UNDERSTANDING UNDERSTANDING DESCRIPTION AND DESCRIPTION AND

CORRELATIONCORRELATION

CORRELATION COEFFICIENTS: CORRELATION COEFFICIENTS: DESCRIBING THE STRENGTH DESCRIBING THE STRENGTH

OF RELATIONSHIPSOF RELATIONSHIPSPearson r Correlation Coefficient

Strength of relationshipDirection of relationshipValues of r range from 0.00 to ±1.00Scatterplots

CORRELATION COEFFICIENT CORRELATION COEFFICIENT OF OF ±±1.001.00

SCATTERPLOTSSCATTERPLOTS

IMPORTANT CONSIDERATIONSIMPORTANT CONSIDERATIONS

Restriction of RangeCurvilinear Relationship

EFFECT SIZEEFFECT SIZE

General Term that Refers to the Strength of Association Between Variables

Pearson r Correlation Coefficient is One Indicator of Effect Size

Advantage of Reporting Effect Size is that it Provides a Scale of Values that is Consistent Across All Types of Studies

EFFECT SIZEEFFECT SIZE

• Differences in effect sizes• Small effects near r = .15• Medium effects near r = .30• Large effects above r = .40

• Squared value of the coefficient r² - transforms the value of r to a percentage• Percent of shared variance between the two

variables

REGRESSION EQUATIONSREGRESSION EQUATIONS

Calculations used to predict a person’s score on one variable when that person’s score on another variable is already known

General Form: Y=a + bX

Y = Score we wish to predict

X = Score that is known

a = constant

b = weighing adjustment

MULTIPLE CORRELATIONMULTIPLE CORRELATION

Used to combine a number of predictor variables to increase the accuracy of prediction of a given criterion or outcome variable

Symbolized RY=a+b1X1 + b2X2 +…+bnXn

a=constant, b=weights, X=predictor R2

PARTIAL CORRELATION AND PARTIAL CORRELATION AND THE THIRD-VARIABLE THE THIRD-VARIABLE

PROBLEMPROBLEMProvides a Way of Statistically Controlling

Third Variables

STRUCTURAL MODELSSTRUCTURAL MODELS

Expected Pattern of Relationships Among a Set of VariablesPath analysis