# Ordinal Regression Exercise

We have seen that Black Caribbean students are systematically under-represented relative to White British students in entry to higher tiers of the age 14 national mathematics test. This difference remains significant even after controlling for prior attainment, socio-economic class of the home and gender. However are there other variables in the LSYPE dataset that may account for their under-representation in entry to the higher tiers?

Use the LSYPE 15,000 dataset  to work through each of the following questions. Answer them in full sentences with supporting tables or graphs where appropriate as this will help when you to better understand how you may apply these techniques to your own research. The answers are on the next page.

Note: The variable names as they appear in the SPSS dataset are listed in italics. We have also included some hints in italics.

Question 1

Explore the relationship between ethnic group (ethnic2) and a) having an identified Special Educational Need (sen), b) whether the student reported truanting at any time during year 9 (truancy) and c) whether the student has been excluded from school at any point during Years 7 and 9 (exclude). What are the differences between Black Caribbean and White British students on these variables? Are any differences statistically significant?

Use crosstabs and chi-square analyses.

Question 2

Complete an ordinal regression similar to the one we have used as an example throughout this module but entering the variables SEN, truancy and exclude along with the factors (ethnic2, gender and sec2) and the covariate (ks2stand). Are SEN, truancy and exclude related to the likelihood of a student being entered to a higher mathematics tier? What are the odds ratios for these three new variables?

Use the Parameter Estimates Table and calculate the odds ratios.

Question 3

Does the addition of these new variables change the ethnic Odds Ratios substantially compared to Figure 5.8.3 (Page 5.3)? Are Black Caribbean students still under-represented relative to White British students in entry to the higher maths tiers?

Compare the two Parameter Estimate Tables.

Question 4

Is the assumption of ‘Proportional Odds’ met for this final version of the model?

Request a 'Test of Parallel Lines' from the 'Output' submenu when running the regression analysis.

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