squared. Notice the “squared” in...