Regression to the mean in test–retest data; evaluating an intervention
education
At a large secondary school, 180 Year 11 students sat a maths test in Term 1 and a similar test in Term 3. Both tests have mean 60 and standard deviation 15, and the correlation between students' Term 1 and Term 3 scores is r=0.6.
The 18 students who scored below 40 in Term 1 (mean 35) took a catch-up programme. Their mean in Term 3 was 46. The principal says the programme raised scores by 11 points.
Figure 1 shows each student's Term 1 and Term 3 scores (illustrative data with these summary statistics). The line shows where a student would be if they scored the same in both terms.
Scatterplot of Term 3 score against Term 1 score for 180 students, with the 18 catch-up programme students (Term 1 below 40) shown in a different colour and a line marking equal scores in both terms; most low scorers are above the line and most high scorers are below it. Data are illustrative.Facts you may need
(a)
Write the regression equation for predicting Term 3 score from Term 1 score, and predict the Term 3 score for a student who scored 35 in Term 1.
(b)
Use your answer to (a) and Figure 1 to evaluate the principal's claim.
(c)
Design a study that would fairly evaluate the catch-up programme.
(d)
Give TWO other situations where regression to the mean could create a misleading conclusion. Explain the likely effect of each.
A catch-up programme that 'works' — Scholarship Statistics | Xametric
