Person:

Rubin, Donald

The effects of a job-training program on both employment and wages are evaluated, using data from a randomized study. Principal stratification is used to address, simultaneously, the complications of noncompliance, wages that are only partially defined because of nonemployment, and unintended missing outcomes. The first two complications are of substantive interest, whereas the third is a nuisance. The objective is to find a parsimonious model that can be used to inform public policy. We conduct a likelihood-based analysis using finite mixture models estimated by the EM algorithm. We maintain an exclusion restriction assumption for the effect of assignment on employment and wages for noncompliers, but not on missingness. We provide estimates under the Missing at Random assumption, and assess the robustness of our results to deviations from it. The plausibility of meaningful restrictions is investigated by means of scaled log-likelihood ratio statistics. Substantive conclusions include the following. For compliers, the effect on employment is negative in the short term; it becomes positive in the long term, but these effects are small at best. For always employed compliers, i.e., compliers who are employed whether trained or not trained, positive effects on wages are found at all time periods. Our analysis reveals that background characteristics of individuals differ markedly across the principal strata. We found evidence that the program should have been better targeted, in the sense of being designed diffrently for different groups of people, and specific suggestions are offered. Previous analyses of this data set, which did not address all complications in a principled manner, led to less nuanced conclusions about Job Corps.

The Neyman–Fisher controversy considered here originated with the 1935 presentation of Jerzy Neyman’s Statistical Problems in Agricultural Experimentation to the Royal Statistical Society. Neyman asserted that the standard ANOVA F-test for randomized complete block designs is valid, whereas the analogous test for Latin squares is invalid in the sense of detecting differentiation among the treatments, when none existed on average, more often than desired (i.e., having a higher Type I error than advertised). However, Neyman’s expressions for the expected mean residual sum of squares, for both designs, are generally incorrect. Furthermore, Neyman’s belief that the Type I error (when testing the null hypothesis of zero average treatment effects) is higher than desired, whenever the expected mean treatment sum of squares is greater than the expected mean residual sum of squares, is generally incorrect. Simple examples show that, without further assumptions on the potential outcomes, one cannot determine the Type I error of the F-test from expected sums of squares. Ultimately, we believe that the Neyman–Fisher controversy had a deleterious impact on the development of statistics, with a major consequence being that potential outcomes were ignored in favor of linear models and classical statistical procedures that are imprecise without applied contexts.

A number of mixture modeling approaches assume both normality and independent observations. However, these two assumptions are at odds with the reality of many data sets, which are often characterized by an abundance of zero-valued or highly skewed observations as well as observations from biologically related (i.e., non-independent) subjects. We present here a finite mixture model with a zero-inflated Poisson regression component that may be applied to both types of data. This flexible approach allows the use of covariates to model both the Poisson mean and rate of zero inflation and can incorporate random effects to accommodate non-independent observations. We demonstrate the utility of this approach by applying these models to a candidate endophenotype for schizophrenia, but the same methods are applicable to other types of data characterized by zero inflation and non-independence.

Anthrax, caused by the bacterium Bacillus anthracis, can be a highly lethal acute disease in humans and animals. Prior to the 20th century, it led to thousands of deaths each year. Anthrax infection became extremely rare in the United States in the 20th century, thanks to extensive animal vaccination and anthrax eradication programs. The 2001 anthrax attacks in the United States drew this formidable disease back into the public spotlight.

Methods for comparing two or more statistical significance (p) levels are described; these methods are more rigorous, systematic, and informative than the comparisons that are commonly made by using a significant/not significant dichotomy. Formulas are provided for calculating the significance level of a comparison between two or more p levels.

Studies employing within-subjects designs may be compared with those employing between-subjects designs in a variety of ways. We discuss and illustrate the comparisons of variabilities, including within-condition variances and precisions as well as the comparisons of means and of mean differences. Our discussion emphasizes the importance of trying to understand the sources of differences.

We introduce the binomial effect size display (BESD), which is useful because it is (a) easily understood by researchers, students, and lay persons; (b) widely applicable; and (c) conveniently computed. The BESD displays the change in success rate (e.g., survival rate, improvement rate, etc.) attributable to a new treatment procedure. For example, an r of .32, the average size of the effect of psychotherapy, is said to account for "only 10% of the variance"; however, the BESD shows that this proportion of variance accounted for is equivalent to increasing the success rate from 34% to 66%, which would mean, for example, reducing an illness rate or a death rate from 66% to 34%.

This article presents a general set of procedures for comparing the effect sizes of two or more independent studies. The procedures include a method for calculating the approximate significance level for the heterogeneity of effect sizes of studies and a method for calculating the approximate significance level of a contrast among the effect sizes. Although the focus is on effect size as measured by the standardized difference between the means (d) defined as (Mi — M-^/S, the procedures can be applied to any measure of effect size having an estimated variance. This extension is illustrated with effect size measured by the difference between proportions.

We describe procedures for (a) assessing the heterogeneity of a set of effect sixes derived from a meta-analysis, (b) testing for trends by means of contrasts among the effect sizes obtained, and (c) evaluating the practical importance of the average effect size obtained. On the basis of applying these procedures to data presented in Hyde (1981) on cognitive gender differences, we conclude the following: (a) that for all four areas of cognitive skill investigated, effect sizes for gender differences differed significantly across studies (at least at p < .001); (b) that studies of gender differences conducted more recently show a substantial gain in cognitive performance by females relative to males (unweighted mean r across four cognitive areas = .40); (c) that studies of gender differences show male versus female effect sizes of practical importance equivalent to outcome rates of 60% versus 40%.