THE PRODUCT MOMENT CORRELATION

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31-Dec-09
THE PRODUCT MOMENT CORRELATION
The PRODUCT MOMENT CORRELATION is a method of
giving a number that describes the strength of
the and correlation. The following slides will
show you how to calculate this value.
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The number will be between -1 and 1 -1 ? Perfect
negative correlation 0 ? No correlation 1 ?
Perfect positive correlation
Which has the better correlation?
The PRODUCT MOMENT CORRELATION is a method of
giving a number that describes the correlation.
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First find the numbers called Sxx Sx2 (Sx)2
n (n 10 for the above) Syy Sy2 (Sy)2
n (n 10 for the above) Sxy Sxy
(SxSy) n (n 10 for the above)
These will be in the data book that you have in
the exam
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Sx2 463 (Sx)2 3721 n 10 Sy2
400 (Sy)2 3600 n 10 Sxy 422 (Sx)(Sy)
3660 n 10
Sxx Sx2 (Sx)2 n ? 463 372.1 90.9 Syy
Sy2 (Sy)2 n ? 400 360 40 Sxy Sxy
(SxSy) n ? 422 366 56
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Sxx ? Sx2 (Sx)2 n 90.9 Syy ? Sy2 (Sy)2
n 40 Sxy ? Sxy (SxSy) n 68
Product Moment coefficient r r Sxy
v(SxxSyy) r 56 v(90.9 x 40) r 56 60.29 r
0.929
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Sx2 572 (Sx)2 4900 n 10 Sy2
480 (Sy)2 4096 n 10 Sxy 514 (Sx)(Sy)
4480 n 10
Sxx Sx2 (Sx)2 n ? 572 490 82 Syy
Sy2 (Sy)2 n ? 480 409.6 70.4 Sxy
Sxy (SxSy) n ? 514 448 66
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Sxx Sx2 (Sx)2 n ? 572 490 82 Syy
Sy2 (Sy)2 n ? 480 409.6 70.4 Sxy
Sxy (SxSy) n ? 514 448 66
Product Moment coefficient r r Sxy
v(SxxSyy) r 66 v(82 x 70.4) r 56 76 r
0.74
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PRODUCT MOMENT CORRELATION r 0.93
PRODUCT MOMENT CORRELATION r 0.74