The Relationship Between the Phi Coefficient and the G Index1

Abstract

The value of the phi coefficient (Φ) cannot, in general, be uniquely determined from the G index. Its value is shown to obey the inequalities

G-1/3+G ≤ Φ ≤ 1+G/3-G if -1 < G < 1

When G equals -1 or 1 so does Φ. As a consequence of this Φ is too unstable over item reflection when used as a measure of similarity between individuals. G is a more suitable choice.