Statistical Test: Yule's Q, or Phi
Statistical Measure: Fisher's exact test, or Refer critical ratio of phi to a table of the unit normal curve, or Pearson chi-square
Notes: In this case, Yule's Q is equivalent to Goodman and Kruskal's Gamma and Phi is equivalent to Pearson's product moment r. In general, Q will be higher in absolute value than Phi because Q ignores pairs of cases which fall in the same category on one or both of the variables. Pearson chi-squares can be corrected for continuity (Yate's correction) but this is controversial. See Camilli and Hopkins (1978). Yule's Q: Yule, G. V., and Kendall, M. G. An Introduction to the Theory of Statistics Fourteenth edition. London: Griffin, 1957. p. 30 Phi: McNemar, Q. Psychological Statistics. Fourth edition. New York: Wiley 1969. p. 225 Critical ratio of phi: McNemar, Q. Psychological Statistics. Fourth edition. New York: Wiley 1969. p. 227 Fisher's exact test: Siegel, S. Nonparametric Methods for the Behavioral Sciences. New York: McGraw-Hill, 1956. p. 96 Pearson chi-square: Hays, W. L. Statistics for the Social Sciences. Second edition. New York: Holt, Rinehart, and Winston, 1973. p. 735
Software: phi: | SPSS: CROSSTABS | SAS: FREQ (For two dichotomous variables, Cramer's V is equivalent to phi) | Critical ratio of phi: | SPSS: CROSSTABS | SAS: FREQ | Fisher's exact test: | SPSS: CROSSTABS | Pearson chi square: | SPSS: CROSSTABS | SAS: FREQ
Statistical Measure: Fisher's exact test, or Refer critical ratio of phi to a table of the unit normal curve, or Pearson chi-square
Notes: In this case, Yule's Q is equivalent to Goodman and Kruskal's Gamma and Phi is equivalent to Pearson's product moment r. In general, Q will be higher in absolute value than Phi because Q ignores pairs of cases which fall in the same category on one or both of the variables. Pearson chi-squares can be corrected for continuity (Yate's correction) but this is controversial. See Camilli and Hopkins (1978). Yule's Q: Yule, G. V., and Kendall, M. G. An Introduction to the Theory of Statistics Fourteenth edition. London: Griffin, 1957. p. 30 Phi: McNemar, Q. Psychological Statistics. Fourth edition. New York: Wiley 1969. p. 225 Critical ratio of phi: McNemar, Q. Psychological Statistics. Fourth edition. New York: Wiley 1969. p. 227 Fisher's exact test: Siegel, S. Nonparametric Methods for the Behavioral Sciences. New York: McGraw-Hill, 1956. p. 96 Pearson chi-square: Hays, W. L. Statistics for the Social Sciences. Second edition. New York: Holt, Rinehart, and Winston, 1973. p. 735
Software: phi: | SPSS: CROSSTABS | SAS: FREQ (For two dichotomous variables, Cramer's V is equivalent to phi) | Critical ratio of phi: | SPSS: CROSSTABS | SAS: FREQ | Fisher's exact test: | SPSS: CROSSTABS | Pearson chi square: | SPSS: CROSSTABS | SAS: FREQ