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Psyc_315_-_Winter_2010_-_Class_8

Psyc_315_-_Winter_2010_-_Class_8 - Recap of Last Class...

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1 Recap of Last Class Concepts of Correlation • Scatterplots Patterns of Correlation • Questions? Chapter 7 Correlation coefficients Concepts of Correlation 3 Degree of Relationship Low or No Relationship Medium Relationship High or Perfect Relationship Negative (-) Direction Positive (+) Direction
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Patterns of Correlation 4 Correlation Linear Correlation (points roughly follow a straight line) Curvilinear Correlation (points do not follow a straight line) Inverted U U Shaped Positive Negative Low / No Pearson Correlation Coefficient Correlation coefficient : Expresses quantitatively the magnitude & direction of the relationship, and is expressed by r. Only measures linear relationships. 5 Correlation coefficient ( r ) varies between -1 and +1 Value gives us the Magnitude of the Relationship Sign gives us the Direction of the Relationship +ve direction -ve direction +1 or –1 Perfect Relationship 0 No Relationship 0 to <1/>-1 Imperfect Relationship The Covariance A single number that represents the degree and direction of the linear association between two variables. Cov = (X - X)(Y - Y) n Step 1: Express each X and Y as a deviation score: X - X and Y - Y Step 2: Obtain the product of the paired deviation scores for each person (this is the cross product ) Step 3: Sum the cross products: (X - X)(Y - Y) Step 4: Divide by the number of pairs of scores, n 6
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The Covariance Example ( Positive Correlation ) Person X Y X-X Y-Y (X-X)(Y-Y) A 9 13 4 4 16 B 7 9 2 0 0 C 5 7 0 -2 0 D 3 11 -2 2 -4 E 1 5 -4 -4 16 n = 5 X= 5 Y= 9 sum = 28 Cov = 28/5=5.6 7 0 3 6 9 12 15 0 3 6 9 12 X Values Cov = ( X - X )( Y - Y ) n The Covariance Example ( Negative Correlation ) Person X Y X-X Y-Y (X-X)(Y-Y) A 9 5 4 -4 -16 B 7 11 2 2 4 C 5 7 0 -2 0 D 3 9 -2 0 0 E 1 13 -4 4 -16 n = 5 X= 5 Y= 9 sum = -28 Cov = -28/5 = -5.6 8 0 3 6 9 12 15 0 3 6 9 12 X Values Cov = ( X - X )( Y - Y ) n The Covariance Example ( Zero Correlation ) Person X Y X-X Y-Y (X-X)(Y-Y) A 9 13 4 2.8 11.2 B 7 9 2 -1.2 -2.4 C 5 7 0 -3.2 0.0 D 3 9 -2 -1.2 2.4 E 1 13 -4 2.8 -11.2 n = 5 X= 5 Y= 10.2 sum = 0 Cov = 0/5 = 0 9 0 3 6 9 12 15 0 3 6 9 12 X Values Cov = ( X - X )( Y - Y ) n
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The Pearson Product-Moment Coefficient of Correlation Correlation coefficient, r , indicates the precise degree of linear correlation between two variables Can vary from -1 (perfect negative correlation) through 0 (no correlation) to +1 (perfect positive correlation) r is more useful than Covariance because it is independent of the underlying scales of the two variables if two variables produce an r of .5, for example, r will still equal .5 after any linear transformation of the two variables linear transformation
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