Example
Suppose that we have two variables, sex (male or female) and handedness (right- or left-handed). Further suppose that 100 individuals are randomly sampled from a very large population as part of a study of sex differences in handedness. A contingency table can be created to display the numbers of individuals who are male and right-handed, male and left-handed, female and right-handed, and female and left-handed. Such a contingency table is shown below.
| Right-handed | Left-handed | Totals | |
|---|---|---|---|
| Males | 43 | 9 | 52 |
| Females | 44 | 4 | 48 |
| Totals | 87 | 13 | 100 |
The numbers of the males, females, and right- and left-handed individuals are called marginal totals. The grand total, i.e., the total number of individuals represented in the contingency table, is the number in the bottom right corner.
The table allows us to see at a glance that the proportion of men who are right-handed is about the same as the proportion of women who are right-handed although the proportions are not identical. The significance of the difference between the two proportions can be assessed with a variety of statistical tests including Pearson's chi-squared test, the G-test, Fisher's exact test, and Barnard's test, provided the entries in the table represent individuals randomly sampled from the population about which we want to draw a conclusion. If the proportions of individuals in the different columns vary significantly between rows (or vice versa), we say that there is a contingency between the two variables. In other words, the two variables are not independent. If there is no contingency, we say that the two variables are independent.
The example above is the simplest kind of contingency table, a table in which each variable has only two levels; this is called a 2 x 2 contingency table. In principle, any number of rows and columns may be used. There may also be more than two variables, but higher order contingency tables are difficult to represent on paper. The relation between ordinal variables, or between ordinal and categorical variables, may also be represented in contingency tables, although such a practice is rare.
Read more about this topic: Contingency Table
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