It is more common for educational and psychological data to be nonnormal than to be approximately normal. This tendency may lead to bias and error in point estimates of the Pearson correlation coefficient. In a series of Monte Carlo simulations, the Pearson correlation was examined under conditions of normal and nonnormal data, and it was compared…

Most questions in social and biomedical sciences are causal in nature: what would happen to individuals, or to groups, if part of their environment were changed? In this groundbreaking text, two world-renowned experts present statistical methods for studying such questions. This book starts with the notion of potential outcomes, each corresponding…

Meehl's taxometric method was developed to distinguish categorical and continuous constructs. However, taxometric output can be difficult to interpret because expected results for realistic data conditions and differing procedural implementations have not been derived analytically or studied through rigorous simulations. By applying bootstrap…

This quantitative analysis of published results on the effect of coaching on Scholastic Aptitude Test scores differs from previous studies by separating out the within-study sampling error from the variation in coaching effectiveness. The authors conclude that the size of the positive effect seems too small to be practically important. (Author/SK)

This paper illustrates an application of Efron's bootstrap to the repeated measures design. While this approach does not require parametric assumptions, it does utilize distributional information in the sample. By appropriately resampling from study data, the bootstrap may determine accurate sampling distributions for estimators, effects, or…

The use of and emphasis on statistical significance testing has pervaded educational and behavioral research for many decades in spite of criticism by prominent researchers in this field. Much of the controversy is caused by lack of understanding or misinterpretations. This paper reviews criticisms of statistical significance testing and discusses…

Sampling error refers to variability that is unique to the sample. If the sample is the entire population, then there is no sampling error. A related point is that sampling error is a function of sample size, as a hypothetical example illustrates. As the sample statistics more and more closely approximate the population parameters, the sampling…

Examines relationships among the parameters of the Zipf size-frequency distribution as well as its sampling properties. Highlights include its importance in bibliometrics, tables for the sampling distribution of the maximal value of a finite Zipf distribution, and an approximation formula for confidence intervals. (Author/LRW)

This simple method for simulating the Central Limit Theorem with students in a beginning nonmajor statistics class requires students to use dice to simulate drawing samples from a discrete uniform distribution. On a chalkboard, the distribution of sample means is superimposed on a graph of the discrete uniform distribution to provide visual…

A method is presented that eliminates some interpretational limitations arising from assumptions implicit in the use of arbitrary rules of thumb to interpret exploratory factor analytic results. The bootstrap method is presented as a way of approximating sampling distributions of estimated factor loadings. Simulated datasets illustrate the…

The wide availability of large amounts of inexpensive computing power has encouraged statisticians to explore many approaches to a basis for inference. This paper presents one such "computer-intensive" approach: the bootstrap of Bradley Efron. This methodology fits between the cases where it is assumed that the form of the distribution…

Advances in computer technology are making it possible for educational researchers to use simpler statistical methods to address a wide range of questions with smaller data sets and fewer, and less restrictive, assumptions. This digest introduces computationally intensive statistics, collectively called resampling techniques. Resampling is a…

The sampling errors of maximum likelihood estimates of item-response theory parameters are studied in the case where both people and item parameters are estimated simultaneously. A check on the validity of the standard error formulas is carried out. The effect of varying sample size, test length, and the shape of the ability distribution is…