research methods: correlation i
DESCRIPTION
lecture 1 from a college level research methods in psychology course taught in the spring 2012 semester by Brian J. Piper, Ph.D. ([email protected]) at Linfield College, correlation, assumptionsTRANSCRIPT
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Correlation
Brian J. Piper, Ph.D., M.S.
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Objectives
• Scatterplots• Correlation
– r– r2
• Regression
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Sir Francis Galton
• Polymath: meteorology, geography• Behavioral Genetics
– Twin studies– Eugenics
1822-1911
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Scatterplot
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Scatterplots Aren’t Perfect
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Big-Picture
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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
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Assumptions of Correlation
• 1) interval or ratio data• 2) X & Y normally distributed• 3) linear relationship
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Also, degrees of freedom = N - 2
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Age Differences in Tower of London Behavior (N=325)
Piper et al. (2012) Behavior Research Methods, 44, 110-123. http://pebl.sourceforge.net/
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Tower of LondonExample #2
•Developed by Tim Shallice in 1982 as a simplified version of the Tower of Hanoi
•Sensitive to brain damage
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Dose-Response (Example #3)• Threshold Model: This is the
standard model in pharmacology. Increasing the dose beyond a certain point will produce a linear response.
• Caffeine example: Increasing the dose of caffeine will cause an increase response (e.g. heart rate).
Threshold Model
0
1
2
3
4
5
6
7
8
1 2 3 4 5 6
Dose
Re
spo
nse
a
a= No Observable Effect Level
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Restriction of Range
• Optimal test of your hypothesis of a correlation requires as much variability as possible
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Restriction of Range
• Optimal test of your hypothesis of a correlation requires as much variability as possible
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Coefficient of Determination
• r2 = proportion of variance accounted for
r r2
.80 .64
.40 .16
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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/
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Terminology
• Correlational Design: several variables measured simultaneously
• Correlation (r): statistic• Amphetamine dose and locomotor activity
example
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Directionality
• # of Churches (A) & # violent crimes (B) have r = +0.30
• Does A cause B?• Does B cause A?
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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?
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Exercise
• Correlation among measures?• Paired t-test?