Selecting Statistics  


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

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