Describes the relationship between two or more variables.

Describes the strength of the relationship in terms of a number from -1.0 to +1.0.

Describes the direction of the relationship as positive or negative.

Types of CorrelationsVariable X increasesVariable Y increases

Positive CorrelationValue ranging from .00 to 1.00Example: the more you eat, the more weight you will gain

Types of CorrelationsVariable X decreasesVariable Y decreases

Positive CorrelationValue ranging from .00 to 1.00Example: the less you study, the lower

your test score will be

Types of CorrelationsVariable X increasesVariable Y decreases

Negative CorrelationValue ranging from -1.00 to .00Example: the older you are, the less

flexible your body is

Types of CorrelationsVariable X decreasesVariable Y increases

Negative CorrelationValue ranging from -1.00 to .00Example: the less time you study, the

more errors you will make

Correlation Strength

.00 - .20 Weak or none .20 - .40 Weak.40 - .60 Moderate.60 - .80 Strong.80 - 1.00 Very strong

Positive or Negative? IQ and reading achievement Anxiety and test scores Amount of calories consumed and weight gain. Amount of exercise and weight gain Reading achievement and math achievement Foot size and math ability

Caution!Correlation does not indicate causation.Correlation only establishes that a

relationship exists; it reflects the amount of variability that is shared between two variables and what they have in common.

Examples:Amount of ice sold and number of bee

stings.SAT scores and GPA in college.

A Picture of CorrelationA scattergram or scatter plot visually

represents a correlationThe X axis is on the horizontalThe Y axis is on the vertical.

Correlation: IQ and GPAIQ GPA110 2.5140 4.080 1.0100 2.0130 3.590 1.5120 3.070 .5

43210

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GPA

IQ

Correlation: IQ and ErrorsIQErrors

80 14120 6100 1090 12130 4110 8140 270 16 151050

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Errors

IQ

Correlation: IQ and WeightIQ Weight120 170100 16070 120140 13090 200130 11080 150110 140

200190180170160150140130120110

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Weight

IQ

CautionDo not interpret the coefficient of correlation

as a percent!

If you want to know the percentage of variance in one variable that is accounted for by the variance in the other variable, compute the coefficient of determination

Coefficient of DeterminationSquare the coefficient of correlation.r = .50r 2 = .25 or 25 %Twenty five percent of the variance in one

variable can be accounted for by the variance in the other variable.

Example: Coefficient of Determination

The correlation between IQ and reading at its highest level: r = .60

r2 = .36 or 36 %

Thirty six percent of reading achievement is related to IQ. Reading achievement and IQ share 36% of the variance.

Factors Influencing CorrelationWhen interpreting the correlation coefficient,

always consider the nature of the population in which the two variables were observed.

The correlation coefficient will vary from one population to another.

Factors Influencing CorrelationThe relationship of variables may differ from

population to population.Example: Physical prowess and age are

correlated between the ages of 10 and 16.Example: Physical prowess and age are not

correlated between the ages of 20 and 26.

Factors Influencing CorrelationHigher correlations are expected in a

heterogeneous population than in a homogeneous one.Example: In elementary and high school, there

is a positive correlation between height and success in basketball.

Example: In the pros, there is no such correlation.

Factors Influencing CorrelationThere may be a correlation between two

variables not because there is a relationship between them but because both are related to a third variable.Example: Average teacher salary for 20 years

and the cost of hard liquor.

Choosing Correlation FormulasX is nominal dataY is nominal data

Correlation Formula: Phi coefficientExample: Correlation of sex

(male/female) and choice of car color (red, black, blue,

white, silver)

Choosing Correlation FormulasX is nominal dataY is ordinal data

Correlation Formula: Rank biserial coefficient

Example: Correlation of race and rank in school

Choosing Correlation FormulasX is nominal dataY is interval data

Correlation Formula: Point biserialExample: Correlation of sex and GPA

Choosing Correlation FormulasX is ordinal dataY is ordinal or interval data (interval data

must be converted to ordinal) Correlation Formula: Spearman rank coefficient Example: Correlation between rank and GPA

Choosing Correlation Formulas X is intervalY is interval

Correlation Formula: Pearson correlation coefficient Example: Age and the number of minutes it takes to

solve a problem

THANK YOU !!