# Module 4 Exercise Answers

There is arguably more than one way to achieve this but we have gone for a bar graph which uses
The mean
The table below shows that age 11 score is indeed a statistically significant predictor of
See
In order to explore just how much impact adding age 11 score as an explanatory variable has we re-ran the model but entered
As we have discussed on We can see where these reduction are calculated in the ‘Model summary’ which shows the -2LL for Block 1 is 14447 and for block 2 9056, hence the reduction in -2LL associated with adding age 11 score of 5391. More importantly the Model Summary shows us the Nagelkerke
pseudo-R The classification table (third table down) shows us just how much more accurately block 2 predicts the outcome compared to block 1. The model defined as block 1 correctly classifies 64.1% of cases – an improvement over the baseline model but still not great. The inclusion of
Below you will see the ‘Variables in the Equation’ table for block 2 with the ‘sig’ and Exp(B) columns from the same table for block 1. These are taken from the same SPSS output that we generated for question 3. Notice how in most cases the odds ratios [Exp(B)] are less in block 2 than they were in block 1. For example, as highlighted, students from a managerial or professional family background [SECshort(2)] are 4.7 times more likely to achieve
Before exploring the interaction statistically it is worth first examining the relationship by looking at a line graph (though remembering that this graph does not account for the influence of other explanatory variables such as gender and ethnicity).
As you may recall from
Let us check the ‘Variables in the equation’ for the logistic regression model when we include a
As we saw on
Yes, because p=.009 for the interaction term in the ‘Variables in the Equation’ table.
The OR is 3.68 / 1 = 3.68. Among students from routine, semi-routine and long-term unemployed homes those from single parent families are over 3.5 times more likely to be entitled to a FSM than those from dual parent families.
This OR is 0.31 / 0.05 = 6.2. Among pupils from managerial and professional homes those from single parent families are 6.2 times more likely to be entitled to a free school meal than those from dual parent families.
The OR for the increase in the odds of being entitled to a free school meal for single parent families from managerial homes vs. the increase for single parent families from routine homes is 6.2 / 3.68 = 1.68. So the proportionate increase in the odds of being eligible for a FSM is greater among high SEC families. We do not have to calculate this because this is what the exponent of the SEC*Single parent interaction tells us: Exp(.52) = 1.68 (note that the figure is slightly different from the logit of .56 shown in the table due to rounding). In short the OR for an interaction between two categorical variables is the ratio of two ORs! If the two ORs are identical then the ratio of the two ORs should equal 1.0. To the extent that the two component ORs are not the same then the interaction OR will depart from 1.0. So to conclude, while the absolute level of entitlement to a free school meal is higher among single parent families from routine homes than among single parent families from managerial homes (as we see in the graph) the |