Phi Coefficient (in Generalizability Theory)

The ϕ coefficient in generalizability theory—not to be confused with the ϕ correlation coefficient used to estimate the degree of association between dichotomous categorical variables or the ϕ (λ) statistic used to estimate the dependability of test scores at various cut points—is one of two coefficients used in generalizability theory (or G theory) to estimate score dependability (which is analogous to score reliability in classical test theory). The first coefficient, which is often called the generalizability coefficient (or G coefficient), is used to estimate the dependability of scores for tests designed for relative decisions (also known as norm-referenced decisions like those typically made with standardized tests). The second, which is often called the ϕ coefficient, is used to estimate the dependability of scores on a ...