The document discusses correlation and regression, emphasizing the work of Sir Francis Galton and Karl Pearson, and outlines the assumptions necessary for correlation analysis. It includes examples like the Tower of London task and explores concepts like dose-response relationships and the coefficient of determination (r²). The document also highlights the importance of variability for accurate hypothesis testing in correlation studies.

1. Correlation
Brian J. Piper, Ph.D., M.S.

2. Objectives
• Scatterplots
• Correlation
–r
– r2
• Regression

3. Sir Francis Galton
• Polymath: meteorology, geography
• Behavioral Genetics 1822-1911
– Twin studies
– Eugenics

4. Scatterplot

5. Scatterplots Aren’t Perfect

6. Big-Picture

7. Karl Pearson’s Product-Moment
Correlation (r)
• Range: -1.0 to 0 to +1.0
• Sign: + or –
• Strength: +1.0/-1.0 or 0.0
1857-1936

8. Assumptions of Correlation
• 1) interval or ratio data
• 2) X & Y normally distributed
• 3) linear relationship

9. Also, degrees of freedom = N - 2

11. Age Differences in Tower of London
Behavior (N=325)
Piper et al. (2012) Behavior Research Methods, 44, 110-123. http://pebl.sourceforge.net/

12. Tower of London
Example #2
•Developed by Tim
Shallice in 1982 as a
simplified version of the
Tower of Hanoi
•Sensitive to brain
damage

13. Dose-Response (Example #3)
• Threshold Model: This is the Threshold Model
standard model in pharmacology. 8
Increasing the dose beyond a 7
6
certain point will produce a linear
Response
5
response. 4
3
• Caffeine example: Increasing the 2
dose of caffeine will cause an 1 a
0
increase response (e.g. heart 1 2 3 4 5 6
rate). Dose
a= No Observable Effect Level

14. Restriction of Range
• Optimal test of your hypothesis of a correlation
requires as much variability as possible

15. Restriction of Range
• Optimal test of your hypothesis of a correlation
requires as much variability as possible

16. Coefficient of Determination
• r2 = proportion of variance accounted for
r r2
.80 .64
.40 .16

17. Tower of London by Age
Best Performance
Trail Making Test: 19.5
Tower of London: 40.9
Piper et al. (2012) Behavior Research Methods, 44, 110-123. . http://pebl.sourceforge.net/

18. Terminology
• Correlational Design: several variables
measured simultaneously
• Correlation (r): statistic
• Amphetamine dose and locomotor activity
example

19. Directionality
• # of Churches (A) & # violent crimes (B) have r
= +0.30
• Does A cause B?
• Does B cause A?

20. Directionality
• # of Churches (A) & # violent crimes (B) have r
= +0.30
• Does A cause B?
• Does B cause A?
• Does a 3rd variable (population size, C)
independently cause A & B?

21. Exercise
• Correlation among measures?
• Paired t-test?