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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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IQ
Correlation: IQ and WeightIQ Weight120 170100 16070 120140 13090 200130 11080 150110 140
200190180170160150140130120110
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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
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