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Correlation

Correlation. Introduction. Two meanings of correlation Research design Statistical Relationship Scatterplots. Relationship Scatterplots Quantification of relationship Correlation coefficient range +1.0 to - 1.0. r = .20. r = .50. r = .80. r = -.10. r = -.60. r = -.90.

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Correlation

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  1. Correlation

  2. Introduction • Two meanings of correlation • Research design • Statistical • Relationship • Scatterplots

  3. Relationship • Scatterplots • Quantification of relationship • Correlation coefficient • range +1.0 to - 1.0

  4. r = .20

  5. r = .50

  6. r = .80

  7. r = -.10

  8. r = -.60

  9. r = -.90

  10. Pearson Product Moment Correlation

  11. Relationship • Scatterplots • Quantification of relationship • Correlation coefficient • range +1.0 to - 1.0 • Pearson Product Moment Correlation

  12. Covariance

  13. Assumptions when using Pearson: • The relationship is linear. • The scale of measurement is interval or ratio • That there is a bivariate normal distribution - X and Y scores are normally distributed in the population. • Homogeneity of variance - at each X score Y scores in the population are normally distributed and vice versa.

  14. Significance of correlations

  15. Interpreting correlations r2 • proportional reduction in error

  16. Effect sizeand Power • Cohen • .10 small effect size • .30 medium effect size • .50 large effect size • To get power of .80, number of participants required are: • 783 for small effect size • 85 for medium effect size • 28 for large effect size

  17. Potential Problems • Correlation and causality 2. Restricted range 3. Outliers.

  18. Alternative Correlational Techniques • Point - biserial coefficientrpb • The Phi coefficient - φ • Spearman Rank Order Correlation

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