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.
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
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.
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.
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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