1. A Significance Test for r An estimator r    = 0 ? t-test

2. A Significance Test for r t test = r SE r = r 1 - r 2 n - 2 = r 1 - r 2 df = n - 2

3. A Significance Test for r H 0 :  = 0 H A :   0 t test = rn - 2 1 - r 2

4. Example Research question: Is there a significant relationship between TVDI and soil moisture in the Glyndon data set?

5. t test = r SE r = r 1 - r 2 n - 2 = r 1 - r 2 A Significance Test for r  r & n

6. A Significance Test for r: Sample Size For example, suppose we have three samples of variables X and Y of sizes n = 10, n = 100, and n = 1000, all with r = 0.5  = 0.05

7. Orange County, North Carolina Economic Development Commission Housing http://www.co.orange.nc.us/ecodev/stats/homestat.htm

9. Tired of calculating r manually?  S-Plus

11. Correlation Coefficients Pearson’s Product Moment Correlation Coefficient  interval or ratio data only What about ordinal data?

12. Spearman’s Rank Correlation Coefficient r s = 1 -  di2di2 i=1 i=n n 3 - n 6

13. http://www.mnstate.edu/wasson/ed602spearcorr.htm Spearman’s Rank Correlation Coefficient: Example

15. A Significance Test for r s SE r s = 1 n -1 t test = rsrs SE r s = r s n -1 df = n - 1

16. http://www.mnstate.edu/wasson/ed602spearcorr.htm Spearman’s Rank Correlation Coefficient: Example

17. Pearson’s r - Assumptions 1.Interval or ratio scale data 2.Selected randomly 3.Linear 4.Joint bivariate normal distribution  S-Plus (qqnorm)