The import or force of the result of a statistical test has long been portrayed as consistent with deductive reasoning. The simplest form of deductive argument has a first premise with conditional form, such as p[right arrow]q, which means that "if p is true, then q must be true." Given the first premise, one can either affirm or deny…

White and Gorard make important and relevant criticisms of some of the methods commonly used in social science research, but go further by criticising the logical basis for inferential statistical tests. This paper comments briefly on matters we broadly agree on with them and more fully on matters where we disagree. We agree that too little…

Recent concerns about a shortage of capacity for statistical and numerical analysis skills among social science students and researchers have prompted a range of initiatives aiming to improve teaching in this area. However, these projects have rarely re-evaluated the content of what is taught to students and have instead focussed primarily on…

Null hypothesis significance testing (NHST) has been the subject of debate for decades and alternative approaches to data analysis have been proposed. This article addresses this debate from the perspective of scientific inquiry and inference. Inference is an inverse problem and application of statistical methods cannot reveal whether effects…

In his article, "An Alternative to Null-Hypothesis Significance Tests," Killeen (2005) urged the discipline to abandon the practice of "p[subscript obs]"-based null hypothesis testing and to quantify the signal-to-noise characteristics of experimental outcomes with replication probabilities. He described the coefficient that he…

The aim of the current study is to validate the invariance of major profile patterns derived from multidimensional scaling (MDS) by bootstrapping. Profile Analysis via Multidimensional Scaling (PAMS) was employed to obtain profiles and bootstrapping was used to construct the sampling distributions of the profile coordinates and the empirical…

To characterise statistical inference in the workplace this paper compares a prototypical type of statistical inference at work, statistical process control (SPC), with a type of statistical inference that is better known in educational settings, hypothesis testing. Although there are some similarities between the reasoning structure involved in…

The sense that replicability is an important aspect of empirical science led Killeen (2005a) to define "p[subscript rep]," the probability that a replication will result in an outcome in the same direction as that found in a current experiment. Since then, several authors have praised and criticized 'p[subscript rep]," culminating…

Both researchers and teachers of statistics have made considerable efforts during the last decades to re-conceptualize statistics courses in accordance with the general reform movement in mathematics education. However, students still hold misconceptions about statistical inference even after following a reformed course. The study presented in…

The use of finite intersection tests (FIT) to unify methods for simultaneous inference and to test orthogonal contrasts is discussed. Multiple comparison procedures that combine FIT with sequential hypothesis testing are illustrated, and a simulation strategy is presented to generate values needed for FIT methods. (SLD)

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…

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…

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)

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…