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We discuss the two most popular frameworks for identification, estimation and inference in regression discontinuity (RD) designs: the continuity-based framework, where the conditional expectations of the potential outcomes are assumed to be continuous functions of the score at the cutoff, and the local randomization framework, where the treatment assignment is assumed to be as good as randomized in a neighborhood around the cutoff. Using various examples, we show that (i) assuming random assignment of the RD running variable in a neighborhood of the cutoff implies neither that the potential outcomes and the treatment are statistically independent, nor that the potential outcomes are unrelated to the running variable in this neighborhood; and (ii) assuming local independence between the potential outcomes and the treatment does not imply the exclusion restriction that the score affects the outcomes only through the treatment indicator. Our discussion highlights key distinctions between “locally randomized” RD designs and real experiments, including that statistical independence and random assignment are conceptually different in RD contexts, and that the RD treatment assignment rule places no restrictions on how the score and potential outcomes are related. Our findings imply that the methods for RD estimation, inference, and falsification used in practice will necessarily be different (both in formal properties and in interpretation) according to which of the two frameworks is invoked.

When there are few treated clusters in a pure treatment or difference-in-differences setting, t tests based on a cluster-robust variance estimator can severely over-reject. Although procedures based on the wild cluster bootstrap often work well when the number of treated clusters is not too small, they can either over-reject or under-reject seriously when it is. In a previous paper, we showed that procedures based on randomization inference (RI) can work well in such cases. However, RI can be impractical when the number of possible randomizations is small. We propose a bootstrap-based alternative to RI, which mitigates the discrete nature of RI p values in the few-clusters case. We also compare it to two other procedures. None of them works perfectly when the number of clusters is very small, but they can work surprisingly well.

Single subject research has long been employed to evaluate intervention effectiveness with students with learning or behavioral disabilities. Typically, the results of single subject research are presented on graphic displays and analyzed by a method of visual inspection, in which analysts simultaneously consider such data elements as level change, slope change, and variability in baseline and treatment data. However, over the years several concerns regarding visual inspection have emerged, including relatively low inter-rater reliabilities. This chapter reviews the arguments in favor of visual inspection as an analytic tool, and also summarizes the arguments favoring statistical analysis of single case data. The use of randomization tests is recommended, and an example is provided of its use in research with students with learning and behavioral disorders.

Job Corps is the United State’s largest and most comprehensive training program for disadvantaged youth aged 16–24 years old. A randomized social experiment concluded that, on average, individuals benefited from the program in the form of higher weekly earnings and employment prospects. At the same time, “young adults” (ages 20–24) realized much higher impacts relative to “adolescents” (ages 16–19). Employing recent nonparametric bounds for causal mediation, we investigate whether these two groups’ disparate effects correspond to them benefiting differentially from distinct aspects of Job Corps, with a particular focus on the attainment of a degree (GED, high school, or vocational). We find that, for young adults, the part of the total effect of Job Corps on earnings (employment) that is due to attaining a degree within the program is at most 41% (32%) of the total effect, whereas for adolescents that part can account for up to 87% (100%) of the total effect. We also find evidence that the magnitude of the part of the effect of Job Corps on the outcomes that works through components of Job Corps other than degree attainment (e.g., social skills, job placement, residential services) is likely higher for young adults than for adolescents. That those other components likely play a more important role for young adults has policy implications for more effectively servicing participants. More generally, our results illustrate how researchers can learn about particular mechanisms of an intervention.

Shuffling a deck of cards is normally used for randomization. An imperfect shuffle would not produce the desired randomization, since there would be residual correlation with the original order. On the other hand, from the classical card magic literature it is known that eight successive perfect riffle shuffles returns the deck to the original order. The question addressed here is whether this observation is in fact unusual and surprising. Although a general closed‐form analytical solution does not appear to be possible, a simple program could be written to determine deck sizes and numbers of shuffles for which eventual reordering occurs. This computational approach correctly predicts the original observation of eight shuffles for a deck of 52 cards; in fact if the trivial solutions of integral multiples of eight shuffles are discarded, eight shuffles appears to be the unique solution for a 52 card deck.

The purpose of this paper is to present the results of a pilot trial, investigating the accessibility provided by a tablet computer (Apple iPad) to individuals with visual impairment. The study was designed around an N-of-1 randomised controlled trial (RCT), which was replicated for 12 participants. It served as an opportunity to evaluate the use N-of-1 trials in studies involving people who are visually impaired.

The study centred round an N-of-1 RCT, comparing the accessibility provided by control equipment (Windows computer) against the intervention equipment (Apple iPad). Twelve participants conducted six tests on the equipment as per randomisation, followed by a quantitative-based evaluation and short interviews.

One-sided individual randomisation tests showed a significant result for overall satisfaction in favour of the tablet at the 0.05 significance level for seven of the participants. Participants identified several strengths of the iPad in helping a partially sighted user in accessing the internet: inbuilt zoom and magnification options; increased control as a result of the touch screen; and accessibility tools being built into the operating system. The main limitation suggested was the way the zoom function operates by enlarging the onscreen keyboard. This caused difficulties for those with more severe visual impairments using this function in inputting text.

There has been limited research to substantiate positive reviews of the tablet computer for low-vision users. The results of this pilot study gives evidence in support of these potential benefits, and demonstrates the importance of a more thorough investigation.

Leadership training has led to a large amount of research due to the belief that such training can lead to (or more precisely cause) positive changes in followers’ behavior and work performance. This chapter describes some of the conditions necessary for research to show a causal relationship between leadership training and outcomes. It then describes different research designs, employed in leadership training research, and considers the types of problems that can affect inferences about causality. The chapter focuses on the role of randomization of leaders (e.g., into training vs. non-training conditions) as a key methodological procedure and alludes to problems of achieving this in field settings.

This paper aims to evaluate the use of Mendelian randomization (MR) analyses for judging the effects of alcohol consumption on the risk of coronary heart disease (CHD).

This paper presents a review of methodology for MR and describes its early application to judging health effects of alcohol, current uses and a recommended approach of combining MR results with those from observational and experimental studies.

Early applications of MR to health effects of alcohol consumption were inadequate for providing unbiased results, but newer attempts using polygenic scores show promise. It is important to combine data from MR analyses with those from observational and experimental studies to obtain an unbiased and scientifically sound estimate of alcohol’s effects on health.

Giving advice to the public regarding alcohol consumption must be based on accurate, unbiased scientific data; this paper describes attempts to use MR for achieving this goal.

Given that light-to-moderate alcohol intake is associated with a lower risk of CHD, type II diabetes mellitus and total mortality, it is important to be able to evaluate both the benefits and harms from alcohol before giving advice regarding drinking.

This is part of a group of three papers dealing with the potential health benefits and harms associated with alcohol consumption.

The application of far-infrared energy to skin is expected to lead to vasodilatation of the skin surface, consequently warming the skin, and promoting sleep induction. The purpose of this paper was to test whether bedsheets impregnated with bioceramic far-infrared technology would improve the perception of sleep in a sample of healthy adults.

Twenty-nine adults consented to participate, randomizing 17 to the far-infrared bedsheets and 12 to the control bedsheets. Two of the control participants dropped out prior to randomization and prior to completing any assessments and therefore are excluded from the analyses. After baseline assessment, participants slept on their randomly assigned sheets for five weeks, followed by a one week “wash out”. Insomnia symptoms were assessed with the Insomnia Severity Index, depression symptoms with the Patient Health Questionnaire, “vigor” and “fatigue” with the Profile of Mood States, and napping behavior with daily sleep diaries.

During the period of randomization, the participants on the far-infrared sheets reported fewer insomnia symptoms and less napping. This advantage was lost during the wash out period.

Far-infrared technology produces benefits on reported sleep in healthy normal adults.

This paper covers different types of research designs, like, longitudinal, cross-section and sequential design, experimental design (including factorial experimental design), and correlational design, with illustrative examples. This paper will help a scholar to know how choice of research design depends on a number of parameters, highlighted by author.