Tests of Association

Understanding the chi square test of independence

The chi square test of independence also referred to as the chi-square test of association is a statistical test used to examine the relationship or association between two variables measured on a categorical scale. In simpler used, this test determines whether a given set of categorical variables are independent or not. In a chi-square test of independence, a contingency table is used to analyze the data. A contingency table, also referred to as a cross-tabulation or a two-way table is the arrangement of data such that the variables are classified based on two categorical variables. The categories contained in variable one are placed in the rows section of the table and the categories of the second variables are placed in the column section. The corresponding frequencies of each intersecting row and column is expressed in the table's cells. In other words, each of the cell in the table will be a count of the specific pair of categories from the row section and column section.

The chi-square test of association commonly used to test the relationship or association between two or more variables measured on a categorical scale. This test can only be applied to categorical variables only. However, while a chi-square test of independence will be used to identify the relationship or association between two categorical variables, it cannot be used to imply causations. In other words, when a chi-square determines that two categorical variables are associated to one another, it does not mean that one variable causes the other.

The test statistic used for the chi-square test of association is expressed using X2. This statistic is computed using the following expression;

Where we have;

• Oij is the observed count in cell from the ith row to the jth column of the contingency table.
• eij is the observe count in cell from the ith row to the jth column of the contingency table.
• R and C are the row and column variables observations used to calculate the degrees of freedom, df = (R - 1)(C - 1).

With this test statistic, the hypothesis test examined using a chi square test of independence can be expressed in two ways;

• Null hypothesis, H0: The categorical variable 1 is independent of the categorical variable 2
• Alternative hypothesis, H1: The categorical variable 1 is not independent of the categorical variable 2

Or the following set of hypotheses may be employed;

• Null hypothesis, H0: The categorical variable 1 is not associated with categorical variable 2
• Alternative hypothesis, H1: The categorical variable 1 is associated with categorical variable 2

When you decide that you are going to conduct a chi-square test of association, the first step to determine whether the data being used for the analysis can actually be used to the test. This involves checking for various assumptions that are required to get valid and accurate results, these assumptions are;

1. The two variables being examined must be measured at an ordinal or nominal level. This means that they should be categorical variables.
2. The two variables being examined must containing two or more groups. For example, a group with two gender groups, ale and female or so on.

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