Chi-Square and Tests of Contingency Tables

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 deferentially 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 for Independence

One of the most frequent uses of X2 is for testing the null hypothesis that two criteria of classification, when applied to a population of subjects (or objects), are independent. Two criteria of classification are said to be independent if the distribution of one criterion in no way depends on the distribution of the other. If the two criteria of classification are not independent, there is an association between them.

 When data are arranged in table form for the chi-square independence test, the table is called a contingency table. The table is made up of R rows and C columns.

For the degree of freedom=(R-1)(C-1)

For the expected value=

Example:

Problem 1. A market research firm wishes to know whether they can conclude that, for adults in a certain city, the brand of car driven is associated with the drivers area of residence. A random sample of 500 adult drivers is interviewed to determine what brand of car they drive and in what area of residence they live. Test the claim at α=0.05.

The table shows the results:

 

Step 1.

Ho: The brand of car and the area of residence are independent of each other.

H1: The brand of car and the area of residence are dependent of each other. (claim) 

Step 2.

C.V. =9.488

d.f= (R-1) (C-1) = (2) (2) = 4

Step 3.Using the formula: 

χ2 = 19.82

Step 4.

Reject the null hypothesis.

There is enough evidence to support the claim.

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The chi-square test of significance is useful as a tool to determine whether or not it is worth the researcher's effort to interpret a contingency table. A significant result of this test means that the cells of a contingency table should be interpreted. A non-significant test means that no effects were discovered and chance could explain the observed differences in the cells. In this case, an interpretation of the cell frequencies is not useful. 

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By Tito Nuevacobita Jr. 

III-GOLD