Small sample sizes contribute to several problems in research and knowledge advancement. This conceptual replication study confirmed and extended the inflation of type II errors and confidence intervals in correlation analyses of small sample sizes common in kinesiology/exercise science. Current population data (N = 18, 230, & 464) on four…

Although parallel analysis has been found to be an accurate method for determining the number of factors in many conditions with complete data, its application under missing data is limited. The existing literature recommends that, after using an appropriate multiple imputation method, researchers either apply parallel analysis to every imputed…

Randomized A/B tests within online learning platforms enable us to draw unbiased causal estimators. However, precise estimates of treatment effects can be challenging due to minimal participation, resulting in underpowered A/B tests. Recent advancements indicate that leveraging auxiliary information from detailed logs and employing design-based…

Randomized controlled trials (RCTs) admit unconfounded design-based inference--randomization largely justifies the assumptions underlying statistical effect estimates--but often have limited sample sizes. However, researchers may have access to big observational data on covariates and outcomes from RCT non-participants. For example, data from A/B…

Cluster randomized trials involving participants nested within intact treatment and control groups are commonly performed in various educational, psychological, and biomedical studies. However, recruiting and retaining intact groups present various practical, financial, and logistical challenges to evaluators and often, cluster randomized trials…

This article presents a simple approach to making quick sample size estimates for basic hypothesis tests. Although there are many sources available for estimating sample sizes, methods are not often integrated across statistical tests, levels of measurement of variables, or effect sizes. A few parameters are required to estimate sample sizes and…

Increasing the correlation between the independent variable and the mediator ("a" coefficient) increases the effect size ("ab") for mediation analysis; however, increasing a by definition increases collinearity in mediation models. As a result, the standard error of product tests increase. The variance inflation caused by…

Evaluators of education interventions are increasingly designing studies to detect impacts much smaller than the 0.20 standard deviations that Cohen (1988) characterized as "small." While the need to detect smaller impacts is based on compelling arguments that such impacts are substantively meaningful, the drive to detect smaller impacts…

The standard error of equating quantifies the variability in the estimation of an equating function. Because common items for deriving equated scores are treated as fixed, the only source of variability typically considered arises from the estimation of common-item parameters from responses of samples of examinees. Use of alternative, equally…

Utilizing planned missing data (PMD) designs (ex. 3-form surveys) enables researchers to ask participants fewer questions during the data collection process. An important question, however, is just how few participants are needed to effectively employ planned missing data designs in research studies. This article explores this question by using…

Issues with correlation attenuation due to measurement error are well documented. More than a century ago, Spearman proposed a correction for attenuation. However, this correction has seen very little use since it can potentially inflate the true correlation beyond one. In addition, very little confidence interval (CI) research has been done for…

Confidence interval estimation is a fundamental technique in statistical inference. Margin of error is used to delimit the error in estimation. Dispelling misinterpretations that teachers and students give to these terms is important. In this note, we give examples of the confusion that can arise in regard to confidence interval estimation and…

Previous studies of different methods of testing mediation models have consistently found two anomalous results. The first result is elevated Type I error rates for the bias-corrected and accelerated bias-corrected bootstrap tests not found in nonresampling tests or in resampling tests that did not include a bias correction. This is of special…

The distance between nonparametric and parametric item characteristic curves has been proposed as an index of goodness of fit in item response theory in the form of a root integrated squared error index. This article proposes to use the posterior distribution of the latent trait as the nonparametric model and compares the performance of an index…

This "What Works Clearinghouse Procedures and Standards Handbook (Version 3.0)" provides a detailed description of the standards and procedures of the What Works Clearinghouse (WWC). The remaining chapters of this Handbook are organized to take the reader through the basic steps that the WWC uses to develop a review protocol, identify…