Some implications of the logical calculus for empirical classes for social science methodology

An exposition of a calculus for empirical classes (CEC), one of the few attempts by logicians to deal with the problem of constructs and indicators, is presented. The CEC provides the groundwork for a formal structure for the situation in which individuals have a degree of membership in various classes rather than having either membership or nonmembership—a situation nearly always true in empirical research. The CEC is presented and its relation to various social science concepts is mentioned. An application of the CEC model to latent structure analysis (LSA) suggests alternatives to the local independence assumption including one called the local scale assumption, which has a close relation to a Guttman scale.     

Variable error: variance-covariance heterogeneity, block size and type L error rates

The degree to which blocked (VE) data satisfies the assumptions of compound symmetry required for a repeated measures ANOVA was studied. Monte Carlo procedures were used to study the effect of violation of this assumption, under varying block sizes, on the Type l error rate. Populations of 10,000 subjects for each of two groups, the underlying variance-covariance matrices reflecting a specific condition of violation of the homogeneity of covariance assumptions, was generated based on each of three actual experimental data sets. The data were blocked in various ways, VE calculated, and subsequently analyzed by a repeated measures ANOVA. The complete process was replicated for four covariance homogeneity conditions for each of the three data sets, resulting in a total of 22,000 simulated experiments. Results indicated that the Type l error rate increases as the degree of heterogeneity within the variance-covariance matrices increases when raw (unblocked) data are analyzed. With VE, the effects of within-matrix heterogeneity on the Type l error rate are inconclusive. However, block size does seem to affect the probability of obtaining a significant interaction, but the nature of this relationship is not clear as there does not appear to be any consistent relationship between the size of the block and the probability of obtaining significance. For both raw and VE data there was no inflation in the number of Type l errors when the covariances within a given matrix were homogeneous, regardless of the differences between the group variance-covariance matrices.     

Investigation of Body Comparison Among Adolescent Girls1

Grade differences in appearance and nonappearance social comparisons, and targets for body comparison were examined in adolescent girls. A model describing potential contributors to, and consequences of, body comparison tendency was examined. Girls (n= 545) completed measuring social comparisons, targets for comparisons, dieting in response to comparisons, body attitudes, eating patterns, psychological variables, height, and weight. Appearance and nonappearance social comparisons increased with age. Girls reported comparing their bodies most frequently with peers and fashion models. Body comparison tendency was significantly predicted by: importance of thinness, internalization of socio‐cultural ideal, friend concern with weight, body image instability, competitiveness, grade, public self‐consciousness, perfectionism, and family concern with weight. Predictors of dieting in response to body comparison were also explored.     

The conditioning of textual responses using “extrinsic” reinforcers

Six 4-year-old Ss were presented with a textual program consisting of 26 words arranged so the word stimuli were gradually combined into sentences and then short “stories.” Three Ss were given the No-Reinforcement condition first, and only social reinforcers were presented. They were switched to the Reinforcement condition as soon as they requested discontinuance of the activity. The other three Ss were given Reinforcement—No Reinforcement—Reinforcement treatments. The No-Reinforcement treatment in this case lasted until S requested discontinuance of the activity. The reinforcers were mixed edibles and trinkets, as well as tokens backed up by small plastic toys on a 1:24 ratio. The unit of response was the number of new texts acquired as a result of each of the 45-min experimental sessions. It was demonstrated that the program, procedure, and reinforcement conditions produced curves which are analogous to those produced in common operant-conditioning procedures. The results indicate that other operant principles may be studied in this significant area of human behavior, with important practical consequences.     

Statistical power for the two-factor repeated measures ANOVA

Determining a priori power for univariate repeated measures (RM) ANOVA designs with two or more within-subjects factors that have different correlational patterns between the factors is currently difficult due to the unavailability of accurate methods to estimate the error variances used in power calculations. The main objective of this study was to determine the effect of the correlation between the levels in one RM factor on the power of the other RM factor. Monte Carlo simulation procedures were used to estimate power for the A, B, and AB tests of a 2×3, a 2×6, a 2×9, a 3×3, a 3×6, and a 3×9 design under varying experimental conditions of effect size (small, medium, and large), average correlation (.4 and .8), alpha (.01 and .05), and sample size (n = 5, 10 ,15, 20, 25, and 30). Results indicated that the greater the magnitude of the differences between the average correlation among the levels of Factor A and the average correlation in the AB matrix, the lower the power for Factor B (and vice versa). Equations for estimating the error variance of each test of the two-way model were constructed by examining power and mean square error trends across different correlation matrices. Support for the accuracy of these formulae is given, thus allowing for direct analytic power calculations in future studies.     

Homosexualität und Prägung

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