A note on syntactical and semantical functions

We say that a semantical function is correlated with a syntactical function F iff for any structure A and any sentence we have A F A .It is proved that for a syntactical function F there is a semantical function correlated with F iff F preserves propositional connectives up to logical equivalence. For a semantical function there is a syntactical function F correlated with iff for any finitely axiomatizable class X the class ^–1X is also finitely axiomatizable (i.e. iff is continuous in model class topology).     

A note on measuring human functions in systems

Abstract.— Performances in different man-machine system functions are usually not directly comparable_: It is suggested that some functions may be measured through quantities corresponding to β and d' of the signal Detection Theory. Necessary assumptions are that the task can be reduced to a binary decision and that the decision depends upon a subjective value of certainty which vanes in one dimension. The method of measurement is illustrated by an example with a hypothetical system comprising three functions: detecting, identifying and interpreting.     

A note on monotonicity of item response functions for ordered polytomous item response theory models

A monotone relationship between a true score (τ) and a latent trait level (θ) has been a key assumption for many psychometric applications. The monotonicity property in dichotomous response models is evident as a result of a transformation via a test characteristic curve. Monotonicity in polytomous models, in contrast, is not immediately obvious because item response functions are determined by a set of response category curves, which are conceivably non-monotonic in θ. The purpose of the present note is to demonstrate strict monotonicity in ordered polytomous item response models. Five models that are widely used in operational assessments are considered for proof: the generalized partial credit model (Muraki, 1992, Applied Psychological Measurement, 16, 159), the nominal model (Bock, 1972, Psychometrika, 37, 29), the partial credit model (Masters, 1982, Psychometrika, 47, 147), the rating scale model (Andrich, 1978, Psychometrika, 43, 561), and the graded response model (Samejima, 1972, A general model for free-response data (Psychometric Monograph no. 18). Psychometric Society, Richmond). The study asserts that the item response functions in these models strictly increase in θ and thus there exists strict monotonicity between τ and θ under certain specified conditions. This conclusion validates the practice of customarily using τ in place of θ in applied settings and provides theoretical grounds for one-to-one transformations between the two scales.     

Lacking power impairs executive functions

Four experiments explored whether lacking power impairs executive functioning, testing the hypothesis that the cognitive presses of powerlessness increase vulnerability to performance decrements during complex executive tasks. In the first three experiments, low power impaired performance on executive-function tasks: The powerless were less effective than the powerful at updating (Experiment 1), inhibiting (Experiment 2), and planning (Experiment 3). Existing research suggests that the powerless have difficulty distinguishing between what is goal relevant and what is goal irrelevant in the environment. A fourth experiment established that the executive-function impairment associated with low power is driven by goal neglect. The current research implies that the cognitive alterations arising from powerlessness may help foster stable social hierarchies and that empowering employees may reduce costly organizational errors.     

Analyzing coefficients of psychophysical power functions

Somemathematical properties of coefficients of power functions were analyzed. The size of correlations between intercepts (the logarithm of the coefficient) andexponent.s depends on the choice of unit of measurement of the physical stimuli. When the mean of logarithms of a set of responses is uncorrelated with the exponent, the absolute size of the correlation between the intercept and the exponent increases as the geometricmean of the stimulus measures deviatesfrom one. When the geometric mean is less than one, the correlation is positive, and when it is greater than one, the correlation is negative. Similar trends hold for a nonzero correlation between the exponent and the mean logarithm of a set of responses. The power of statistical tests of differences between mean intercepts also depends on the geometric mean of the stimuli. Power is reduced as the geometric mean deviates from one. Effects are illustrated with real data.     

A note on reliability

A formula for internal consistency reliability is developed within the framework of the analysis of variance. The test items are assumed to be homogeneous, but may have any weights. Data needed for computation are the student test scores, and the total number of items answered so as to have the same weight. It is shown that this formula reduces to the Kuder-Richardson (21) for item weights of one and zero. Some empirical validation is offered.Social Security Board (on military leave.)