### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 119-134 |

Journal | Applied psychological measurement |

Volume | 2 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1978 |

### Keywords

- IR-98582

### Cite this

*Applied psychological measurement*,

*2*(1), 119-134. https://doi.org/10.1177/014662167800200112

}

*Applied psychological measurement*, vol. 2, no. 1, pp. 119-134. https://doi.org/10.1177/014662167800200112

**Coefficients for tests from a decision theoretic point of view.** / van der Linden, Willem J.; Mellenbergh, Gideon J.

Research output: Contribution to journal › Article › Academic

TY - JOUR

T1 - Coefficients for tests from a decision theoretic point of view

AU - van der Linden, Willem J.

AU - Mellenbergh, Gideon J.

PY - 1978

Y1 - 1978

N2 - From a decision theoretic point of view a general coefficient for tests, d, is derived. The coefficient is applied to three kinds of decision situations. First, the situation is considered in which a true score is estimated by a function of the observed score of a subject on a test (point estimation). Using the squared error loss function and Kelley’s formula for estimating the true score, it is shown that d equals the reliability coefficient from classical test theory. Second, the situation is considered in which the observed scores are split into more than two categories and different decisions are made for the categories (multiple decision). The general form of the coefficient is derived, and two loss functions suited to multiple decision situations are described. It is shown that for the loss function specifying constant losses for the various combinations of categories on the true and on the observed scores, the coefficient can be computed under the assumptions of the beta-binomial model. Third, the situation is considered in which the observed scores are split into only two categories and different decisions are made for each category (dichotomous decisions). Using a loss function that specifies constant losses for combinations of categories on the true and observed score and the assumption of an increasing regression function of t on x, it is shown that coefficient d equals Loevinger’s coefficient H between true and observed scores. The coefficient can be computed under the assumption of the beta-binomial model. Finally, it is shown that for a linear loss function and Kelley’s formula for the regression of the true score on the observed score, the coefficient equals the reliability coefficient of classical test theory.

AB - From a decision theoretic point of view a general coefficient for tests, d, is derived. The coefficient is applied to three kinds of decision situations. First, the situation is considered in which a true score is estimated by a function of the observed score of a subject on a test (point estimation). Using the squared error loss function and Kelley’s formula for estimating the true score, it is shown that d equals the reliability coefficient from classical test theory. Second, the situation is considered in which the observed scores are split into more than two categories and different decisions are made for the categories (multiple decision). The general form of the coefficient is derived, and two loss functions suited to multiple decision situations are described. It is shown that for the loss function specifying constant losses for the various combinations of categories on the true and on the observed scores, the coefficient can be computed under the assumptions of the beta-binomial model. Third, the situation is considered in which the observed scores are split into only two categories and different decisions are made for each category (dichotomous decisions). Using a loss function that specifies constant losses for combinations of categories on the true and observed score and the assumption of an increasing regression function of t on x, it is shown that coefficient d equals Loevinger’s coefficient H between true and observed scores. The coefficient can be computed under the assumption of the beta-binomial model. Finally, it is shown that for a linear loss function and Kelley’s formula for the regression of the true score on the observed score, the coefficient equals the reliability coefficient of classical test theory.

KW - IR-98582

U2 - 10.1177/014662167800200112

DO - 10.1177/014662167800200112

M3 - Article

VL - 2

SP - 119

EP - 134

JO - Applied psychological measurement

JF - Applied psychological measurement

SN - 0146-6216

IS - 1

ER -