Two- and three-level designs in educational and psychological research can involve entire populations of Level-3 and possibly Level-2 units, such as schools and educational districts nested within a given state, or neighborhoods and counties in a state. Such a design is of increasing relevance in empirical research owing to the growing popularity…

For ease of instruction in the classroom, the one-way analysis of variance F statistic is rewritten in terms of pairwise differences in individual sample means instead of differences of individual sample means from the overall sample mean. Likewise, the Kruskal-Wallis statistic may be rewritten in terms of pairwise differences in individual…

In today's data-driven and data-informed educational landscape, leaders face increasing pressure to make decisions and present results based on what appear to be comprehensive statistical analyses. However, the ethical implications of these responsibilities can be complex, particularly when statistical results carry the potential to be…

In carrying out surveys involving sensitive characteristics, randomized response models have been considered among the best techniques since they provide the maximum privacy protection to the respondents and procure honest responses. Over the years, researchers have carried out studies on the estimation of proportions of the population possessing…

Previous researchers have proposed the a priori procedure, whereby the researcher specifies, prior to data collection, how closely she wishes the sample means to approach corresponding population means, and the degree of confidence of meeting the specification. However, an important limitation of previous research is that researchers sometimes are…

Experimental psychology is witnessing an increase in research on individual differences, which requires the development of new tasks that can reliably assess variations among participants. To do this, cognitive researchers need statistical methods that many researchers have not learned during their training. The lack of expertise can pose…

When well-implemented, mediation analyses play a critical role in probing theories of action because their results help lay the ground work for the critical development of a treatment and the iterative advancement of theories that are foundational to a discipline. Despite strong interest in designs that incorporate mediation, few studies have…

Computer simulation can be used to demonstrate why the unbiased sample variance uses degrees of freedom (n-1). This is first demonstrated for sampling from a normal random variable, and in additional simulations for some selected non-normal random variables, namely, chi-square and binomial.

Sample representativeness is an important piece to consider when evaluating the quality of a screening assessment. If you are trying to determine whether or not the screening tool accurately measures children's skills, you want to ensure that the sample that is used to validate the tool is representative of your population of interest.

This article discusses the estimation of a population proportion, using the auxiliary information available, which is incorporated into the estimation procedure by a probit model fit. Three probit regression estimators are considered, using model-based and model-assisted approaches. The theoretical properties of the proposed estimators are derived…

Within psychology and the social sciences, Ordinary Least Squares (OLS) regression is one of the most popular techniques for data analysis. In order to ensure the inferences from the use of this method are appropriate, several assumptions must be satisfied, including the one of constant error variance (i.e. homoskedasticity). Most of the training…

Across all social science disciplines, but in particular public administration, there is a shared concern about the costs of using traditional random samples to generate data, and its impact on researchers' ability to engage in "quality" research. As a result of these costs, more academics, practitioners, and students are turning to…

The statistical concept of sampling is often given little direct attention, typically reduced to the mantra "take a random sample". This low resource and adaptable activity demonstrates sampling and explores issues that arise due to biased sampling.

The resources needed to conduct high-quality and large-scale survey research are often beyond the reach of institutional researchers and higher education analysts. However, the National Center for Education Statistics (NCES) provides many national student surveys that researchers can utilize. We outline four NCES studies--the High School…

Reproducibility crises have arisen in psychology and other behavioral sciences, spurring efforts to ensure research findings are credible and replicable. Although reforms are occurring at professional levels in terms of new publication parameters and open science initiatives, the credibility and reproducibility of undergraduate research deserves…