Crosstab software can give you two sets of results within your crosstab table: numbers and percentages. It’s essential to understand the meaning of each set of results and helpful to know how to calculate the latter.
The Numbers
Your standard crosstab table typically looks something like this:
Column 1 | Column 2 | Row Totals | |
Row 1 | A | b | a + b |
Row 2 | c | d | c + d |
Column Totals | a + c | b + d | a + b + c + d |
The numbers within the cells – represented by a, b, c and d – are called cell counts. Each cell count corresponds to the row and column directly above and to the left of the number. Adding the cell counts in the row total and column total cells give you the total number of observations in each category. Row and column totals are also known as marginal frequencies.
The cell count that adds all the numbers together in the lowermost cell on the right gives you the total number of observations in the overall table.
The Percentages
Converting the numbers to percentages can be helpful to determine the proportion of the row or column that falls into a particular category. Percentages can add a layer of meaning and importance to the numbers by helping you understand the picture as a whole.
Calculating percentages can be done using mathematical formulas.
Row percentages are calculated as below, with the row totals always equaling 100 percent.
Column 1 | Column 2 | Row Totals | |
Row 1 | a | B | a + b |
Row 1 Percentage | a / (a + b) | b / (a + b) | (a + b) / (a + b) = 100% |
Row 2 | c | D | c + d |
Row 2 Percentage | c / (c + d) | d / (c + d) | (c + d) / (c + d) = 100% |
Column Totals | a + c | b + d | a + b + c + d |
Percentage of Total | (a + c)/(a + b + c + d) | (b + d)/(a + b + c + d) | (a + b + c + d)/(a + b + c + d) = 100% |
Column percentages are calculated as below, with the column totals always equaling 100 percent.
Column 1 | Column 2 | Row Totals | |
Row 1 | A | b | a + b |
Column 1 Percentage | a / (a + c) | b / (b + d) | (a + b) / (a + b + c + d) = 100% |
Row 2 | C | d | c + d |
Column 2 Percentage | c / (a + c) | d / (b + d) | (c + d) / (a + b + c + d) = 100% |
Column Totals | a + c | b + d | a + b + c + d |
Percentage | (a + c) / (a + c) = 100% | (b + d) / (b + d) = 100% | (a + b + c + d)/(a + b + c + d) = 100% |
Total percentages are calculated as below, with the denominators for all equations equal to the total number of observations, or (a + b + c + d).
Column 1 | Column 2 | Row Totals | |
Row 1 | A | b | a + b |
Percentage of Total | a / (a + b + c + d) | b / (a + b + c + d) | (a + b) / (a + b + c + d) |
Row 2 | c | d | c + d |
Column 2 Percentage | c / (a + b + c + d) | d / (a + b + c + d) | (c + d) / (a + b + c + d) |
Column Totals | a + c | b + d | a + b + c + d |
Percentage of Total | (a + c) /(a + b + c + d) | (b + d) /(a + b + c + d) | (a + b + c + d)/(a + b + c + d) = 100% |
Even if your crosstab software automatically computes the percentages for you, it never hurts to be as smart as your software – or at least understand how it calculates your results.