Skew and internal consistency

The effects of skew on the standardized item alpha were examined with Monte Carlo techniques. Alphas computed from normal variables were compared with alphas from lognormal variables, ranks, and skewed versus normal Likert-type variables. The extent and direction of skew were varied, as was the size of the population interitem correlation (rho), the number of items, and the number of categories for Likert-type variables. Because the average interitem correlation affects alpha and skew affects the average interitem correlation, the effect of skew on the average interitem correlation also was examined. Results indicated that skew decreased the average interitem correlation and produced small decreases in alpha that were largest when skew was large, rho was small, items were skewed in opposite directions, and there were fewer items.     

Power functions of loudness magnitude estimations and auditory brainstem evoked responses

The correspondence between subjective and neural response to change in acoustic intensity was considered by deriving power functions from subjective loudness estimations and from the amplitude and latency of auditory brainstem evoked response components (BER). Thirty-six subjects provided loudness magnitude estimations of 2-sec trains of positive polarity click stimuli, 20/sec, at intensity levels ranging from 55 to 90 dB in 5-dB steps. The loudness power function yielded an exponent of .48. With longer trains of the same click stimuli, the exponents of BER latency measures ranged from -.14 for wave I to -.03 for later waves. The exponents of BER amplitude-intensity functions ranged from .40 to .19. Although these exponents tended to be larger than exponents previously reported, they were all lower than the exponent derived from the subjective loudness estimates, and a clear correspondence between the exponents of the loudness and BER component intensity functions was not found.     

Consistency of magnitude estimations with conceptual data dimensions used for sonification

In two experiments listeners assessed how sounds represented data, as might be used in sonification. In Experiment 1, 209 undergraduates used magnitude estimation to define the relationship between three sound attributes (frequency, tempo, modulation index) and 10 data dimensions (size, temperature, pressure, velocity, number of dollars, urgency, proximity, attractiveness, danger, mass). Polarities and slopes (i.e. power function exponents) are reported and compared to predictions from the literature. In Experiment 2, 226 new participants demonstrated polarities and slopes are stable across a direct replication. Results show that listener expectations depend on both sound and data dimensions in use. While there are some unanimous expectations across listeners, there are also differences due to different mental models formed by participants, which may relate to listening experience. Copyright © 2006 John Wiley & Sons, Ltd.     

Size,convexity, and curvature magnitude estimations of curvilinear forms

Groups of Os made magnitude estimates of size, convexity, and curvature of patterns along a shape continuum. College Os repeated the procedure for a given physical measure in three successive sessions, but high school Os made only one set of estimates. The apparent size for the patterns was found to grow with an exponent between .700 and .755 for high school and college Os. The magnitude estimates for convexity and curvature were less reliable than the size estimates both between college and high school Os and within college Os over successive sessions. The magnitude estimates from the high school and college Os showed a faster apparent growth of curvature than of convexity.     

Modification of magnitude estimations in thermotactile perception during self-generated and externally generated movements

Fourteen participants felt a 'cold' stimulus move across a fingertip. When movement was self-controlled, the stimulus was reported as feeling less 'cold' than when movement was externally generated.     

Repeated magnitude estimations with a variable standard: Sequential effects and other properties

Twelve Ss made magnitude estimations of the loudness of each one of a sequence of pure tones according to the rule R(N) = R(N - 1) · [S(N)/S(N - 1)], where R(N) is the response on Trial N, R(N - 1) is the response on Trial N - 1, and S(N)/S(N - 1) is the judged ratio of the “loudness” of the pure tone presented on Trial N to that of the pure tone presented on Trial N - 1. It was found that these magnitude estimations were assimilated toward the immediately preceding stimuli as far as five trials back in the sequence of stimuli. In addition, ratio judgments were consistently asymmetric and the data displayed a form of “time order error.” In all cases, there are similar effects displayed in category judgment data. These and other data imply that at least some kinds of magnitude estimations may involve a judgment of the “difference” or “distance” between pairs of stimuli as a first step in the production of the response required by the judgment situation.     

A note on the internal consistency of the sexual orientation method

The S.O.M. was administered to two samples of homosexuals. There was some reduction in the number of inconsistent response patterns when a modified scoring system was used. Further examination of the data indicated that an inconsistent style of response might not be simply an index of faking.     

Coefficient alpha and related internal consistency reliability coefficients

The author studied the conditions under which coefficient alpha and 10 related internal consistency reliability coefficients underestimate the reliability of a measure. Simulated data showed that alpha, though reasonably robust when computed on n components in moderately heterogeneous data, can under certain conditions seriously underestimate the reliability of a measure. Consequently, alpha, when used in corrections for attenuation, can result in nontrivial overestimation of the corrected correlation. Most of the coefficients studied, including lambda 2, did not improve the estimate to any great extent when the data were heterogeneous. The exceptions were stratified alpha and maximal reliability, which performed well when the components were grouped into two subsets, each measuring a different factor, and maximized lambda 4, which provided the most consistently accurate estimate of the reliability in all simulations studied.     

A note on item analysis and the criterion of internal consistency

The implications contained in Richardson's article on item analysis in March 1936 issue ofPsychometrika are examined in the light of multiple factor theory. It is shown that item analysis is a necessary, but not a sufficient condition for the construction of a test which shall measure a single trait. The intercorrelations of certain items selected by a method of item analysis are examined, found to contain many zero and some negative correlations. Multiple factor analysis showed that eight traits were measured by the items which had been asserted to measure only one.     

On quantifying the magnitude of sex-role endorsement

The conception of sex-role attributes as multidimensional has led to the development of the median split and various difference score approaches for assigning individuals to sex-rote categories. In response to the criticisms of information loss and imprecision when applying such methods, this report presents a data manipulation (medz) which combines the masculine and feminine scales in an additive rather than subtractive manner, upholds the continuous nature of the variables, and utilizes the median split for categorization. Comparisons of this technique with the t ratio, difference/median split, and direct difference approaches indicate greater differentiation among androgynous subjects when assessed according to the medz. An application of the process and some rationale for its implementation are provided.     

Imputation of missing categorical data by maximizing internal consistency

This paper suggests a method to supplant missing categorical data by reasonable replacements. These replacements will maximize the consistency of the completed data as measured by Guttman's squared correlation ratio. The text outlines a solution of the optimization problem, describes relationships with the relevant psychometric theory, and studies some properties of the method in detail. The main result is that the average correlation should be at least 0.50 before the method becomes practical. At that point, the technique gives reasonable results up to 10–15% missing data.We thank Anneke Bloemhoff of NIPG-TNO for compiling and making the Dutch Life Style Survey data available to use, and Chantal Houée and Thérèse Bardaine, IUT, Vannes, France, exchange students under the COMETT program of the EC, for computational assistance. We also thank Donald Rubin, the Editors and several anonymous reviewers for constructive suggestions.     

Effects of stimulus context on magnitude estimations and category ratings of perceived loudness--the spacing of intensity intervals

Effects of stimulus context on magnitude estimations and on category ratings were examined for a range of stimulus intensities of a 1-kHz tone. The stimuli were distributed in equal-interval steps of energy so they formed a perceptual cluster of high-intensity tones with a perceptual outlier at the lowest intensity. According to the Invariance Principle, the shape of the response function should not be affected by the distribution of stimulus intensities. However, neither magnitude estimations nor category ratings yielded the linear functions predicted from the Invariance Principle when plotted on log-log axes. Instead, both procedures yielded concave-upward response functions for the group data as well as for the individual data sets of the six subjects. Moreover, unlike previous reports of a nonlinear relationship, we found a linear relationship between magnitude estimations and category ratings. Rather than implying an equivalence of the underlying sensory scales, however, our results may imply subjects used a similar attention strategy for both procedures. We consider some theoretical suggestions, including an attention-band concept, for modification of a multistage stimulus-response (S-R) transformation model.