Phi Tests for Nominal Data

Abstract

Nominal data are the simplest type of data. Unlike ordinal data (Chap. 9) and continuous data (Chaps. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33 and 34), they are assumed not to have a stepping function. Examples are genders. Age classes, family names. Of nominal data the simplest versions are the bifurcated data (binary data, dichotomous data, yes no data). As an example, 75 males and 75 females may be assessed for successful exams:

Success	Yes	No
Males	50(a)	25(b)
Females	50(c)	25(d)

The value of [(a × d) – (b × c)] can be used to estimate the level of association. In the above example the level of association is 0. The gender does not give the faintest prediction of the chance of a successful exam. In the underneath example the level of association equals 1 (100 %).

Success	Yes	No
Males	50(a)	0(b)
Females	0(c)	50(d)

The outcome predicts the chance of a successful exam with 100 % certainty. Phi values, otherwise called Cramer’s V’s, are used to calculate the precise level of association.