lecture 1 from a college level research methods in psychology course taught in the spring 2012 semester by Brian J. Piper, Ph.D. (psy391@gmail.com) at Linfield College, correlation, assumptions

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?