# **Interpreting Crosstabulations in SPSS**

**CASE STUDY: CROSS TABULATIONS IN SPSS**

Refer to the attached printout of a cross-tab between two ordinal variables and associated output. Write out the five steps of a hypothesis test (Step 1 = Assumptions, … , Step 5 = Conclusions) on that sheet.

**Solution: **We are going to perform a Cross tabulation of the variables “Prayer Frequency” and “Fundamentalist”. We test for the existence of a relationship between those two variables. In order to test for the existence of a relationship, we use the SPSS output shown above.

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__The Assumptions__:

We use Kendall’s tau-b, Kendall’s tau-c and Gamma to check for a relationship, which is appropriate because we are analyzing twp Ordinal variables

__The hypotheses__:

We want to test the following null and alternative hypotheses:

Ho: There is not relationship between ''Prayer Frequency'' and ''Fundamentalist''

Ha: There is a relationship between ''Prayer Frequency'' and ''Fundamentalist''

In order to test these hypotheses we use SPSS crosstabs analysis and the Kendall’s tau-b, Kendall’s tau-c and Gamma statistics.

__Level of Significance__:

We choose the level of significance$\alpha =0.05$. The level of significance corresponds to the probability to make a Type I error, which is the probability of the rejecting the null hypothesis when it is actually true.

__Results__:

The significance of the Kendall’s tau-b, Kendall’s tau-c and Gamma statistics is *p = 0.000* for all of them, *which indicates that there is a relationship between the two variables. *Since the p-values are all less than 0.05, our previously chosen level of significance, we have enough evidence to reject the null hypothesis.

__Conclusions__:

*We reject the null hypothesis at the 0.05 level of significance*, which means that we accept that there is a relationship between the variables, with a 0.05 significance level. The value of the Kendall’s tau-b, Kendall’s tau-c and Gamma is small (0.262, 0.282, 0.360 respectively) which is indication of a rather weak relationship.

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