Tests are perfectly reliable

Abstract

All test items are perfectly reliable. The unreliability of tost moms results solely from person fluctuations. The theory implies that: (1) test length effects are a sampling phenomenon; (2) person roliabilities can be compared from perRon characteristic curves; (3) all ICC for a unidimensional test have the s m e slope; (4) ICC are not necessarily invariant from one group to another; and (6) reliabilities of groups can be compared from ICC.A reliability coefficient of the theory is defined as the proportion of variance in obtained scores attributable to variance in average attribute level for subjects. Lower bounds for the classical reliability coefficient are also lower bounds for the new coefficient. Statistics calculated from this coefficient have no useful application.

The person response function as a tool in person-fit research

“…Properties of the PRF Weiss (1973) and Lumsden (1978) suggested m consider the PRF to be the probability that person i (i = 1 ..... n) obtains a 1 score on an item (denoted by random variable Si = 1) as a function of some item difficulty scale. With respect to the PRF, we assume that: 1.…”

“…A relatively rare approach to identifying aberrants is the use of the person response function (PRF), first discussed by Weiss (1973) and Lumsden (1978), and later discussed and applied by Trabin and Weiss (1983), Klauer and Rettig (1990), and Nering and Meijer (1998). The PRF, to be defined in greater detail later on, defines the probability of giving correct answers to dichotomous items as a function of an item difficulty scale.…”

Detection of aberrant responding on a personality scale in a military sample: An application of evaluating person fit with two-level logistic regression.

“…In Reise's (2000) approach, logistic regression is used for estimation of the parameters of a person response function (PRF; Lumsden, 1978;Nering & Meijer, 1998;Trabin & Weiss, 1983;Weiss, 1973, as cited in . The PRF shows the relationship between item endorsement and item severity for each person.…”

A Pearson-Type-VII item response model for assessing person fluctuation

“…However, the literature is scattered, and the phenomenon appears under such different names as 'oscillations' (Hull, 1917(Hull, , 1943, 'individual unreliability' (Mitra & Fiske, 1956), 'type-1 spontaneous variability' (Fiske & Rice, 1955), 'tremors' (Lumsden, 1977), and 'fluctuations' (Lumsden, 1978;Thouless, 1936), which is the term used here. Hull (1917) considered momentary variability to be a universal principle of behaviour and was the first to deal with the topic systematically.…”

“…However, 26 PSYCHOMETRIKA most of them converge essentially to the same basic model: a threshold model for binary items in which the individual fluctuation is assumed to be Gaussian. In a set of three papers, Lumsden (1977Lumsden ( , 1978Lumsden ( , 1980 gave what is probably the best-known systematization of this type of model. Furthermore, he provided a rationale based on Thurstone scaling and also related the different variations of the basic model to item response theory (IRT).…”