Measures of Association 770 the value of the chi square statistic provides a test whether or not there is a statistical relationship between the variables in the cross classification table. While the chi square test is a very useful means of testing for a rela- tionship,it suffers from several weakenesses.One difficulty with the test is that it does not indicate the nature of the relationship.From the chi square statistic itself.it is not possible to determine the extent to which one vari- able changes,as values of the other variable change.About the only way to do this is to closely examine the table in order to determine the pattern of the relationship between the two variables. A second problem with the chi square test for independence is that the size of the chi square statistic may not provide a reliable guide to the strength of the statistical relationship between the two variables.When two different cross classification tables have the same sample size,the two variables in the table with the larger chi square value are more strongly related than are the two variables in the table with the smaller chi square value.But when the sample sizes for two tables differ.the size of the chi square statistic is a misleading indicator of the extent of the relationship between two variables. This will be seen in Example 11.2.1. A further difficulty is that the value of the chi square statistic may change depending on the number of cells in the table.For example,a table with 2 columns and 3 rows may give a different chi square value than does a cross classification table with 4 columns and 5 rows,even when the relationship between the two variables and the sample sizes are the same.The number of rows and columns in a table are referred to as the dimensions of the table.Tables of different dimension give different degrees of freedom,partly correcting for this problem.But it may still be misleading to compare the chi square statistic for two tables of quite different dimensions In order to solve some of these problems,the chi square statistic can be adjusted to take account of differences in sample size and dimension of the table.Some of the measures which can be calculated are phi,the contingency coefficient,and Cramer's V.Before examining these measures,the following example shows how sample size affects the value of the chi square statistic. Example 11.2.1 Effect of Sample Size on the Chi Square Statistic The hypothetical examples of Section 6.2 of Chapter 6 will be used to illustrate the effect of sample size on the value of the chi square statistic. The data from Tables 6.9 and 6.10 will first be used to illustrate how a largerMeasures of Association 770 the value of the chi square statistic provides a test whether or not there is a statistical relationship between the variables in the cross classification table. While the chi square test is a very useful means of testing for a rela￾tionship, it suffers from several weakenesses. One difficulty with the test is that it does not indicate the nature of the relationship. From the chi square statistic itself, it is not possible to determine the extent to which one vari￾able changes, as values of the other variable change. About the only way to do this is to closely examine the table in order to determine the pattern of the relationship between the two variables. A second problem with the chi square test for independence is that the size of the chi square statistic may not provide a reliable guide to the strength of the statistical relationship between the two variables. When two different cross classification tables have the same sample size, the two variables in the table with the larger chi square value are more strongly related than are the two variables in the table with the smaller chi square value. But when the sample sizes for two tables differ, the size of the chi square statistic is a misleading indicator of the extent of the relationship between two variables. This will be seen in Example 11.2.1. A further difficulty is that the value of the chi square statistic may change depending on the number of cells in the table. For example, a table with 2 columns and 3 rows may give a different chi square value than does a cross classification table with 4 columns and 5 rows, even when the relationship between the two variables and the sample sizes are the same. The number of rows and columns in a table are referred to as the dimensions of the table. Tables of different dimension give different degrees of freedom, partly correcting for this problem. But it may still be misleading to compare the chi square statistic for two tables of quite different dimensions. In order to solve some of these problems, the chi square statistic can be adjusted to take account of differences in sample size and dimension of the table. Some of the measures which can be calculated are phi, the contingency coefficient, and Cramer’s V. Before examining these measures, the following example shows how sample size affects the value of the chi square statistic. Example 11.2.1 Effect of Sample Size on the Chi Square Statistic The hypothetical examples of Section 6.2 of Chapter 6 will be used to illustrate the effect of sample size on the value of the chi square statistic. The data from Tables 6.9 and 6.10 will first be used to illustrate how a larger