# 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 |