In many sports contests, the equilibrium requires players to randomize across repeated rounds, i.e., exhibit no temporal predictability. Such sports data present a window into the (in)efficiency of random sequence generation in a natural competitive environment, where the decision makers (tennis players) are both highly experienced and incentivized compared to laboratory studies. I resolve a long-standing debate about whether professional players’ tennis serve directions are serially independent (Hsu, Huang & Tang, 2007) or not (Walker & Wooders, 2001) using a new dataset that is two orders of magnitude larger than those studies. I examine both between- and within-player determinants of the degree of serial (in)dependence. Evidence of the existence of significant serial dependence across serves is presented, even among players ranked Number 1 in the world. Furthermore, significant heterogeneity was found with respect to the strength of serial dependence and also its sign. A novel finding is that Number 1 and Number 2 ranked players tend to under-alternate on average, whereas in line with previous findings, the lower-ranked the players, the greater their tendency to over-alternate. Within-player analyses show that high-ranked players do not condition their randomization behavior on their opponent’s ranking. However, the under-alternation of top players would be consistent with a best-response to beliefs that the population of opponents over-alternates on average. Finally, the degree of observed serial dependence is not systematically related to other match variables proxying for match difficulty, fatigue, and psychological pressure.

The effectiveness of many widely used conservation interventions is poorly understood because of a lack of high-quality impact evaluations. Randomized control trials (RCTs), in which experimental units are randomly allocated to treatment or control groups, offer an intuitive way to calculate the impact of an intervention by establishing a reliable counterfactual scenario. As many conservation interventions depend on changing people's behaviour, conservation impact evaluation can learn a great deal from RCTs in fields such as development economics, where RCTs have become widely used but are controversial. We build on relevant literature from other fields to discuss how RCTs, despite their potential, are just one of a number of ways to evaluate impact, are not feasible in all circumstances, and how factors such as spillover between units and behavioural effects must be considered in their design. We offer guidance and a set of criteria for deciding when RCTs may be an appropriate approach for evaluating conservation interventions, and factors to consider to ensure an RCT is of high quality. We illustrate this with examples from one of the few concluded RCTs of a large-scale conservation intervention: an incentive-based conservation programme in the Bolivian Andes. We argue that conservation should aim to avoid a rerun of the polarized debate surrounding the use of RCTs in other fields. Randomized control trials will not be feasible or appropriate in many circumstances, but if used carefully they can be useful and could become a more widely used tool for the evaluation of conservation impact.

While junior clinical researchers at academic medical institutions across the US often desire to be actively engaged in randomized-clinical trials, they often lack adequate resources and research capacity to design and implement them. This insufficiency hinders their ability to generate a rigorous randomization scheme to minimize selection bias and yield comparable groups. Moreover, there are limited online user-friendly randomization tools. Thus, we developed a free robust randomization app (RRApp). RRApp incorporates 6 major randomization techniques: simple randomization, stratified randomization, block randomization, permuted block randomization, stratified block randomization, and stratified permuted block randomization. The design phase has been completed, including robust server scripts and a straightforward user-interface using the “shiny” package in R. Randomization schemes generated in RRApp can be input directly into the Research Electronic Data Capture (REDCap) system. RRApp has been evaluated by biostatisticians and junior clinical faculty at the Icahn School of Medicine at Mount Sinai. Constructive feedback regarding the quality and functionality of RRApp was also provided by attendees of the 2016 Association for Clinical and Translational Statisticians Annual Meeting. RRApp aims to educate early stage clinical trialists about the importance of randomization, while simultaneously assisting them, in a user-friendly fashion, to generate reproducible randomization schemes.

Monozygotic (MZ) and dizygotic (DZ) twins participate in research that partitions variance in health, disease, and behavior into genetic and environmental components. However, there are other innovative roles for twins in medical research. One such way is involving MZ and/or DZ twins in co-twin control-designed randomized controlled trials (RCTs). To our knowledge, no reviews have been conducted that summarizes the involvement of twins in RCTs. Therefore, we conducted a systematic literature search using the U.S. Clinical Trials Database, NHS electronic databases, MEDLINE, EMBASE, and PsychINFO for RCTs on publications involving MZ and/or DZ twins as RCT participants. Out of the 186,027 clinical trials registered in the U.S. clinical trial register ClinicaTrails.gov, only six RCTs used twins as participants. From 1,598 articles identified in our search, 50 peer-reviewed English language publications met our pre-defined inclusion criteria. Sample sizes for RCTs have ranged from a total number of participants from 2 to 1,162; however, 32 (64%) studies had a sample size of 100 or less, and of those, 12 (24%) had fewer than 10. Both MZ and DZ twins have been recruited to the RCTs. In most instances (33/50) each twin from a pair were assigned to different study arms. Most of those studies included MZ twins only. Despite the methodological advantages, the use of MZ and DZ twins as participants in interventional RCTs appeared limited. The continuous development of innovative twin designs, especially RCTs, indicates that twin research can extend beyond the more widely recognized heritability estimates.

We study automorphism groups of randomizations of separable structures, with focus on the ℵ0-categorical case. We give a description of the automorphism group of the Borel randomization in terms of the group of the original structure. In the ℵ0-categorical context, this provides a new source of Roelcke precompact Polish groups, and we describe the associated Roelcke compactifications. This allows us also to recover and generalize preservation results of stable and NIP formulas previously established in the literature, via a Banach-theoretic translation. Finally, we study and classify the separable models of the theory of beautiful pairs of randomizations, showing in particular that this theory is never ℵ0-categorical (except in basic cases).

Every complete first order theory has a corresponding complete theory in continuous logic, called the randomization theory. It has two sorts, a sort for random elements of models of the first order theory, and a sort for events. In this paper we establish connections between properties of countable models of a first order theory and corresponding properties of separable models of the randomization theory. We show that the randomization theory has a prime model if and only if the first order theory has a prime model. And the randomization theory has the same number of separable homogeneous models as the first order theory has countable homogeneous models. We also show that when T has at most countably many countable models, each separable model of TR is uniquely characterized by a probability density function on the set of isomorphism types of countable models of T. This yields an analogue for randomizations of the results of Baldwin and Lachlan on countable models of ω1-categorical first order theories.

Randomized controlled trials (RCTs), typically, randomize participants to one of two intervention groups. It has been shown, however, that about 25% of RCTs published in the scientific literature randomize participants to three or more treatment groups. These studies are called ‘multi-arm’ trials: there may be, for instance, two or more experimental intervention groups with a common control group, or two control intervention groups such as a placebo group and a standard treatment group. A special case of multi-arm studies are factorial trials, which address two or more intervention comparisons carried out simultaneously, using four or more intervention groups.