B Notation

The notation in this chapter follows Wright and Masters (1982).

Section Symbol Term Description
4.4 \(\beta_n\) Ability True (but unknown) developmental score of child \(n\)
4.4 \(\delta_i\) Difficulty True (but unknown) difficulty of item \(i\)
4.4 \(\delta_q\) Difficulty The combined difficulty of the items in equate group \(q\)
4.4 \(\pi_{ni}\) Probability True (but unknown) probability that child \(n\) passes item \(i\)
4.4 \(l\) Count The number of items in the equate group
4.4 \(w_i\) Count The number of respondents with an observed score on item \(i\)
4.6 \(P_{ni}\) Probability Estimated probability that child \(n\) passes item \(i\)
4.6 \(x_{ni}\) Data Observed response of child \(n\) on item \(i\), 0 or 1
4.6 \(W_{ni}\) Variance Variance of \(x_{ni}\)
4.6 \(z_{ni}\) Residual Standardized residual between \(x_{ni}\) and \(P_{ni}\)
4.6 \(N_i\) Count Number of responses on item \(i\)
5.6 \(r\) Correlation Correlation coefficient
6 \(D\) Score Developmental score of a child: D-score
6.2 \(sem\) Error Standard Error of Measurement: precision of the D-score