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

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

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

6. Population Sample A X A µ _ Sample B X B Sample E X E Sample D X D Sample C X C _ _ _ _  sasa sbsb scsc sdsd sese n n n nn

7. Population Sample A Sample B Sample E Sample D Sample C _  XY r XY

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

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

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

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

12. Population Sample A Sample B Sample E Sample D Sample C _  XY r XY

13. 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 H 0 :  XY = 0 H 1 :  XY  0 where r N - 2 1 - r 2 t =

14. -1  r  +1 -1    +1 Pearson’s r 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. -1  r  +1 -1    +1 Pearson’s r Pearson’s r can also be interpreted as the expected value of z Y given a value of z X. tend to deviate from the mean of X when they are expressed in standard deviation units. The expected value of z Y is z X *r If you are predicting z Y from z X where there is a perfect correlation (r=1.0), then z Y =z X.. If the correlation is r=.5, then z Y =.5z X.

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

18. Spearman’s Rank Order Correlation r s Point Biserial Correlation r pb