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http://www.york.ac.uk/depts/maths/histstat/people/

October 28 and 29. Sir Francis Galton. Karl Pearson. http://www.york.ac.uk/depts/maths/histstat/people/. Source: Raymond Fancher, Pioneers of Psychology. Norton, 1979. A correlation coefficient is a numerical expression of the degree of relationship between two continuous variables.

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  1. October 28 and 29 Sir Francis Galton Karl Pearson http://www.york.ac.uk/depts/maths/histstat/people/

  2. Source: Raymond Fancher, Pioneers of Psychology. Norton, 1979.

  3. A correlation coefficient is a numerical expression of the degree of relationship between two continuous variables.

  4. A correlation coefficient is a numerical expression of the degree of relationship between two continuous variables. What might be some practical uses of such a statistic?

  5. Pearson’s r -1  r  +1 -1    +1

  6. SampleC XC _ sc SampleD XD n _ sd Population n SampleB XB _  µ sb n SampleE XE SampleA XA _ _ se sa n n

  7. SampleC SampleD rXY Population rXY SampleB XY rXY SampleE SampleA _ rXY rXY

  8. Pearson’s r -1  r  +1 -1    +1 Pearson’s r is a function of the sum of the cross-product of z-scoresfor x and y.

  9. Pearson’s r  zxzy r = Where z is based on an uncorrected standard deviation, SS N N

  10. Pearson’s r  zxzy r = if z is based on a corrected standard deviation, SS N-1 N-1

  11. N  XY -  X  Y [N  X2 - ( X)2] [N  Y2 - ( Y)2] r = Pearson’s r … or, for your convenience,

  12. SampleC SampleD rXY Population rXY SampleB XY rXY SampleE SampleA _ rXY rXY

  13. r N - 2 t = 1 - r2 The familiar t distribution, at N-2 degrees of freedom, can be used to test the probability that the statistic r was drawn from a population with  = 0 H0 :  XY = 0 H1 :  XY  0 where

  14. Pearson’s r -1  r  +1 -1    +1 Pearson’s r can also be interpreted as how far the scores of Y individuals tend to deviate from the mean of X when they are expressed in standard deviation units.

  15. Pearson’s r -1  r  +1 -1    +1 Pearson’s r can also be interpreted as the expected value of zYgiven a value of zX. tend to deviate from the mean of X when they are expressed in standard deviation units. Theexpected value of zY is zX*r If you are predicting zY from zX where there is a perfect correlation (r=1.0), then zY=zX.. If the correlation is r=.5, then zY=.5zX.

  16. Factors that affect r • Non-linearity • Restriction of range / variability • Outliers • Reliability of measure / measurement error

  17. Spearman’s Rank Order Correlation rs Point Biserial Correlation rpb

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