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 (r s )

3. 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 <.50Moderate 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 (D 2 )

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

9. Review - Steps to Completing Regression (by hand) 1.Construct a data table (1 observation per row) 2. Compute each X i Y i, and ΣX i Y i 3.Compute n, ΣX i, ΣY i 4.Compute means (M X, M Y ) 5.Compute ΣX i 2, ΣY i 2, ((ΣX i ) 2, (ΣY i ) 2 ) 6.Compute the SS(X), SS(Y), and SP XY 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 (M X, M Y ) 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 X i Y i, and Σ X i Y i 3.Compute n, ΣX i, ΣY i 4.Compute means ( M X, M Y ) 5.Compute ΣX i 2, ΣY i 2, (ΣX i ) 2, (ΣY i ) 2 6.Compute the SS(X), SS(Y), SP XY 7. Compute

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

12. Interpreting Scatterplots

14. Correlation?

15. Not much

16. Other problems