Correlation

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Correlation
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Correlation Coefficient

• aka Pearson Product-Moment Correlation
  Coefficient.
• Correlation coefficient summarizes the relations
  b/t 2 variables, both direction and degree
  (closeness). Scattergram summary.
• Sample r population ? (Greek rho).
• Can take values from 1 thru 0 to 1.
• Sign tells direction ( or -) magnitude or value
  tells closeness or degree.

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Positive Correlation
When one variable increases, the other also
increases.
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Negative Correlation
When one variable increases, the other decreases.
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Zero Correlation
No relation when one variable increases, the
other variable neither increases nor decreases.
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Correlation Sign Magnitude
The sign indicates the direction of the
relationship. If positive, they increase
together. If negative, when one goes up the
other goes down.
The absolute value tells the strength of the
relationship. Values close to 1 and 1 indicate
very strong relations. As r ? 0, the
relationship is weaker. If r0, no relation. If
r1, perfect relation.
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Perfect Positive Correlation (r 1)
Notice the straight line. When r1 or -1, all
the points will fall on a line.
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Example Correlations
Variable X Variable Y
Salary Taxes paid
Shyness people greeted at party
Price of car Prestige of car
Price of quartz watch Accuracy of time kept
Income of sales people Number of cars sold
Anxiety Memory exam
Correlation
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Computing the Correlation
The definition
The correlation coefficient, r, is the average
cross-product of z scores. zX is X in z-score
form, zY is Y in z-score form and we multiply the
two. We add them all and divide by N to get the
average.
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Computational Example
-1.58 (60-66.8)/4.31
-1.51(102-150.7)/32.2
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Some examples
X Y correlation
Extroversion Job Performance of Managers .10
Corporate social responsibility Corporate financial performance .20
Job performance supervisor report Job performance peer report .30
High School SAT College GPA (year 1) .60
Weight-self report Weight-measured .90
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Review

• What are the maximum and minimum values of r?
• What does r summarize?
• What is the symbol for the population value of r?
• How does r show direction of relations?
• How does r show magnitude of relations?

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Test Questions
B
D
A
C
Which figure shows the most positive correlation?
A, B, C, D?
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Test Questions

• Which of the four choices below shows the
  correlation with the strongest association
  between X and Y?
• a. -.50
• b. .0
• c. .25
• d. 1.02