The Behrens-Fisher problem arises when one seeks to make inferences about the means of two normal populations without assuming the variances are equal. This paper presents a review of fundamental concepts and applications used to address the Behrens-Fisher problem under fiducial, Bayesian, and frequentist approaches. Methods of approximations to…

Regardless of the related discipline, students in statistics courses invariably have difficulty understanding the connection between the numerical values calculated for end-of-the-chapter exercises and their usefulness in decision making. This disconnect is, in part, due to the lack of time and opportunity to actually design the experiments and…

Derived a confidence interval for a ratio of correlated mean absolute deviations. Simulation results show that it performs well in small sample sizes across realistically nonnormal distributions and that it is almost as powerful as the most powerful test examined by R. Wilcox (1990). (SLD)

Offering perspectives in the teaching of statistics assists students, immersed in the study of detail, to see the leading principles of the subject more clearly. Especially helpful can be a perspective on the logic of statistical inductive reasoning. Such a perspective can bring to prominence a broad principle on which both interval estimation and…

Responds to Biskin's comments (this issue) on the significance test controversy. Highlights areas of agreement (importance of replication evidence, importance of effect sizes) and disagreement (influence of sample size, evaluation of populations vs. samples, significance of Carver's article). Includes further recommendations for reporting research…

Analyzed 150 articles from the "Journal of Applied Psychology" (JAP) from 1940 to 1999 to determine statistical reporting practices related to null hypothesis significance testing, American Psychological Association guidelines, and reform recommendations. Findings show little evidence that decades of cogent criticisms by reformers have…

Many research-related classes in social sciences present probability as a unified approach based upon mathematical axioms, but neglect the diversity of various probability theories and their associated philosophical assumptions. Although currently the dominant statistical and probabilistic approach is the Fisherian tradition, the use of Fisherian…

Instructional alignment is the extent to which stimulus conditions match three instructional components. This paper demonstrates a new perspective in which instructional alignment generates larger effects in research and practice for less "cost" than other instructional constructs. (VM)

This paper addresses the state of the art regarding the use of statistical significance tests (SSTs). How social science research will be conducted in the future is impacted directly by current debates regarding hypothesis testing. This paper: (1) briefly explicates the current debate on hypothesis testing; (2) reviews the newly published report…

Computation of a one-way analysis of variance (ANOVA) "F" ratio from descriptive statistics in the absence of raw data is corrected from two sources. Means associated with inferential statistical hypotheses are identified as estimable population parameters. (Author)

Significance tests are often used inappropriately in counseling research. In addition to comments on the significance test controversy (Vacha-Haase and Nilsson, this issue), a wider historical context and personal experiences are provided. The controversy is discussed, and seven recommendations for using significance tests are included. (EMK)

Introduces the three subsequent articles from this special section, which extend the discussion of future prospects for progress in the reporting and interpreting of effect sizes by researchers. The authors of these pieces represent diverse views. (SLD)

Examines potential problems in the use of inferential statistics for single population proportions, differences between two population proportions, and quotients of two population proportions. Discusses hypothesis testing versus interval estimation. Emphasizes the importance of selecting the appropriate formula for the standard error and…

Makes the case that science is best served when researchers focus on the size of effects and their practical significance. Advocates the use of confidence intervals for deciding whether chance or sampling variability is an unlikely explanation for an observed effect. Calls for more emphasis on effect sizes in the next edition of the American…

An index that measures the degree of comfort a researcher has relative to statistical inference application is proposed. The index is calculated by selecting and weighting components inherent in the conduct of hypothesis tests and confidence intervals, and its values range from zero to one. To organize the components of the index, inference…