"Percentaging" contingency tables: It really does matter how you do it

Contingency tables display the co-occurrence of categorical variables. The frequencies of occurrence in each category of each variable are converted into percentages in order to facilitate the interpretation of the relationship between the variables. "Percentaging" a contingency table is not easy, however. One has to be careful regarding how the percentaging is done (down the columns, across the rows, or by total sample size). Using an artificial example and a real-world example, we show how percentaging is carried out and how the proper interpretation of the findings depends upon the direction in which the calculations are performed.