1. Association Predicting One Variable from Another

2. Correlation Usually refers to Pearson’s r computed on two interval/ratio scale variables. It measures the degree to which variance in one variable is “explained” by a second variable It measures the strength of a linear relationship between the variables

3. Definition of r

4. Properties of r r is symmetrical and varies from -1 to +1 0 indicates no correlation or relationship ±1 indicates a perfect correlation (knowledge of one variable makes it possible to predict the second one without any error).

5. Properties of r 2 r 2 is symmetrical and varies from 0 to 1 r 2 is the proportion of the variability in one variable that is “explained by” the other variable cor.test(x, y, method=“pearson”) cor(x, y, method=“pearson”)

12. Spearman’s rho For rank/ordinal data. Pearson correlation computed on ranks If Spearman coefficient is larger than Pearson, it may indicate a non- linear relationship Ties make it difficult to compute p values

13. Kendall’s tau For rank/ordinal data Evaluate pairs of observations (x i, y i ) and (x j, y j ) Concordant – (x i > x j ) and (y i > y j ) OR (x i < x j ) and (y i < y j ) Discordant – (x i > x j ) and (y i y j )

14. Kendall’s tau-a

15. Kendall’s tau b Divide by total number of pairs adjusted for all ties

16. Kendall’s tau c For grouped (tabled data) where the table is not square (rows ≠ columns)

17. Nominal Measures Measures based on Chi-Square: –Phi coefficient –Cramer’s V –Contingency coefficient –Odds ratio

18. Phi and Cramer’s V Phi ranges from 0 to 1 in a 2x2 table but can exceed 1 in larger tables. Cramer’s V adds a correction to keep the maximum value at 1 or less:

19. Contingency Coefficient Ranges from 0 to <1 depending on the number of rows and columns with 1 indicating a high relationship and 0 indicating no relationship

20. Odds Ratio For 2 x 2 tables it shows the relative odds between the two variables ab cd

21. > Table <- xtabs(~Sex+Goods, data=EWG2) > Table Goods Sex Absent Present Female 38 28 Male 16 30 > ChiSq <- chisq.test(Table) > ChiSq Pearson's Chi-squared test with Yates' continuity correction data: Table X-squared = 4.7644, df = 1, p-value = 0.02905

22. library(vcd) > assocstats(Table) X^2 df P(> X^2) Likelihood Ratio 5.7073 1 0.016894 Pearson 5.6404 1 0.017552 Phi-Coefficient : 0.224 Contingency Coeff.: 0.219 Cramer's V : 0.224 > cor(as.numeric(EWG2$Sex), as.numeric(EWG2$Goods), use="complete.obs") [1] 0.2244111 > oddsratio(Table, log=FALSE) [1] 2.544643