# Module 5 Exercise Answers

The following cross-tabulations were created using the
Analyze>Descriptive Statistics>Crosstabs option on SPSS. We have also included the row percentages and Pearson’s Chi-square for each crosstab (the results of which are reported above each table). If you are unsure about how to do this we describe the process on Page 2.2. Note that we have re-sized each table and added the numeric codes for each category. This is to make them easier to interpret here so don’t worry if your output looks slightly different (though the actual figures should be the same!).
Chi-square = 48.03, df = 7,
Chi-square = 66.56, df = 7,
Chi-square = 121.85, df = 7, The results indicate that there are statistically significant associations between ethnicity and each of SEN, truancy and exclusion – in short that there are significant differences between ethnic groups with regard to these three variables. Let us explore the specific comparison between White British and Black Caribbean students more closely. We can see that Black Caribbean students are more likely to be identified as having special educational needs (12.5%) than White British students (7.7%). They are also more likely to report truanting (20.3% of students) compared to White British students (15.8%). Finally they are nearly twice as likely to be excluded as White British students with 20% having been excluded compared to only 10.4% of White British students. There seem to be grounds to include all three of these explanatory variables in any model which attempts to account for ethnic differences in entry to different test tiers.
An Ordinal Regression was completed using the model as shown in
Let’s look at the coefficients for our three new explanatory variables (
- SEN Exp (.603) = 1.83
- Exclude Exp (.604) = 1.83
- Truancy Exp (.273) = 1.31
In SPSS ordinal regression the reference category for nominal explanatory variables is indicated by the value 1, and for all three variable the value ‘1’ indicates ‘yes’. The fact that the ORs are greater than 1 tells us that students who do not have SEN, who do not report truanting and who have never been excluded from school are
In the original model - before we entered In our new model (see table below) we can see that the logit for Black Caribbean students (ethnic2=5) is -.348 which is an odds ratio of Exp (-.189) = 0.71. Thus the under-representation of Black Caribbean students is very slightly reduced, but not by much. The statistical significance of the coefficient for Black Caribbean is still very high (
It is worth noting that the test of parallel lines for the model is significant, so strictly speaking the proportional odds assumption is rejected, although we should remember the anti-conservative nature of this test.
For completeness you
You will see that with the inclusion of |