# 5.10 Reporting the Results of Ordinal Regression

Perhaps the most noteworthy outcome from the analysis of the example completed above is the finding that Black Caribbean students are under-represented in entry to the higher mathematics test tiers relative to White British students in the ratio 0.66:1, i.e. the odds of being entered to the higher tiers for Black Caribbean students are about two-thirds the odds for White British students. As we saw in Module 4 (Page 4.8) we can express this in % terms by subtracting 1 from the OR and multiplying by 100: (0.66-1)*100 = a 34% decrease in the odds for Black Caribbean students. Put the other way round the odds for White British students of being entered for higher tiers are (1/.66)=1.5 times or 50% greater than the odds for Black Caribbean students. Importantly our models show that this finding cannot be explained in terms of the prior attainment of the students or by differences in social class composition. If you are interested to see a full ordinal analysis of the tiering data and how it is reported then you can find this in the following journal article:

• Strand, S. (2011). The White British-Black Caribbean achievement gap: Tests, tiers and teacher expectations. British Educational Research Journal, available online at iFirst.

This shows how an ordinal model was built hierarchically over a series of steps, looking first at prior attainment then progressively adding further explanatory variables. Note that the results from an analysis of the summary LSYPE dataset used here will not agree precisely with the analyses presented in the paper because slightly different variables are used, and the data in the paper have been weighted to account for selection and non-response issues and for clustering within schools, but the overall pattern of findings will be similar. The paper also discusses in depth the interpretation of the model findings, and what these mean in relation to policy and practice. Statistical models are only useful if the results and their implications can be communicated clearly to the intended audiences.