The average test score for the data underlying the graphs in Figure 3 and Figure 5, as a proportion of the maximum possible score, was .71, corresponding to a raw test score of 49.85. Kane (1977) article, unambiguously referring to the index of dependability as Φ . Dimitrov (2003) wrote“Brennan and Kane (1977) introduced a dependability index, Φ(λ) ....” Both of these references areincorrect. Brennan and Kane’s (1977) article never used the Greek letter Φ for the index of dependability; it
was consistently denoted as M(C). It is apparent that the preferred notation for the Brennan-Kane dependability index changed at some point, from M(C) to Φ(λ), probably in Brennan (1980).
Such notational discrepancies are of course not important in and of themselves. I have mentionedthem in an effort to clarify this area of the literature, and to assist users of the Lertap 5 software system; the Lertap manual uses the term M(C), not Φ(λ), when it refers to the index of dependability.
The magnitude of the index of dependability depends on the cut score. The C in M(C) and the λ in Φ(λ) refer to the value used for the cut score, expressed as a proportion. For example, M(.50) and Φ(.50) would refer to the value of the dependability index when the cut score has been set to 50% of the maximum possible test score.
Figure 5 graphically portrays the relationship between Φ(λ) and cut score. The straight line in Figure 5corresponds to the value of coefficient alpha for the data whose standard errors of measurement are plotted in Figure 3 above; in this case α = 0.83. The other line in Figure 5 traces the value of Φ(λ) for various values of λ , the cut score. (Note that the cut score values seen along the abscissa of Figure 5 are in fact proportions – the decimal point has been omitted.)The average test score for the data underlying the graphs in Figure 3 and Figure 5, as a proportion of the maximum possible score, was .71, corresponding to a raw test score of 49.85.