Correlation --- Basic Concepts
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Correlation --- Basic Concepts. Consists of a set of ordered pairs Indicates both the magnitude and direction of the relationship between variables Range is from -1.0 to +1.0. 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60. * *

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Consists of a set of ordered pairs

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Consists of a set of ordered pairs

Correlation --- Basic Concepts

  • Consists of a set of ordered pairs

  • Indicates both the magnitude and direction of the relationship between variables

  • Range is from -1.0 to +1.0


Consists of a set of ordered pairs

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Son’s Height

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Fathers Height (in inches)


Consists of a set of ordered pairs

  • Consider these --- A correlation exists between:

  • The total amount of losses in a fire and the number of

  • firemen that were putting out the fire

  • Cigarette smokers and lower GPAs

  • The number of churches in a city and amount of alcohol

  • consumed

  • The amount of fat in diets and cancer rates


Consists of a set of ordered pairs

False Rejections

Correct Acceptances

Good

Job Performance

Poor

False Acceptances

Correct Rejections

Test scores

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Fail

Cut-off score


Consists of a set of ordered pairs

Computation of Standard Deviation & Variance

Deviation scores (scores minus the mean)

Squared deviation scores

TestScores

X

10

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50

-20

-10

0

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x

x2

400

100

0

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400

EX2 = 1000 (Sum of the squared deviation scores)

EX = 150

(EX/N) = 30 (Mean)

Mean of the sum of the squared deviation scores

EX2/N = 200 (the variance or s2)

= standard deviation or s

s2

200

= 14.14 (standard deviation)


Consists of a set of ordered pairs

Computational Formula for r

2 2

X Y XY X Y

1 4 4 1 16

2 3 6 4 9

3 5 15 9 25

4 7 28 16 49

5 6 30 25 36

X = 15 Y = 25  XY = 83  X = 55  Y = 135

N XY – ( X) ( Y) 5(83) – (15)(25)

[N X – ( X) ][N Y - ( Y) ] [5(55) – (15) ][5(135) – (25)

415 – 375 40 40

(275 – 225)(675 – 625) (50)(50) 50

r = =

= = = = .80

  • 2 2 2 2 2


Consists of a set of ordered pairs

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Positive Correlation

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Test Scores


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Negative Correlation

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Absenteeism (in hours)


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False Rejections

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Poor

False Acceptances

Correct Rejections

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Fail

Pass

Test Scores

Significant Correlation


Consists of a set of ordered pairs

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False Acceptances

Correct Rejections

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Fail

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No Correlation

Test Scores


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False Rejections

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Poor

False Acceptances

Correct Rejections

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Test Scores

Significant Correlation


Consists of a set of ordered pairs

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False Rejections

Correct Acceptances

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Poor

False Acceptances

Correct Rejections

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Fail

Pass

Test Scores

Significant Correlation


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