CHI-SQUARE AND TESTS OF CONTINGENCY TABLES

Hypothesis tests may be performed on contingency tables in order to decide whether or not effects are present. Effects in a contingency table are defined as relationships between the row and column variables; that is, are the levels of the row variable diferentially distributed over levels of the column variables. Significance in this hypothesis test means that interpretation of the cell frequencies is warranted. Non-significance means that any differences in cell frequencies could be explained by chance.

Test using Contingency Tables

Table 12.1

Event	E1	E2	E3	…	Ek
Observed Frequency	o1	o2	o3	…	ok
Expected Frequency	e1	e2	e3	…	ek

Table 12.1, in which the observed frequencies occupy a single row, is called a one-way classification table. Since the number of columns is k, this is also called a 1 x k (read “1 by k”) table. By extending these ideas, we can arrive at two-way classification tables, or h x k tables, in which the observed frequencies occupy h rows and k columns. Such tables are often called contingency tables.

        Corresponding to each observed frequency in an h x k contingency table, there is an expected (or theoretical) frequency that is computed subject to some hypothesis according to rules of probability. These frequencies, which occupy the cells of a contingency table, are called cell frequencies. The total frequency in each row or each column is called the marginal frequency.

  

By: Lera Gay Bacay