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

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

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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.

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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.

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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.

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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

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Educational Statistics Computation X Predictor Y Response

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Educational Statistics Conceptual / Computational Formulas

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

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Educational Statistics Conceptual Formula

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

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Educational Statistics Computational Formula

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Educational Statistics Problems Effecting the Interpretation Non Linear Relationship

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Educational Statistics Problems Effecting the Interpretation Outliers

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