# B Notation

The notation in this chapter follows .

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