Minimum Detectable Effect Research Articles

Physical and geochemical responses to bottom trawling on naturally disturbed sediments in the eastern Bering Sea

Abstract Recent concerns that commercial bottom trawling can contribute to a significant release of sequestered marine carbon have highlighted a need for research in this area. Here, a Before-After Control-Impact (BACI) experimental design was utilized in a previously untrawled area of the eastern Bering Sea. Six pairs of experimental and control corridors were sampled before, after, and 1 year after a trawl disturbance. Each experimental corridor was fished four consecutive times over ∼12 h with a commercial otter trawl. Results were contextualized with minimum detectable effects (MDE), and showed no evidence of a trawl effect on total organic carbon (P = .999, MDE ± 0.05% TOC), total nitrogen (P = .999, MDE ± 0.02% TN), δ13C, and δ15N isotope ratios and sediment size classes. Interannual changes observed in δ15N, sand, silt, and clay are attributed to natural variation. The study suggests that the characteristics of the study site, such as storm disturbances, high sand content, and low carbon content, limited the bottom-trawl effect on sediment composition following this initial trawl disturbance. The findings highlight the importance of site-specific studies that account for local conditions to support best management practices for commercial bottom trawling.

A Practical Guide to Power Analyses of Moderation Effects in Multisite Individual and Cluster Randomized Trials

Multisite trials that randomize individuals (e.g., students) within sites (e.g., schools) or clusters (e.g., teachers/classrooms) within sites (e.g., schools) are commonly used for program evaluation because they provide opportunities to learn about treatment effects as well as their heterogeneity across sites and subgroups (defined by moderating variables). Despite the rich opportunities they present, a critical step in ensuring those opportunities is identifying the sample size that provides sufficient power to detect the desired effects if they exist. Although a strong literature base for conducting power analyses for the moderator effects in multisite trials already exists, software for power analysis of moderator effects is not readily available in an accessible platform. The purpose of this tutorial paper is to provide practical guidance on implementing power analyses of moderator effects in multisite individual and cluster randomized trials. We conceptually motivate, describe, and demonstrate the calculation of statistical power and minimum detectable effect size difference (MDESD) using highly accessible software. We conclude by outlining guidelines on power analysis of moderator effects in multisite individual randomized trials (MIRTs) and multisite cluster randomized trials (MCRTs).

Impact of poor prognostic risk for chronic low back pain on functionality and lumbopelvic stability: a cross-sectional observational study

Internal load to deal with physical exercise demand depends on the psychophysical capacity. As psychosocial aspects affect patients suffering chronic low back pain (CLBP), we hypothesized that the higher the risk of poor prognosis, the lower the psychophysical capacity and, consequently, the worse the performance in functional tasks that involve walking. To verify the impact of the risk of poor prognosis of patients with CLBP on functional performance and physiological intensity (PI), representative of the task internal load, in a walking test and on lumbopelvic region static and dynamic stability. Cross-sectional observational study. Volunteers of both sexes, physically inactive, were divided into four groups according to the Start Back Screening Tool: control (CG) CLBP free, and low (LrG), medium (MrG), high (HrG) poor prognostic risk. The outcomes were static stability, with emphasis on the action of the transverse and multifidus muscles, and dynamic stability of the lumbopelvic region, both measured by a biofeedback pressure unit, as well as functional capacity, and physiological intensity in the 6-minute walk test. The GEE and complementary metrics (minimum detectable change and effect size) were used for statistical analysis. The sample consisted of 70 volunteers. The outcomes were proportionally affected by the risk of poor prognosis (the higher the risk, the worst performance) and the complementary metrics corroborated inferential statistics. The risk of poor prognosis negatively and proportionally impacts both the static and dynamic lumbopelvic stabilization capacity and the performance and the PI in walking of individuals with CLBP.

PUMP: Estimating Power, Minimum Detectable Effect Size, and Sample Size When Adjusting for Multiple Outcomes in Multi-Level Experiments

<b>PUMP</b>: Estimating Power, Minimum Detectable Effect Size, and Sample Size When Adjusting for Multiple Outcomes in Multi-Level Experiments

The Impact of Implant Angulation on the Stress Distribution and Survival Rate of Implant-Supported Fixed Dental Prostheses: A Retrospective Study.

Background Implant-supported fixed dental prostheses (FDPs) have become a reliable method for the rehabilitation of edentulous patients, offering improved contour, function, esthetics, and overall oral health. This retrospective study aimed to evaluate the impact of implant angulation on the stress distribution and survival rate of implant-supported FDPsusingfinite element analysis (FEA). Methods A retrospective cross-sectional design was employed, utilizing existing patient records and radiographic data. The study followed the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) guidelines for transparent and comprehensive reporting. Sample size calculation was based on a reference study, considering a standard deviation of 2.5 for stress distribution measurements and a minimum detectable effect size of 1.0. Data collection included demographic and clinical characteristics, implant selection and placement details, prosthetic design and fabrication, as well as stress distribution analysis using FEA. Results The study included a total of 307 participants who met the inclusion criteria. Demographic variables demonstrated a balanced gender distribution (p = 0.172), with 51.5% males and 48.5% females. Smoking status (p < 0.001) and income level (p = 0.026) were significantly associated with the research outcomes. Implant characteristics analysis revealed three main types: NobelReplace Select (53.6%), Straumann Bone Level (31.9%), and BioHorizons Tapered Internal (14.5%). Implant type (p < 0.001), length (p = 0.003), diameter (p = 0.019), and manufacturer (p < 0.001) were all found to have statistically significant associations with the research outcomes. Conclusion The findings of this retrospective study highlight the importance of implant angulation on the stress distribution and survival rate of implant-supported FDPs. The evaluation of stress distribution patterns and the analysis of implant characteristics provide valuable insights for optimizing implant design and placement strategies.

Correspondence measures for assessing replication success.

Given recent evidence challenging the replicability of results in the social and behavioral sciences, critical questions have been raised about appropriate measures for determining replication success in comparing effect estimates across studies. At issue is the fact that conclusions about replication success often depend on the measure used for evaluating correspondence in results. Despite the importance of choosing an appropriate measure, there is still no widespread agreement about which measures should be used. This article addresses these questions by describing formally the most commonly used measures for assessing replication success, and by comparing their performance in different contexts according to their replication probabilities-that is, the probability of obtaining replication success given study-specific settings. The measures may be characterized broadly as conclusion-based approaches, which assess the congruence of two independent studies' conclusions about the presence of an effect, and distance-based approaches, which test for a significant difference or equivalence of two effect estimates. We also introduce a new measure for assessing replication success called the correspondence test, which combines a difference and equivalence test in the same framework. To help researchers plan prospective replication efforts, we provide closed formulas for power calculations that can be used to determine the minimum detectable effect size (and thus, sample sizes) for each study so that a predetermined minimum replication probability can be achieved. Finally, we use a replication data set from the Open Science Collaboration (2015) to demonstrate the extent to which conclusions about replication success depend on the correspondence measure selected. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Self-selection versus population-based sampling for evaluation of an agronomy training program in Uganda

ABSTRACT One of the challenges in evaluating the impact of agronomy training programs, particularly on downstream impacts such as yield, is identifying a sample of farmers who are likely to participate in the training. We assess farmers’ participation in a farm business training activity before the agronomy training intervention as a sample identification mechanism. The screening activity was designed to appeal to the same group of farmers targeted by a coffee agronomy training program, while having minimal impact on the program’s goal of increasing coffee yields. A three-session training on farm business management was conducted in 22 study villages in central Uganda. Coffee agronomy training was then offered in half of these villages, based on random assignment. The results show that 52% of coffee farmers who attended the first business training session subsequently attended agronomy training, compared to 22% of those identified through a census. Applying these results to the design of a large ongoing randomised controlled trial, we find that using a self-selected sample reduces the minimum detectable effect of agronomy training on coffee yield to 15.83%, compared to 38% if population-based sampling were used.

Experimental Design and Power for Moderation in Multisite Cluster Randomized Trials

Multisite cluster randomized trials (MCRTs), in which, the intermediate-level clusters (e.g., classrooms) are randomly assigned to the treatment or control condition within each site (e.g., school), are among the most commonly used experimental designs across a broad range of disciplines. MCRTs often align with the theory that programs are delivered at a cluster-level (e.g., teacher professional development) and provide opportunities to explore treatment effect heterogeneity across sites. In designing experimental studies, a critical step is the statistical power analysis and sample size determination. However, the statistical tools for power analysis of moderator effects in three-level MCRTs are not available. In this study, we derived formulas for calculating the statistical power and the minimum detectable effect size difference (MDESD) with confidence intervals for investigating the effects of various moderators in three-level MCRTs. We considered the levels of the moderators (level-1, −2, and −3), the scales of the moderators (binary and continuous), and random and nonrandomly varying slopes of the (moderated) treatment effects. We validated our formulas through Monte Carlo simulations. Finally, we conclude with directions for future work.

How Many Cases per Cluster? Operationalizing the Number of Units per Cluster Relative to Minimum Detectable Effects in Two-Level Cluster Randomized Evaluations with Linear Outcomes

In cluster randomized evaluations, a treatment or intervention is randomly assigned to a set of clusters each with constituent individual units of observations (e.g., student units that attend schools, which are assigned to treatment). One consideration of these designs is how many units are needed per cluster to achieve adequate statistical power. Typically, researchers state that “about 30 units per cluster” is the most that will yield benefit towards statistical precision. To avoid rules of thumb not grounded in statistical theory and practical considerations, and instead provide guidance for this question, the ratio of the minimum detectable effect size (MDES) to the larger MDES with one less unit per cluster is related to the key parameters of the cluster randomized design. Formulas for this subsequent difference effect size ratio (SDESR) at a given number of units are provided, as are formulas for finding the number of units for an assumed SDESR. In general, the point of diminishing returns occurs with smaller numbers of units for larger values of the intraclass correlation.

Moving Forward to a World Beyond 0.2, 0.5, and 0.8 Effects Sizes: New Cutoffs for School-Based Anti-Bullying Interventions.

Effect sizes of school-based intervention are commonly described as small to moderate when using Cohen's conventional effect size cutoffs (small [0.2], medium [0.5], and large [0.8]). However, Jacob Cohen's rule of thumb might vary across different areas of research, nature of the intervention, and population, because effect sizes are context-dependent. Moreover, when planning research studies, minimum detectable effect sizes are used to calculate the sample size. In the present study, we investigate whether conventional effect size cutoffs (small [0.2], medium [0.5], and large [0.8]) represent the reported distribution of effect sizes in school-based anti-bullying intervention. To determine small, medium, and large effect sizes, we calculated the effect size distribution (ESD) using 50th percentile effect size (medium effect) of the distributions of effect sizes provided by a recent meta-analysis on school-based anti-bullying intervention. Also, the 25th and 75th percentile effects, as they are equidistant from the average effect size, were used redefining small and large effects, respectively. Results showed that 0.07, 0.123, and 0.227 represent small, medium, and large effect sizes in anti-bullying interventions. Our results indicate that Cohen's suggested effect size thresholds (0.2, 0.5, and 0.8) overestimate effect sizes when compared to the real-world context of school based anti-bullying interventions. We also propose sample sizes required to reliably detect small, medium, and large percentile effect sizes in anti-bullying interventions.

Design Parameters for Planning the Sample Size of Individual-Level Randomized Controlled Trials in Community Colleges.

The last two decades have seen a dramatic increase in randomized controlled trials (RCTs) conducted in community colleges. Yet, there is limited empirical information on the design parameters necessary to plan the sample size for RCTs in this context. For a blocked student-level random assignment research design, key design parameters for the minimum detectable true effect (MDTE) are the within-block outcome standard deviation and the within-block outcome variance explained by baseline covariates like student characteristics . We provide empirical estimates of these key design parameters, discussing the pattern of estimates across outcomes (enrollment, credits earned, credential attainment, and grade point average), semesters, and studies. The main analyses use student-level data from 8 to 14 RCTs including 5,649-7,099 students (depending on the outcome) with follow-up data for 3years. The following patterns are observed: the within-block standard deviation and therefore the MDTE can be much larger in later semesters for enrollment outcomes and cumulative credits earned; there is substantial variation across studies in for degree attainment; and baseline covariates explain less than 10% of the variation in student outcomes. These findings indicate that when planning the sample size for a study, researchers should be mindful of the follow-up period, use a range of values to calculate the MDTE for outcomes that vary across studies, and assume a value of between 0 and 0.05. A public database created for this paper includes parameter estimates for additional RCTs and students.

Integrated Sustainable childhood Pneumonia and Infectious disease Reduction in Nigeria (INSPIRING) through whole system strengthening in Jigawa, Nigeria: study protocol for a cluster randomised controlled trial

BackgroundChild mortality remains unacceptably high, with Northern Nigeria reporting some of the highest rates globally (e.g. 192/1000 live births in Jigawa State). Coverage of key protect and prevent interventions, such as vaccination and clean cooking fuel use, is low. Additionally, knowledge, care-seeking and health system factors are poor. Therefore, a whole systems approach is needed for sustainable reductions in child mortality.MethodsThis is a cluster randomised controlled trial, with integrated process and economic evaluations, conducted from January 2021 to September 2022. The trial will be conducted in Kiyawa Local Government Area, Jigawa State, Nigeria, with an estimated population of 230,000. Clusters are defined as primary government health facility catchment areas (n = 33). The 33 clusters will be randomly allocated (1:1) in a public ceremony, and 32 clusters included in the impact evaluation.The trial will evaluate a locally adapted ‘whole systems strengthening’ package of three evidence-based methods: community men’s and women’s groups, Partnership Defined Quality Scorecard and healthcare worker training, mentorship and provision of basic essential equipment and commodities. The primary outcome is mortality of children aged 7 days to 59 months. Mortality will be recorded prospectively using a cohort design, and secondary outcomes measured through baseline and endline cross-sectional surveys.Assuming the following, we will have a minimum detectable effect size of 30%: (a) baseline mortality of 100 per 1000 livebirths, (b) 4480 compounds with 3 eligible children per compound, (c) 80% power, (d) 5% significance, (e) intra-cluster correlation of 0.007 and (f) coefficient of variance of cluster size of 0.74. Analysis will be by intention-to-treat, comparing intervention and control clusters, adjusting for compound and trial clustering.DiscussionThis study will provide robust evidence of the effectiveness and cost-effectiveness of community-based participatory learning and action, with integrated health system strengthening and accountability mechanisms, to reduce child mortality. The ethnographic process evaluation will allow for a rich understanding of how the intervention works in this context. However, we encountered a key challenge in calculating the sample size, given the lack of timely and reliable mortality data and the uncertain impacts of the COVID-19 pandemic.Trial registrationISRCTN 39213655. Registered on 11 December 2019

Embedding a Proof-of-Concept Test in an At-Scale National Policy Experiment: Greater Policy Learning But at What Cost to Statistical Power? The Social Security Administration’s Benefit Offset National Demonstration (BOND)

A randomized experiment that measures the impact of a social policy in a sample of the population reveals whether the policy will work on average with universal application. An experiment that includes only the subset of the population that volunteers for the intervention generates narrower “proof-of-concept” evidence of whether the policy can work for motivated individuals. Both forms of learning carry value, yet evaluations rarely combine the two designs. The U.S. Social Security Administration conducted an exception, the Benefit Offset National Demonstration (BOND). This article uses BOND to examine the statistical power implications and potential gains in policy learning—relative to costs—from combining volunteer and population-representative experiments. It finds that minimum detectable effects of volunteer experiments rise little when one adds a population-representative experiment, but those of a population-representative experiment double or quadruple with the addition of a volunteer experiment.

How to improve the design of experimental studies in computing education: Evidence from the international assessments.

Cluster randomized trials are frequently used in educational research for methodological reasons. This study aims to improve the efficiency of cluster randomized trials on computer/information literacy and computational thinking. The study employs a two-level hierarchical linear model to estimate (i) intraclass correlation coefficients, (ii) the amount of explained variances given selected predictors, and (iii) minimum detectable effect sizes given the set of plausible scenarios. Two data cycles from the International Computer and Information Study were used. The covariates at the student level are gender, interest in ICT, parents’ highest education level, ICT self-efficacy, and experience with computers. The covariates at school/teacher level are teacher’s ICT use, ratio of school size to the number of computers for student use, availability of ICT resources at school, approximate teacher age, and ICT self-efficacy. Findings showed that the most precise effect could be measured when student and teacher/school covariates are both adopted. Lastly, it was revealed that increasing the number of schools is effective to get the most precise effect.

Detection of Clenbuterol-Induced Changes in Heart Rate Using At-Home Recorded Smartwatch Data: Randomized Controlled Trial.

BackgroundAlthough electrocardiography is the gold standard for heart rate (HR) recording in clinical trials, the increasing availability of smartwatch-based HR monitors opens up possibilities for drug development studies. Smartwatches allow for inexpensive, unobtrusive, and continuous HR estimation for potential detection of treatment effects outside the clinic, during daily life.ObjectiveThe aim of this study is to evaluate the repeatability and sensitivity of smartwatch-based HR estimates collected during a randomized clinical trial.MethodsThe data were collected as part of a multiple-dose, investigator-blinded, randomized, placebo-controlled, parallel-group study of 12 patients with Parkinson disease. After a 6-day baseline period, 4 and 8 patients were treated for 7 days with an ascending dose of placebo and clenbuterol, respectively. Throughout the study, the smartwatch provided HR and sleep state estimates. The HR estimates were quantified as the 2.5th, 50th, and 97.5th percentiles within awake and asleep segments. Linear mixed models were used to calculate the following: (1) the intraclass correlation coefficient (ICC) of estimated sleep durations, (2) the ICC and minimum detectable effect (MDE) of the HR estimates, and (3) the effect sizes of the HR estimates.ResultsSleep duration was moderately repeatable (ICC=0.64) and was not significantly affected by study day (P=.83), clenbuterol (P=.43), and study day by clenbuterol (P=.73). Clenbuterol-induced changes were detected in the asleep HR as of the first night (+3.79 beats per minute [bpm], P=.04) and in the awake HR as of the third day (+8.79 bpm, P=.001). The median HR while asleep had the highest repeatability (ICC=0.70). The MDE (N=12) was found to be smaller when patients were asleep (6.8 bpm to 11.7 bpm) than while awake (10.7 bpm to 22.1 bpm). Overall, the effect sizes for clenbuterol-induced changes were higher while asleep (0.49 to 2.75) than while awake (0.08 to 1.94).ConclusionsWe demonstrated the feasibility of using smartwatch-based HR estimates to detect clenbuterol-induced changes during clinical trials. The asleep HR estimates were most repeatable and sensitive to treatment effects. We conclude that smartwatch-based HR estimates obtained during daily living in a clinical trial can be used to detect and track treatment effects.Trial RegistrationNetherlands Trials Register NL8002; https://www.trialregister.nl/trial/8002

Bayesian interpretation of immunotherapy trials with dynamic treatment effects

IntroductionThe mechanism of action of immune checkpoints inhibitors hinders the writing of rational statistical analysis plans for phase III randomised clinical trials (RCTs) because of their unpredictable dynamic effects. The purpose is to illustrate the advantages of Bayesian reporting of treatment efficacy analysis in immunotherapy RCTs, in contrast to frequentist reporting. MethodFourteen RCTs (one with two pairwise comparisons) that failed to achieve their primary objective (overall survival, OS) were selected. These RCTs were reanalysed using Bayesian Cox models with dynamic covariate coefficients and time-invariant models. ResultsThe RCTs that met inclusion criteria were 7 lung cancer trials, various other tumours, with antiPD1, antiPDL1 or antiCTLA4 therapies. The minimum detectable effect (δS) was superior to the true benefit observed in all cases, in conditions of non-proportional hazards. Schoenfeld tests indicated the existence of PH assumption violations (p<0.05) in 6/15 cases.The Bayesian Cox models revealed a probability of benefit >79% in all the RCTs, with the therapeutic equivalence hypothesis unlikely. The OS curves diverged after a median of 9.1 months. Since the divergency, no non-proportionality was evinced in 13/15, while the Wald tests achieved p<0.05 in 12/15 datasets. In all cases, the Bayesian Cox models with dynamic coefficients detected fluctuations of the hazard ratio, and increased 2-year OS was the most likely hypothesis. ConclusionWe recommend progressively implementing Bayesian and dynamic analyses in all RCTs of immunotherapy to interpret and assess the credibility of frequentist results.

Power analyses for moderator effects with (non)randomly varying slopes in cluster randomized trials

Researchers often apply moderation analyses to examine whether the effects of an intervention differ conditional on individual or cluster moderator variables such as gender, pretest, or school size. This study develops formulas for power analyses to detect moderator effects in two-level cluster randomized trials (CRTs) using hierarchical linear models. We derive the formulas for estimating statistical power, minimum detectable effect size difference and 95% confidence intervals for cluster- and individual-level moderators. Our framework accommodates binary or continuous moderators, designs with or without covariates, and effects of individual-level moderators that vary randomly or nonrandomly across clusters. A small Monte Carlo simulation confirms the accuracy of our formulas. We also compare power between main effect analysis and moderation analysis, discuss the effects of mis-specification of the moderator slope (randomly vs. non-randomly varying), and conclude with directions for future research. We provide software for conducting a power analysis of moderator effects in CRTs.

Powering population health research: Considerations for plausible and actionable effect sizes.

Evidence for Action (E4A), a signature program of the Robert Wood Johnson Foundation, funds investigator-initiated research on the impacts of social programs and policies on population health and health inequities. Across thousands of letters of intent and full proposals E4A has received since 2015, one of the most common methodological challenges faced by applicants is selecting realistic effect sizes to inform calculations of power, sample size, and minimum detectable effect (MDE). E4A prioritizes health studies that are both (1) adequately powered to detect effect sizes that may reasonably be expected for the given intervention and (2) likely to achieve intervention effects sizes that, if demonstrated, correspond to actionable evidence for population health stakeholders. However, little guidance exists to inform the selection of effect sizes for population health research proposals. We draw on examples of five rigorously evaluated population health interventions. These examples illustrate considerations for selecting realistic and actionable effect sizes as inputs to calculations of power, sample size and MDE for research proposals to study population health interventions. We show that plausible effects sizes for population health interventions may be smaller than commonly cited guidelines suggest. Effect sizes achieved with population health interventions depend on the characteristics of the intervention, the target population, and the outcomes studied. Population health impact depends on the proportion of the population receiving the intervention. When adequately powered, even studies of interventions with small effect sizes can offer valuable evidence to inform population health if such interventions can be implemented broadly. Demonstrating the effectiveness of such interventions, however, requires large sample sizes.

Impact of later retirement on mortality: Evidence from France.

This paper investigates the impact of delaying retirement on mortality among the French population. We take advantage of the 1993 pension reform in the private sector to identify the causal effect of an increase in claiming age on mortality. We use administrative data which provide detailed information on career characteristics, dates of birth and death. Our results, precisely estimated, show that an exogenous increase of one year in the claiming age has no significant impact on the probability to die, measured between age 61 and 79, even when we allow for nonlinear effects of treatment intensity. To test the power of our sample to detect statistically significant effects for rare events like death, we compute minimum detectable effects (MDEs). Our MDE estimates suggest that, if an impact of later retirement on mortality would be detectable, it would remain very small in magnitude.

Development of claims‐based measures of unplanned acute care with superior power for assessing the effectiveness of interventions following acute care

To develop outcome measures that are more sensitive than current measures for evaluating primary or transitional care after hospitalizations, emergency department (ED) visits, or observation stays. Medicare claims data from January 1, 2015, to October 31, 2017, for 1261707 Medicare fee-for-service beneficiaries served by (a) primary care practices participating in Track 1 of the Comprehensive Primary Care Plus (CPC+) initiative, and (b) their matched comparison practices. Given the poor statistical power in many studies to detect effects on readmissions, we developed two novel claims-based measures of unplanned acute care (UAC) following an index acute care event. The first measure assesses the proportion of hospitalizations followed by an unplanned readmission, ED visit, or observation stay within 30days of discharge; the second assesses the proportion of ED visits and observation stays followed by a hospitalization, ED visit, or observation stay within 30days. We calculate minimum detectable effects (MDEs) for both measures and for a conventional measure of 30-day unplanned readmissions, using CPC+data. Repeat UAC events are common among Medicare beneficiaries served by the CPC+practices. In 2017, 22% of discharges and 21% of ED visits and observation stays had a UAC event within 30days. Readmissions were the most common UAC event following discharge, whereas ED visits were most common following index ED visits or observation stays. MDEs are 25%-40% lower for the new measures than for the standard 30-day readmissions measure, indicating better statistical power to detect impacts of primary or transitional care interventions. This study introduces two new claims-based measures to assess quality of care during a patient's vulnerable period following acute care. The new measures complement existing measures, covering a broader range of UAC events than the standard 30-day readmissions measure, and yielding greater statistical power.