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

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

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.

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

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.

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 Low correlation; definite but small relationship Moderate correlation; substantial relationship High correlation; marked relationship Very high correlation; very dependable relationship

Educational Statistics Computation X Predictor Y Response

Educational Statistics Conceptual / Computational Formulas

Educational Statistics Computation / Conceptual Formula X Predictor Y Response (X-  X)(Y-  Y)(X-  X) (Y-  Y)

Educational Statistics Conceptual Formula

Educational Statistics Computation / Computational Formula X Predictor Y Response X 2 Y 2 XY

Educational Statistics Computational Formula

Educational Statistics Problems Effecting the Interpretation  Non Linear Relationship

Educational Statistics Problems Effecting the Interpretation  Outliers