Chapter 8: Relationships among Variables SFM 651: Research Methods Dr. Johnson

Correlation A statistical technique used to determine the relationship between 2 or more variables. Positive – Small –> Small or Large -> Large Ex……Strength and body weight Negative – Small -> Large or Large -> Small Ex……Driving distance vs driving accuracy No relationship – it is more random

Correlation Correlation does not imply cause and effect Necessary, but not sufficient

Pearson Product Moment coefficient of correlation Most commonly used method of computing correlation r There is a line of best fit.

What does r mean? Significance – reliability or confidence in the likelihood of a statistic occurring again if the study were repeated. Coefficient of determination = r² Used to interpret meaningfulness of correlation How much is related to the other = listed as a %

Predictions Line of best fit. Is there a line that most closely fits inside the data? Can be positive or negative

Partial and semi partial correlations A 3rd variable has an effect Shoe size and math score (age?) Semipartial One variable is taken out from other two

Multiple Regressions Model used for predicting a criterion from 2 or more independent variable Golf score Driving distance Driving accuracy Greens in regulation Scrambling Putting

Multiple Regressions Y= A+ (b1X1)+(b2X2)+ …… + (biXi)

Problems with Multiple Regressions Shrinkage – Validity decreases when prediction formula is used with a new sample Population Specificity Regression equation loses accuracy when put into a new sample.

Factor analysis Used to reduce a set of data by grouping similar variables