Occasionally, a researcher will collect data that is categorical in nature. For example, suppose we are interested in whether someone attends church, attends football games, or stays at home on Sundays. We can code the data for purposes of inputting the data into the computer, such that the following scheme is used: 1 = attends church, 2 = attends football games, and 3 = stays home. Suppose we want to see if there is any difference between men and women in regards to how they answer this question. What test can we use?
T test? No, because the data is not metric. The dependent variable (Sunday activity) is nominal and the independent variable is a dichotomous dummy coded variable.
Pearsons R? No, because we are not interested in the relationship between the variables.
The answer is Chi-square analysis. Chi square is the most commonly encountered statistical test for analyzing nominal data. The test is also known as a nonparametric test because it does not rely upon the same assumptions (normality, metric variables, etc.) as many of the other tests we have discovered.
There are 4 requirements for using the Chi square statistical technique:
How does Chi square work? Chi square analysis works by examining the frequency of scores that occur in the study. The frequency of scores that are expected are compared with the actual frequency of scores that is observed, in order to determine if the frequency of scores observed differ significantly from that which could be observed due to chance.
The first form of Chi square analysis that we will discuss is that of the 1x k Chi Square. Here the researcher is interested in examining the frequency of scores for one group of data.
For example, suppose a researcher is interested in examining whether one radio station is more popular among teenagers. A random sample of 100 teenagers is selected, and they are categorized on the basis of their radio station preference. The data are as follows:
Station A 40
Station B 30
Station C 20
Station D 10
These values above are representative of the frequency observed. The next step is to then determine the frequency of scores expected. There are two approaches on how to determine the frequency of scores expected.
Once the frequency observed and the frequency expected is determined, the researcher must state their hypotheses, which are written as follows:
The calculated Chi square value is then compared to a table of known critical values. If the calculated value is greater than the table value, then the researcher rejects the null hypothesis. However, if the calculated value is less than the table value, then the researcher will accept the null hypothesis.
To calculate a 1 x k Chi square in SPSS:
Open the data file
Place the test variable into the test variable list
The second form of Chi square is referred to as the r x k Chi square (r by k). This form of Chi square is used when a researcher wishes to examine more than one group and then compare these groups with respect to some observed frequency. Much of the calculations remain the same with the exception of how the researcher selects the frequency expected.
To determine the frequency expected for a r x k Chi square, the data is entered into a contingency table. For example, consider the following there are 4 groups in a study, Group A received Vitamin C and Had influenza (frequency of 10), Group B received Vitamin C and did not have influenza (frequency of 20), Group C received placebo and had influenza (frequency of 15), and Group D received placebo and did not have influenza (frequency of 15). The total number of subjects in this study is 60. Therefore to determine the frequency expected for Group A, we take the sum of the Column that A is in (25) and multiply it by the sum of the Row that A is in (30), then it is divided by the total number of subjects. Therefore, (25 x 30)/60 equals 12.50. The procedure would then be repeated for each group.
The hypotheses are written the same as a 1 x k Chi square and the rules for accepting or rejecting a null hypothesis remain the same as well.
To conduct a r x k Chi square on SPSS:
Open the data file
Move the first group into the row section
Move the second group into the column section
Place a check mark by Chi-square