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Chapter 21

Chapter 21. Correlation. Correlation. A measure of the strength of a linear relationship Although there are at least 6 methods for measuring correlation, we are going to learn 2: Pearson product-moment correlation coefficient (Pearson ’ s r ) and Spearman ’ s rho ( r s ). Pearson ’ s r.

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Chapter 21

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  1. Chapter 21 Correlation

  2. Correlation • A measure of the strength of a linear relationship • Although there are at least 6 methods for measuring correlation, we are going to learn 2: • Pearson product-moment correlation coefficient (Pearson’s r) and • Spearman’s rho (rs)

  3. Pearson’s r

  4. Pearson’s r

  5. Interpreting Pearson’s r • r’s vary from -1 to +1 +1 = perfect positive linear relationship 0 = no linear relationship -1 = perfect negative linear relationship

  6. Magnitude of the Relationship • Absolute value of r: 0 < r < .25 Low correlation .25 < r < .50 Moderate correlation .50 < r High correlation

  7. Spearman’s Rank-Order Correlation • “Pearson-on-the-Ranks” • Rank each score with respect to the other scores of that variable • Calculate the difference (D) between the ranks of each bivariate observation, or pair of scores • Square the difference (D2)

  8. Spearman’s Rank-Order Correlation • Calculate rs using:

  9. Review - Steps to Completing Regression (by hand) 1. Construct a data table (1 observation per row) 2. Compute each XiYi,and ΣXiYi 3. Compute n, ΣXi, ΣYi 4. Compute means (MX, MY) 5. Compute ΣXi2, ΣYi2, ((ΣXi)2, (ΣYi)2) 6. Compute the SS(X), SS(Y), and SPXY 7. Compute m (slope) and b (Y-intercept) 8. Find a point on the line: use a value of X on either end of the range, and compute the corresponding Y 9. Plot the point (MX, MY) and the point just found 10. Connect the points, label the line with the equation

  10. Review - Steps to Computing a Pearson r 1. Construct a data table (1 observation per row) 2. Compute each XiYi, and ΣXiYi 3. Compute n, ΣXi, ΣYi 4. Compute means ( MX, MY) 5. Compute ΣXi2, ΣYi2, (ΣXi)2, (ΣYi)2 6. Compute the SS(X), SS(Y), SPXY 7. Compute

  11. Review - Steps to Completing Spearman’s rho (rs) 1. Rank each score with respect to the other scores of that variable (highest score gets highest rank of 1) 2. Calculate the difference (Di) between the ranks of each bivariate observation, or pair of scores 3. Square the difference (Di2) 4. Calculate

  12. Interpreting Scatterplots

  13. Correlation?

  14. Not much

  15. Other problems

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