Chapter 12 Chi-Square Tests and Nonparametric Tests

12.1: Chi 2 Test for Difference Between 2 Proportions (Independent Samples) techniques rely on the cross-classification or cross-tabulation table structure. Sometimes called “contingency tables.”

The Chi 2 Test: As with all hypothesis tests, the same steps are used: Develop hypotheses Develop rejection region / decision rule Examine sample / test statistic Make decisions and conclusions.

Mechanics H 0 : pi 1 = pi 2 Point estimate? Test statistic = If H 0 is true, then the test statistic should be small because observed and expected frequencies are close. If H 0 is false, then the test statistic will be large. Assume that expected frequencies greater than 5.

12.2: Chi-Square Test for Differences Among More than Two Proportions Each column of the contingency table contains the data from one of the populations. Stay with 2 rows: one for success and one for failure. Few modifications from 12-2 are required. Post hoc testing is available.

Post hoc testing Marascuilo Procedure compare all pairs of groups. It is a critical range test. Compute the difference in sample proportions for “success” for all pairs. Compute the critical range: Formula 12.6.

12.3: Chi-Square Test of Independence More than 2 populations. Hypotheses slightly different: –H 0 : two categorical variables are independent. –H 1 : two categorical variables are dependent. What are independence and dependence? How many values may each variable assume? Test Statistic and Decision Rule are same as that of Test of Equal Proportions (12-3).

Difference between 12.2 and 12.3 Test of Equal Proportions has 1 factor or variable of interest with 2 or more levels. For each group or level, there are successes and failures. Test of Independence has 2 factors or variables of interest, each of which has two or more levels. Draw a sample and assess the values of both variables.