Variable criteria sequential stopping rule: Validity and power with repeated measures ANOVA,multiple correlation,MANOVA and relation to Chi-square distribution

The variable criteria sequential stopping rule (vcSSR) is an efficient way to add sample size to planned ANOVA tests while holding the observed rate of Type I errors, α_o, constant. The only difference from regular null hypothesis testing is that criteria for stopping the experiment are obtained from a table based on the desired power, rate of Type I errors, and beginning sample size. The vcSSR was developed using between-subjects ANOVAs, but it should work with p values from any type of F test. In the present study, the α_o remained constant at the nominal level when using the previously published table of criteria with repeated measures designs with various numbers of treatments per subject, Type I error rates, values of ρ, and four different sample size models. New power curves allow researchers to select the optimal sample size model for a repeated measures experiment. The criteria held α_o constant either when used with a multiple correlation that varied the sample size model and the number of predictor variables, or when used with MANOVA with multiple groups and two levels of a within-subject variable at various levels of ρ. Although not recommended for use with χ² tests such as the Friedman rank ANOVA test, the vcSSR produces predictable results based on the relation between F and χ². Together, the data confirm the view that the vcSSR can be used to control Type I errors during sequential sampling with any t- or F-statistic rather than being restricted to certain ANOVA designs.     

Extending generalized symmetric means to arbitrary matrix sampling designs

Generalized symmetric means are redefined in a way which allows them to be calculated for any matrix sampling design. It is proved that these sample gsm's are unbiased estimates of the analogous population gsm's. Illustrative examples are given.This paper is based on Applied Technology Center for Education Technical Memorandum 75-03-01. Special appreciation is expressed to Ken Sirotnik and Tom Knapp for their suggestions on clarifing this presentation.     

Confidence intervals and sample size calculations for the weighted eta-squared effect sizes in one-way heteroscedastic ANOVA

Effect size reporting and interpreting practices have been extensively recommended in academic journals when primary outcomes of all empirical studies have been analyzed. This article presents an alternative approach to constructing confidence intervals of the weighted eta-squared effect size within the context of one-way heteroscedastic ANOVA models. It is shown that the proposed interval procedure has advantages over an existing method in its theoretical justification, computational simplicity, and numerical performance. For design planning, the corresponding sample size procedures for precise interval estimation of the weighted eta-squared association measure are also delineated. Specifically, the developed formulas compute the necessary sample sizes with respect to the considerations of expected confidence interval width and tolerance probability of interval width within a designated value. Supplementary computer programs are provided to aid the implementation of the suggested techniques in practical applications of ANOVA designs when the assumption of homogeneous variances is not tenable.     

Decision making under time pressure: An independent test of sequential sampling models

Choice probability and choice response time data from a risk-taking decision-making task were compared with predictions made by a sequential sampling model. The behavioral data, consistent with the model, showed that participants were less likely to take an action as risk levels increased, and that time pressure did not have a uniform effect on choice probability. Under time pressure, participants were more conservative at the lower risk levels but were more prone to take risks at the higher levels of risk. This crossover interaction reflected a reduction of the threshold within a single decision strategy rather than a switching of decision strategies. Response time data, as predicted by the model, showed that participants took more time to make decisions at the moderate risk levels and that time pressure reduced response time across all risk levels, but particularly at the those risk levels that took longer time with no pressure. Finally, response time data were used to rule out the hypothesis that time pressure effects could be explained by a fast-guess strategy.     

Exact tests for the rasch model via sequential importance sampling

Rasch proposed an exact conditional inference approach to testing his model but never implemented it because it involves the calculation of a complicated probability. This paper furthers Rasch’s approach by (1) providing an efficient Monte Carlo methodology for accurately approximating the required probability and (2) illustrating the usefulness of Rasch’s approach for several important testing problems through simulation studies. Our Monte Carlo methodology is shown to compare favorably to other Monte Carlo methods proposed for this problem in two respects: it is considerably faster and it provides more reliable estimates of the Monte Carlo standard error.This Research was supported in part by National Science Foundation grant DMS-0203762 and a University of Pennsylvania Research Foundation grant.The authors are grateful to Don Burdick for helpful comments. In addition, the authors wish to thank the editor, the associate editor, and the referees for their helpful suggestions.This revised article was published online in August 2005 with the PDF paginated correctly.     

One man's group: Brief cognitive-anlaytic group therapy and the use of sequential diagrmmatic reformulation

The application of methods developed for individual work in Cognitive-Analytic Therapy (CAT) as applied to a time-limited group are described. Written and diagrammatic reformulation of patients problems, prepared in pre-group individual sessions, were shared in the group and served to heighten the group process. This is illustrated by following the course of one individual through the group. Outcome measures are reported separately (see Duignan & Mitzman, in press).     

Developmental changes in application of the majority rule in group decisions

This study examined age-related changes in the child's application of the principle of majority rule in group decisions. Following a problem posed by Moessinger (1981), we enquired whether children routinely apply the majority rule when the majority consists of a shifting (variable) set of members across decisions, and alternate between majority and minority when the majority and minority is fixed, i.e. consists of the same individuals each time. In Geneva, Moessinger found that 8-year-olds failed to discriminate between fixed and shifting majorities, while most 13-year-olds (75 per cent) did so. An altered replication was conducted in Australia modifying Moessinger's procedure to control for extraneous variables such as ‘set’ and the need for variety in choice. It was found that on the task 7 per cent of 8-year-olds, 20 per cent of 10-year-olds, 32 per cent of 12-year-olds, and 39 per cent of 14-year-olds discriminated on a behavioural criterion between fixed and shifting majorities. Ten per cent of 8-year-olds, 40 per cent of 10-year-olds, 52 per cent of 12-year-olds, and 55 per cent of 14-year-olds made the discrimination on Moessinger's cognitive ‘reason’ criterion. The results show that development of the conceptual distinction between fixed and shifting majorities is gradual and continuous.     

The variable-criteria sequential stopping rule: Generality to unequal sample sizes,unequal variances,or to large ANOVAs

The variable-criteria sequential stopping rule (SSR) is a method for conducting planned experiments in stages after the addition of new subjects until the experiment is stopped because the p value is less than or equal to a lower criterion and the null hypothesis has been rejected, the p value is above an upper criterion, or a maximum sample size has been reached. Alpha is controlled at the expected level. The table of stopping criteria has been validated for a t test or ANOVA with four groups. New simulations in this article demonstrate that the SSR can be used with unequal sample sizes or heterogeneous variances in a t test. As with the usual t test, the use of a separate-variance term instead of a pooled-variance term prevents an inflation of alpha with heterogeneous variances. Simulations validate the original table of criteria for up to 20 groups without a drift of alpha. When used with a multigroup ANOVA, a planned contrast can be substituted for the global F as the focus for the stopping rule. The SSR is recommended when significance tests are appropriate and when the null hypothesis can be tested in stages. Because of its efficiency, the SSR should be used instead of the usual approach to the t test or ANOVA when subjects are expensive, rare, or limited by ethical considerations such as pain or distress.     

Extending the job design perspective on individual innovation: Exploring the effect of group reflexivity

Extending previous research on group reflexivity as a group level predictor of individual innovation, we examined group reflexivity as a possible moderator of the effect of job control and task complexity on individual innovation. We obtained data on job and group characteristics from 135 members of software development teams; line managers provided ratings on individual innovation. Data were analysed using hierarchical linear modelling. Results lend further support to a positive effect of job design on individual innovation, but no effect was found for group reflexivity. The interplay between job design and group reflexivity reveals a more complex picture. While the positive effect of job control is augmented in the presence of high reflexivity, in contrast, task complexity is negatively associated with innovation in teams with high reflexivity. Results are discussed from a time and cognitive resource perspective. Furthermore, the development of context‐specific models on group reflexivity is proposed.     

The smoked plastic screen: An alternative to the one-way mirror

A double thickness, smoked plastic screen is presented as an alternative to the one-way mirror. Relative to the glass mirror, the use of the plastic screen provides a safe, nondistracting, durable, light weight, and inexpensive method for unobserved viewing without an appreciable loss in light transmission.     

Extending the Basic Local Independence Model to Polytomous Data

Psychometrika - A probabilistic framework for the polytomous extension of knowledge space theory (KST) is proposed. It consists in a probabilistic model, called polytomous local independence model,...     

Extending the expanded model of organizational identification to occupations

We extend Kreiner and Ashforth's (2004) research on the expanded model of organizational identification to the occupational level of self. A survey of 251 customer service representatives from an Indian call center indicates that occupational identification, occupational disidentification, ambivalent occupational identification, and neutral occupational identification are empirically differentiable. Further, each form of identification in the expanded model was related to certain predictors from a set of ten situational and individual difference variables, and to certain outcomes from a set of five adjustment variables. The differing patterns of antecedents and outcomes for each form of occupational identification suggest that each form constitutes a relatively unique phenomenon.     

Extending Holland's theory to the later years

Sixty-five men and women, aged 50 to 88 years, completed Holland's Vocational Preference Inventory (VPI) and a work history questionnaire. Each participant was assigned one-letter Holland personality type codes for his or her first full-time job, longest full-time job, last job (if retired) or present job (if employed), and hobbies. In general, VPI scale scores and high point codes were consistent with the occupational codes but less consistent with the hobby code. The usefulness of Holland's vocational theory to the aged population is discussed.     

Extending the perception of shape from known to unknown shading

Two experiments are reported which demonstrate the effects of light-source position as an intervening variable upon the perception of relief in pictures. In the first experiment, it is shown that the pattern of light (attached shadow) falling upon forms that can be recognized as having unambiguous surface relief (concave and convex parts) influences the perception of forms with ambiguous surface relief. In the second experiment it is demonstrated that cast shadows may also determine the interpretation of ambiguous relief. These findings suggest that light-source position, implicitly or explicitly, mediates the interpretation of surface relief in pictures.     

From observability to manipulability: Extending the inductive arguments for realism

In recent years there have been several attempts to construct inductive arguments for some version of scientific realism. Neither the characteristics of what would count as inductive evidence nor the conclusion to be inferred have been specified in ways that escape sceptical criticism. By introducing the pragmatic criterion of manipulative efficacy for a good theory and by sharpening the specification of the necessary inductive principle, the viability of a mutually supporting pair of argument forms are defended. It is shown that by the use of these forms, taken together, a sequence of inductive arguments could be constructed, given suitable cases histories to serve as evidence. It also shown that the best inductive argument for the most daring realist claim is the weakest when compared with similarly structured arguments for less daring claims.A popular version of this argument appeared in Perspectives on Science, 1994.