Growing single crystals in silica gel

Two types of chemical reactions for crystal growing are discussed. The first is a metathetical reaction to produce calcium tartrate tetrahydrate crystals, the second is a decomplexation reaction to produce cuprous chloride crystals

Assessing the Potential Impact of a Nationwide Class-Based Affirmative Action System

We examine the possible consequences of a change in law school admissions in the United States from an affirmative action system based on race to one based on socioeconomic class. Using data from the 1991-1996 Law School Admission Council Bar Passage Study, students were reassigned attendance by simulation to law school tiers by transferring the affirmative action advantage for black students to students from low socioeconomic backgrounds. The hypothetical academic outcomes for the students were then multiply-imputed to quantify the uncertainty of the resulting estimates. The analysis predicts dramatic decreases in the numbers of black students in top law school tiers, suggesting that class-based affirmative action is insufficient to maintain racial diversity in prestigious law schools. Furthermore, there appear to be no statistically significant changes in the graduation and bar passage rates of students in any demographic group. The results thus provide evidence that, other than increasing their representation in upper tiers, current affirmative action policies relative to a socioeconomic-based system neither substantially help nor harm minority academic outcomes, contradicting the predictions of the "mismatch" hypothesis, which asserts otherwise.Comment: Published at http://dx.doi.org/10.1214/15-STS514 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Criteria for selecting children for speech therapy in the public schools

Thesis (Ed.M.)--Boston Universit

Estimating the Causal Effects of Marketing Interventions Using Propensity Score Methodology

Propensity score methods were proposed by Rosenbaum and Rubin [Biometrika 70 (1983) 41--55] as central tools to help assess the causal effects of interventions. Since their introduction more than two decades ago, they have found wide application in a variety of areas, including medical research, economics, epidemiology and education, especially in those situations where randomized experiments are either difficult to perform, or raise ethical questions, or would require extensive delays before answers could be obtained. In the past few years, the number of published applications using propensity score methods to evaluate medical and epidemiological interventions has increased dramatically. Nevertheless, thus far, we believe that there have been few applications of propensity score methods to evaluate marketing interventions (e.g., advertising, promotions), where the tradition is to use generally inappropriate techniques, which focus on the prediction of an outcome from background characteristics and an indicator for the intervention using statistical tools such as least-squares regression, data mining, and so on. With these techniques, an estimated parameter in the model is used to estimate some global ``causal'' effect. This practice can generate grossly incorrect answers that can be self-perpetuating: polishing the Ferraris rather than the Jeeps ``causes'' them to continue to win more races than the Jeeps $\Leftrightarrow$ visiting the high-prescribing doctors rather than the low-prescribing doctors ``causes'' them to continue to write more prescriptions. This presentation will take ``causality'' seriously, not just as a casual concept implying some predictive association in a data set, and will illustrate why propensity score methods are generally superior in practice to the standard predictive approaches for estimating causal effects.Comment: Published at http://dx.doi.org/10.1214/088342306000000259 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Causal Inference Through Potential Outcomes and Principal Stratification: Application to Studies with "Censoring" Due to Death

Causal inference is best understood using potential outcomes. This use is particularly important in more complex settings, that is, observational studies or randomized experiments with complications such as noncompliance. The topic of this lecture, the issue of estimating the causal effect of a treatment on a primary outcome that is ``censored'' by death, is another such complication. For example, suppose that we wish to estimate the effect of a new drug on Quality of Life (QOL) in a randomized experiment, where some of the patients die before the time designated for their QOL to be assessed. Another example with the same structure occurs with the evaluation of an educational program designed to increase final test scores, which are not defined for those who drop out of school before taking the test. A further application is to studies of the effect of job-training programs on wages, where wages are only defined for those who are employed. The analysis of examples like these is greatly clarified using potential outcomes to define causal effects, followed by principal stratification on the intermediated outcomes (e.g., survival).Comment: This paper commented in: [math.ST/0612785], [math.ST/0612786], [math.ST/0612788]. Rejoinder in [math.ST/0612789]. Published at http://dx.doi.org/10.1214/088342306000000114 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Rerandomization to improve covariate balance in experiments

Randomized experiments are the "gold standard" for estimating causal effects, yet often in practice, chance imbalances exist in covariate distributions between treatment groups. If covariate data are available before units are exposed to treatments, these chance imbalances can be mitigated by first checking covariate balance before the physical experiment takes place. Provided a precise definition of imbalance has been specified in advance, unbalanced randomizations can be discarded, followed by a rerandomization, and this process can continue until a randomization yielding balance according to the definition is achieved. By improving covariate balance, rerandomization provides more precise and trustworthy estimates of treatment effects.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1008 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org