1. Correlation and Regression
Doctor of Education (EdD)
Analysing, Interpreting and Using Educational Research (Research Methodology)

2. Examples of correlation coefficients
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3. r = 0.3
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4. r = 0.5
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5. r = 0.7
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6. r = 0.9
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7. Grammar School selection
A test selects the top 25% at age 11:
11% failed who should not have
18% rightly passed
11% passed who should not have
60% rightly failed
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Based on a correlation of 0.7

8. Variance accounted for
Academic achievement
r = 0.7
(r2 = 0.49)
Cognitive measure of prior attainment / aptitude
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9. Measure of socioeconomic status
Academic achievement
r = 0.3
(r2 = 0.09)
Low SES
Measure of socioeconomic status
High SES
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10. Aggregated or Individual? “Ecological Fallacy”
Academic achievement
Correlations for:
Individual students = 0.3
School means = 0.9
Socioeconomic status
School 1 +
School 2 +
School 3 +
School 4 +
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11. But add one extreme point ...
Beware small samples:
r = 0.03
But add one extreme point ...
r = 0.33
(n = 30)
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12. Restricted range:
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13. © 2005 Robert Coe, University of Durham

14. Regression

15. One school’s maths GCSE grades:
How good are they? A* A B C D E F G U 2 17 25 14 18 11 8 3
45%
% FSM?
=15%
Socioeconomic status?
School % 5A*-C?
=56%
Subject difficulty?
Students’ability?
Prior attainment?
© 2005 Robert Coe, University of Durham

16. Value Added as we know it:
Average performance for people with that test score A* A B C D E F G U
RESIDUAL
Average residual = 0.26
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YELLIS test score

17. Cognitive
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18. Social
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19. © 2005 Robert Coe, University of Durham

20. Output from SPSS:
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21. Issues in regression Check residuals are Normally distributed
Check for collinearity in explanatory variables
Use adjusted R2
Which explanatory variables to include?
© 2005 Robert Coe, University of Durham

22. Doctor of Education (EdD)
Regression to the mean
Doctor of Education (EdD)
Analysing, Interpreting and Using Educational Research (Research Methodology)

23. Measures with less than perfect reliability
A test with test-retest correlation r=0.7 is repeated after an interval. What would you expect for the TEST 2 scores of
A person who achieved a very high score on TEST 1
A person who achieved a very low score on TEST 1
How will the overall distribution of scores on the two tests compare?
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24. © 2005 Robert Coe, University of Durham

25. Two subgroups with different means
Students with high SES tend to get higher test scores.
Two students have the same TEST 1 scores, but one is high SES, the other low SES. What would you expect their TEST 2 scores to be?
© 2005 Robert Coe, University of Durham

26. © 2005 Robert Coe, University of Durham

27. Is social class more important than early ability?
Feinstein, L (2003) ‘Inequality in the early cognitive development of British children in the 1970 cohort’. Economica, 70, 277,
© 2005 Robert Coe, University of Durham
Feinstein (2003)

28. Or is it just regression to the mean?
© 2005 Robert Coe, University of Durham