1. Educational Statistics Copyright © 2014 Robert J. Hall, Ph.D. Correlation

2. Educational Statistics Topics  Measure of Relationship Strength Direction  Scatterplot  Conceptual Formula  Computational Formula  Assumptions  Problems Effecting the Interpretation of the Correlation Coefficient

3. Educational Statistics Measure of Relationship  In a correlational study, two measures -- representing the variables of interest -- are given to one group of subjects.  The subject’s scores on both measures are summarized, and the relationship between the scores on the two measures is examined.

4. Educational Statistics Measure of Relationship  When the correlation coefficient is used to describe a linear relationship, the coefficient can take on values from -1.00 to +1.00. The sign of the correlation indicates the direction of the relationship between two variables.

5. Educational Statistics Measure of Relationship  A positive relationship means that low scores on X go with low scores on Y whereas high scores on X go with high scores on Y.  A negative relationship means that as scores on X increase, scores on Y decrease. The absolute magnitude or size of the correlation coefficient -- that is, ignoring the plus or minus sign -- indicates the strength of the relationship between X and Y.

6. Educational Statistics Measure of Relationship  A correlation of +.95 or of -.95 indicates a very strong relationship between the two variables.  A correlation of 0 indicates that there is no linear relationship between the variables. Guilford's suggested interpretations for values of r. r xy Value Interpretation Less than.20Slight; almost negligible relationship.20 -.40Low correlation; definite but small relationship.40 -.70Moderate correlation; substantial relationship.70 -.90High correlation; marked relationship.90 - 1.00Very high correlation; very dependable relationship

7. Educational Statistics Computation X Predictor Y Response 7.18.3 6.08.0 3.87.0 4.25.6 2.34.4 1.92.5 3.32.8 5.45.0 7.17.2 5.76.3

8. Educational Statistics Conceptual / Computational Formulas

9. Educational Statistics Computation / Conceptual Formula X Predictor Y Response (X-  X)(Y-  Y)(X-  X) (Y-  Y) 7.18.32.422.596.27 6.08.01.322.293.02 3.87.0-0.881.29-1.14 4.25.6-0.48-0.110.05 2.34.4-2.38-1.313.12 1.92.5-2.78-3.218.92 3.32.8-1.38-2.914.02 5.45.00.72-0.71-0.51 7.17.22.421.493.61 5.76.31.020.590.60 4.685.710.00 27.96

10. Educational Statistics Conceptual Formula

11. Educational Statistics Computation / Computational Formula X Predictor Y Response X 2 Y 2 XY 7.18.3 50.4168.8958.93 6.08.0 36.0064.0048.00 3.87.0 14.4449.0026.60 4.25.6 17.6431.3623.52 2.34.4 5.2919.3610.12 1.92.5 3.616.254.75 3.32.8 10.897.849.24 5.45.0 29.1625.0027.00 7.17.2 50.4151.8451.12 5.76.3 32.4939.6935.91 46.8057.10250.34363.23295.19

12. Educational Statistics Computational Formula

13. Educational Statistics Problems Effecting the Interpretation  Non Linear Relationship

14. Educational Statistics Problems Effecting the Interpretation  Outliers