Download presentation

Presentation is loading. Please wait.

1
**Correlation and Regression**

Doctor of Education (EdD) Analysing, Interpreting and Using Educational Research (Research Methodology)

2
**Examples of correlation coefficients**

© 2005 Robert Coe, University of Durham

3
r = 0.3 © 2005 Robert Coe, University of Durham

4
r = 0.5 © 2005 Robert Coe, University of Durham

5
r = 0.7 © 2005 Robert Coe, University of Durham

6
r = 0.9 © 2005 Robert Coe, University of Durham

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 © 2005 Robert Coe, University of Durham 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 © 2005 Robert Coe, University of Durham

9
**Measure of socioeconomic status**

Academic achievement r = 0.3 (r2 = 0.09) Low SES Measure of socioeconomic status High SES © 2005 Robert Coe, University of Durham

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 + © 2005 Robert Coe, University of Durham

11
**But add one extreme point ...**

Beware small samples: r = 0.03 But add one extreme point ... r = 0.33 (n = 30) © 2005 Robert Coe, University of Durham

12
Restricted range: © 2005 Robert Coe, University of Durham

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 © 2005 Robert Coe, University of Durham YELLIS test score

17
Cognitive © 2005 Robert Coe, University of Durham

18
Social © 2005 Robert Coe, University of Durham

19
**© 2005 Robert Coe, University of Durham**

20
Output from SPSS: © 2005 Robert Coe, University of Durham

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? © 2005 Robert Coe, University of Durham

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

Similar presentations

OK

Immunobiology: The Immune System in Health & Disease Sixth Edition

Immunobiology: The Immune System in Health & Disease Sixth Edition

© 2019 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google