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.     

Chalmers on the objects of credence

Chalmers (Mind 120(479): 587–636, 2011a) presents an argument against “referentialism” (and for his own view) that employs Bayesianism. He aims to make progress in a debate over the objects of belief, which seems to be at a standstill between referentialists and non-referentialists. Chalmers’ argument, in sketch, is that Bayesianism is incompatible with referentialism, and natural attempts to salvage the theory, Chalmers contends, requires giving up referentialism. Given the power and success of Bayesianism, the incompatibility is prima facie evidence against referentialism. In this paper, I review Chalmers’ arguments and give some responses on behalf of the referentialist.     

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.     

Improved stopping rules for the design of efficient small-sample experiments in biomedical and biobehavioral research

Sequential stopping rules (SSRs) should augment traditional hypothesis tests in many planned experiments, because they can provide the same statistical power with up to 30% fewer subjects without additional education or software. This article includes new Monte-Carlo-generated power curves and tables of stopping criteria based on the p values from simulated t tests and one-way ANOVAs. The tables improve existing SSR techniques by holding alpha very close to a target value when 1–10 subjects are added at each iteration. The emphasis is on small sample sizes (3–40 subjects per group) and large standardized effect sizes (0.8–2.0). The generality of the tables for dependent samples and one-tailed tests is discussed. SSR methods should be of interest to ethics bodies governing research when it is desirable to limit the number of subjects tested, such as in studies of pain, experimental disease, or surgery with animal or human subjects.     

Body dysmorphic disorder: implications for its validity as a DSM-III-R clinical syndrome

A sample of 258 college students responded to three items in Likert-format designed by the authors to elicit information relating directly to the three criteria for body-dysmorphic disorder described in DSM-III-R (1987). 70% of the participants endorsed some agreement with an item regarding dissatisfaction with some aspect(s) of their bodies. 46% indicated some preoccupation with this aspect of their appearance, and 48% indicated some exaggeration of their perceived body image. Sex differences were significant on all three items. 28% of the sample endorsed all three of the items taken together. These results raise questions about the utility of a diagnosis which, as it is currently defined, could conceivably apply to a large percentage of the population and which disproportionately targets women.     

Long‐Term Outcomes of Lesbian,Gay, Bisexual,and Transgender Recalled School Victimization

The authors examined relationships among recalled and current bullying, shame‐focused coping, and fear of negative evaluation in an adult lesbian, gay, bisexual, and transgender (LGBT) sample. Findings indicated that attack self, withdrawal, and attack other shame‐focused coping fully mediated the relationship between recalled bullying and fear of negative evaluation. Fear of negative evaluation and current bullying victimization were predicted by shame‐focused coping. Findings suggested the importance of addressing histories of school‐related bullying and shame‐focused coping when counseling LGBT persons.     

Can Bayesianism Solve Frege’s Puzzle?

Philosophia - Chalmers (Mind, 125, 499–510, 2016), responding to Braun (Mind, 125, 469–497, 2016), continues arguments from Chalmers (Mind, 120, 587–636, 2011a) for the conclusion...