u Describes the relationship between two or more variables. Describes the strength of the relationship in terms of a number from -1.0 to Describes the direction of the relationship as positive or negative.

Types of Correlations Variable X increases Variable Y increases Positive Correlation Value ranging from.00 to 1.00 Example: the more you eat, the more weight you will gain

Types of Correlations Variable X decreases Variable Y decreases Positive Correlation Value ranging from.00 to 1.00 Example: the less you study, the lower your test score will be

Types of Correlations Variable X increases Variable Y decreases Negative Correlation Value ranging from to.00 Example: the older you are, the less flexible your body is

Types of Correlations Variable X decreases Variable Y increases Negative Correlation Value ranging from to.00 Example: the less time you study, the more errors you will make

Correlation Strength Weak or none Weak Moderate Strong 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 Correlation A scattergram or scatter plot visually represents a correlation The X axis is on the horizontal The Y axis is on the vertical.

Correlation: IQ and GPA IQGPA

Correlation: IQ and Errors IQ Errors

Correlation: IQ and Weight IQWeight

Caution Do 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 Determination Square the coefficient of correlation. r =.50 r 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 r 2 =.36 or 36 % Thirty six percent of reading achievement is related to IQ. Reading achievement and IQ share 36% of the variance.

Factors Influencing Correlation When 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 Correlation The 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 Correlation Higher 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 Correlation There 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 Formulas X is nominal data Y is nominal data Correlation Formula: Phi coefficient Example: Correlation of sex (male/female) and choice of car color (red, black, blue, white, silver)

Choosing Correlation Formulas X is nominal data Y is ordinal data Correlation Formula: Rank biserial coefficient Example: Correlation of race and rank in school

Choosing Correlation Formulas X is nominal data Y is interval data Correlation Formula: Point biserial Example: Correlation of sex and GPA

Choosing Correlation Formulas X is ordinal data Y 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 interval Y is interval Correlation Formula: Pearson correlation coefficient Example: Age and the number of minutes it takes to solve a problem

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