A theoretical distribution for mental test scores

The negative hypergeometric distribution of raw scores on mental tests is derived from certain assumptions relating to test theory. This result is checked empirically in a number of examples. Further derivations lead to the bivariate distribution of parallel tests which is also verified with actual data. The bivariate distribution of raw score and true score is also derived from a further assumption. This distribution is used to set confidence limits for true scores for persons with a given raw score.This work was supported in part by contract Nonr-2752(00) between the Office of Naval Research and Educational Testing Service. Reproduction in whole or in part for any purpose of the United States Government is permitted.     

Some generalizations of a theoretical distribution of mental test scores

The negative hypergeometric distribution may be generalized to provide distributions involving 3, 4, or more parameters. It is shown that, in the case of the binomial error model, such distributions correspond to quadratic, cubic, etc., regressions of true scores on raw scores. Explicit formulas are given for the bivariate moments required to fit these regressions and so estimate the parameters of the generalized hypergeometric distribution. Equations are also developed for fitting the 3- and 4-parameter distributions directly, i.e., without reference to the model, and the method for generalizing these is indicated. The methods developed are applied to objective test data with satisfactory results.This research was supported in part by Office of Naval Research Contract Nonr2752(00).The author is now at the University of Queensland, St. Lucia, Queensland, Australia.     

Receptive training of adjectival inflections in mental retardates

A generalized discrimination of /er/ and /est/ suffixes as labels for stimuli exemplifying comparative or superlative relationships was established in three institutionalized retardates through differential reinforcement. The subjects were first taught correct pointing in response to opposite adjectives (e.g., "big-small") presented as labels for simple visual stimuli, and then taught each of the comparatives, or each of the superlatives possible for those opposites (e.g., "big-bigger" and "small-smaller", or "big-biggest" and "small-smallest"). As training proceeded, novel combinations of the training stimuli were presented as unreinforced probes to display any developing generalization of the training. As training of comparative discrimination proceeded, correct pointing response to comparative probes was high, but correct response to superlative probes was low. When training of superlative discriminations replaced training of comparatives, correct response to superlative probes increased, and correct response to comparative probes remained high.     

Extending the temporal range of psychometric prediction by optimal linear filtering of mental test scores

Incorporating temporal decline in predictive validity into mental testing theory is outlined. Starting from multivariate regression of criterion on repeated measurements, an analytic extension results in a weighting function for repeated measurements, replacing the beta weights. Besides optimizing, the procedure permits an evaluation of any particular prognosis setting: In cases of exponentially declining predictive validity, prognostic range can be extended if concurrent validity is nonperfect by optimal weighting (predictive filtering) of repeated measurements. Considerable gain in prognostic range over the traditional approach can be achieved if predictive validity declines concavely downwards.This work was supported by grant Dr 58/3 from Deutsche Forschungsgemeinschaft.     

Hand Test indices of violent and destructive behavior for institutionalized mental retardates.

The Hand Test (Wagner, 1962) and the maladaptive behavior scale of the AAMD Adaptive Behavior Scale (ABS) were administered to 78 institutionalized retardates (46 males and 32 females) in order to investigate the relationship between violent and destructive behavior and two purported indicants of violent and destructive acting-out behavior on the Hand Test, the acting-out-score (AOS and movement-content response (ACT-MOV). Significant correlations between the two Hand Test indices and the number of types of violent and destructive behavior evinced during a three-month period were obtained.     

Demographic, clinical, and neurocognitive correlates of everyday functional impairment in severe mental illness

Although cognitive deficits often accompany severe mental illness, their implications for everyday functioning remain poorly understood. In this study, an occupational therapist (OT) rated the everyday functioning of 105 adult psychiatric patients. Using demographic, clinical, and cognitive variables, the authors tested alternative models to account for the observed variability in OT ratings. Although age, education, and the presence of schizophrenia each contributed to a model that accounted for 27% of the variation in functional independence, adding terms for auditory divided attention and verbal learning increased the proportion of explained variance to 45% and decreased the beta weights for age and education--but not schizophrenia--to nonsignificant levels. These findings demonstrate the relevance of cognitive performance to everyday functioning in severe mental illness. They are discussed with respect to hypothesized determinants of psychiatric disability.     

On the myth and the reality of the temporal validity degradation of general mental ability test scores

Claims of changes in the validity coefficients associated with general mental ability (GMA) tests due to the passage of time (i.e., temporal validity degradation) have been the focus of an on-going debate in applied psychology. To evaluate whether and, if so, under what conditions this degradation may occur, we integrate evidence from multiple sub-disciplines of psychology. The temporal stability of construct validity is considered in light of the evidence regarding the differential stability of g and the invariance of measurement properties of GMA tests over the adult life-span. The temporal stability of criterion-related validity is considered in light of evidence from long-term predictive validity studies in educational and occupational realms. The evidence gained from this broad-ranging review suggests that temporal degradation of the construct- and criterion-related validity of ability test scores may not be as ubiquitous as some have previously concluded. Rather, it appears that both construct and criterion-related validity coefficients are reasonably robust over time and that any apparent degradation of criterion-related validity coefficients has more to do with changes in the determinants of task performance and changes in the nature of the criterion domain rather temporal degradation per se (i.e., the age of the test scores). A key exception to the conclusion that temporal validity degradation is more myth than reality concerns decision validity. Although the evidence is sparse, it is likely that the utility of a given GMA test score for making diagnostic decisions about an individual deteriorates over time. Importantly, we also note several areas in need of additional and more rigorous research before strong conclusions can be supported.