CorrelationBrian J. Piper, Ph.D., M.S.
Objectives• Scatterplots• Correlation  –r  – r2• Regression
Sir Francis Galton• Polymath: meteorology, geography• Behavioral Genetics                1822-1911  – Twin studies  – Euge...
Scatterplot
Scatterplots Aren’t Perfect
Big-Picture
Karl Pearson’s Product-Moment         Correlation (r)             • Range: -1.0 to 0 to +1.0             • Sign: + or –   ...
Assumptions of Correlation• 1) interval or ratio data• 2) X & Y normally distributed• 3) linear relationship
Also, degrees of freedom = N - 2
Age Differences in Tower of London                    Behavior (N=325)Piper et al. (2012) Behavior Research Methods, 44, 1...
Tower of London      Example #2•Developed by TimShallice in 1982 as asimplified version of theTower of Hanoi•Sensitive to ...
Dose-Response (Example #3) • Threshold Model: This is the                                 Threshold Model   standard model...
Restriction of Range• Optimal test of your hypothesis of a correlation  requires as much variability as possible
Restriction of Range• Optimal test of your hypothesis of a correlation  requires as much variability as possible
Coefficient of Determination• r2 = proportion of variance accounted for      r     r2      .80   .64      .40   .16
Tower of London by Age                                                                Best Performance                    ...
Terminology• Correlational Design: several variables  measured simultaneously• Correlation (r): statistic• Amphetamine dos...
Directionality• # of Churches (A) & # violent crimes (B) have r  = +0.30• Does A cause B?• Does B cause A?
Directionality• # of Churches (A) & # violent crimes (B) have r  = +0.30• Does A cause B?• Does B cause A?• Does a 3rd var...
Exercise• Correlation among measures?• Paired t-test?
Research Methods: Correlation I
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Research Methods: Correlation I

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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

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Research Methods: Correlation I

  1. 1. CorrelationBrian J. Piper, Ph.D., M.S.
  2. 2. Objectives• Scatterplots• Correlation –r – r2• Regression
  3. 3. Sir Francis Galton• Polymath: meteorology, geography• Behavioral Genetics 1822-1911 – Twin studies – Eugenics
  4. 4. Scatterplot
  5. 5. Scatterplots Aren’t Perfect
  6. 6. Big-Picture
  7. 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. 8. Assumptions of Correlation• 1) interval or ratio data• 2) X & Y normally distributed• 3) linear relationship
  9. 9. Also, degrees of freedom = N - 2
  10. 10. Age Differences in Tower of London Behavior (N=325)Piper et al. (2012) Behavior Research Methods, 44, 110-123. http://pebl.sourceforge.net/
  11. 11. Tower of London Example #2•Developed by TimShallice in 1982 as asimplified version of theTower of Hanoi•Sensitive to braindamage
  12. 12. 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). Dosea= No Observable Effect Level
  13. 13. Restriction of Range• Optimal test of your hypothesis of a correlation requires as much variability as possible
  14. 14. Restriction of Range• Optimal test of your hypothesis of a correlation requires as much variability as possible
  15. 15. Coefficient of Determination• r2 = proportion of variance accounted for r r2 .80 .64 .40 .16
  16. 16. Tower of London by Age Best Performance Trail Making Test: 19.5 Tower of London: 40.9Piper et al. (2012) Behavior Research Methods, 44, 110-123. . http://pebl.sourceforge.net/
  17. 17. Terminology• Correlational Design: several variables measured simultaneously• Correlation (r): statistic• Amphetamine dose and locomotor activity example
  18. 18. Directionality• # of Churches (A) & # violent crimes (B) have r = +0.30• Does A cause B?• Does B cause A?
  19. 19. 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?
  20. 20. Exercise• Correlation among measures?• Paired t-test?

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