The statistical analysis of data from small groups

The authors elaborate the complications and the opportunities inherent in the statistical analysis of small-group data. They begin by discussing nonindependence of group members' scores and then consider standard methods for the analysis of small-group data and determine that these methods do not take into account this nonindependence. A new method is proposed that uses multilevel modeling and allows for negative nonindependence and mutual influence. Finally, the complications of interactions, different group sizes, and differential effects are considered. The authors strongly urge that the analysis model of data from small-group studies should mirror the psychological processes that generate those data.     

Comparing associative, statistical, and inferential reasoning accounts of human contingency learning

For more than two decades, researchers have contrasted the relative merits of associative and statistical theories as accounts of human contingency learning. This debate, still far from resolution, has led to further refinement of models within each family of theories. More recently, a third theoretical view has joined the debate: the inferential reasoning account. The explanations of these three accounts differ critically in many aspects, such as level of analysis and their emphasis on different steps within the information-processing sequence. Also, each account has important advantages (as well as critical flaws) and emphasizes experimental evidence that poses problems to the others. Some hybrid models of human contingency learning have attempted to reconcile certain features of these accounts, thereby benefiting from some of the unique advantages of different families of accounts. A comparison of these families of accounts will help us appreciate the challenges that research on human contingency learning will face over the coming years.     

An EEG alpha-detection,feedback stimulation,and data analysis system

A two-channel general-purpose EEG alpha-detection system is described, along with the associated computer hardware and software. A specific application for the study of the human orienting response using alpha-contingent visual stimulation is presented. Limitations are discussed.     

An inferential confidence interval method of establishing statistical equivalence that corrects Tryon's (2001) reduction factor

Evidence of group matching frequently takes the form of a nonsignificant test of statistical difference. Theoretical hypotheses of no difference are also tested in this way. These practices are flawed in that null hypothesis statistical testing provides evidence against the null hypothesis and failing to reject H-sub-0 is not evidence supportive of it. Tests of statistical equivalence are needed. This article corrects the inferential confidence interval (ICI) reduction factor introduced by W. W. Tryon (2001) and uses it to extend his discussion of statistical equivalence. This method is shown to be algebraically equivalent with D. J. Schuirmann's (1987) use of 2 one-sided t tests, a highly regarded and accepted method of testing for statistical equivalence. The ICI method provides an intuitive graphic method for inferring statistical difference as well as equivalence. Trivial difference occurs when a test of difference and a test of equivalence are both passed. Statistical indeterminacy results when both tests are failed. Hybrid confidence intervals are introduced that impose ICI limits on standard confidence intervals. These intervals are recommended as replacements for error bars because they facilitate inferences.     

The knowledge content of statistical data

An information-theoretic framework is used to analyze the knowledge content in multivariate cross classified data. Several related measures based directly on the information concept are proposed: the knowledge content (S) of a cross classification, its terseness (Zeta), and the separability (Gamma _X ) of one variable, given all others. Exemplary applications are presented which illustrate the solutions obtained where classical analysis is unsatisfactory, such as optimal grouping, the analysis of very skew tables, or the interpretation of well-known paradoxes. Further, the separability suggests a solution for the classic problem of inductive inference which is independent of sample size.     

Commentary on high-performance computing and statistical analysis: From large-scale data analysis to smoothing functions

High-performance computing becomes essential to statistical analysis when the database is massive or the number of computations per data element is large. Albert F. Anderson (1997) discusses the application of high-performance computing to massive databases; J. O. Ramsay’s (Ramsay, Heckman, & Silverman, 1997) estimation problems potentially require large numbers of computations per data element.     

Subjects' inferential performance and the interaction of data and hypotheses in probabilistic inference tasks

In a recent paper, Knez (1991) showed an interaction of data and hypotheses in probabilistic inference tasks. The results illustrated two, earlier not obtained, significant main effects on subjects' hypothesis sampling , viz. the effect of different forms of data presentation and subjects' execution of cognitive control over their hypothesis pool throughout the series of trials. The present paper followed up these results in that the subjects' hypothesis testing , in Knez (1991) was subjected to an analysis. Hence, to see if the effects mentioned above significantly influenced the subjects' hypothesis testing, as they did for subjects' hypothesis sampling. The results showed a consistency with Knez (1991), i.e. the results emphasize the interaction of data and hypothesis in probabilistic inference tasks, as well as the subjects' execution of cognitive control over their hypothesis pool concerning both the subjects' hypothesis sampling and testing.     

A critique of the usefulness of inferential statistics in applied behavior analysis

Researchers continue to recommend that applied behavior analysts use inferential statistics in making decisions about effects of independent variables on dependent variables. In many other approaches to behavioral science, inferential statistics are the primary means for deciding the importance of effects. Several possible uses of inferential statistics are considered. Rather than being an objective means for making decisions about effects, as is often claimed, inferential statistics are shown to be subjective. It is argued that the use of inferential statistics adds nothing to the complex and admittedly subjective nonstatistical methods that are often employed in applied behavior analysis. Attacks on inferential statistics that are being made, perhaps with increasing frequency, by those who are not behavior analysts, are discussed. These attackers are calling for banning the use of inferential statistics in research publications and commonly recommend that behavioral scientists should switch to using statistics aimed at interval estimation or the method of confidence intervals. Interval estimation is shown to be contrary to the fundamental assumption of behavior analysis that only individuals behave. It is recommended that authors who wish to publish the results of inferential statistics be asked to justify them as a means for helping us to identify any ways in which they may be useful.     

Children's understanding of inferential knowledge

The understanding of inference as a source of knowledge for 4- and 6-year-old children was investigated. Children and a puppet were shown 2 toys of different colors. The toys were hidden in separate plastic cans. After the puppet looked into 1 of the cans, 6-year-olds, but not 4-year-olds, usually judged that the puppet knew the color of the toy in the other can as well. The finding that 6-year-olds attributed inferential knowledge to another observer is interpreted as evidence that children begin to understand the role of cognitive processes in knowledge acquisition around the age of 6 years.     

Beyond statistical significance: Five principles for the new era of data analysis and reporting

A crisis of confidence in research findings in consumer psychology and other academic disciplines has led to various proposals to abandon, replace, strengthen, or supplement the null hypothesis significance testing paradigm. The proliferation of such proposals, and their often-conflicting recommendations, can increase confusion among researchers. We aim to bring some clarity by proposing five simple principles for the new era of data analysis and reporting of research in consumer psychology. We avoid adding to researchers' confusion and proposing more onerous or rigid standards. Our goal is to offer straightforward practical principles that are easy for researchers to keep in mind while analyzing their data and reporting their findings. These principles involve (1) interpreting p-values as continuous measures of the strength of evidence, (2) being aware of assumptions that determine whether one can rely on p-values, (3) using theory to establish the applicability of findings to new settings, (4) employing multiple measures of evidence and various processes to obtain them, but assigning special privilege to none, and (5) reporting procedures and findings transparently and completely. We hope that these principles provide researchers with some guidance and help to strengthen the reliability of the conclusions derived from their data, analyses, and findings.     

Intuitive statistical inferences about normally distributed data

Several experiments are reported in which subjects are asked to make intuitive judgements about normally distributed samples. Experiments 1 and 2 investigated judgements about population means as a function of the mean, size and variability of the samples. Trends to take account of all three factors, in the normative direction, were shown, but sample size was significant only when numerical displays were used (experiment 1) and variability only when graphical displays were used (experiment 2).In experiment 3a, subjects were asked to estimate variability of samples directly, and were found equally able to do so with either form of data display. Experiment 3b used a simplified procedure and clarified question, and also presented both numerical and graphical displays in the same experiment. Overall, subjects took significant (normative) account of all the relevant sample features. Interactions with form of presentation showed trends consistent with the findings of experiments 1 and 2 but failed to reach significance. A further presentation effect was shown in experiments 2 and 3b, in that subjects' inferences about graphically displayed data appeared to differ somewhat between left and right centered distributions.Overall, subjects performed quite well as intuitive statisticians, though their probability estimates were typically very conservative. The evidence of trends for different modes of presentation of data to induce differential attention to sample features was sufficient to encourage further research on this problem.     

Meta- and statistical analysis of single-case intervention research data: Quantitative gifts and a wish list

In this commentary, we add to the spirit of the articles appearing in the special series devoted to meta- and statistical analysis of single-case intervention-design data. Following a brief discussion of historical factors leading to our initial involvement in statistical analysis of such data, we discuss: (a) the value added by including statistical-analysis recommendations in the What Works Clearinghouse Standards for single-case intervention designs; (b) the importance of visual analysis in single-case intervention research, along with the distinctive role that could be played by single-case effect-size measures; and (c) the elevated internal validity and statistical-conclusion validity afforded by the incorporation of various forms of randomization into basic single-case design structures. For the future, we envision more widespread application of quantitative analyses, as critical adjuncts to visual analysis, in both primary single-case intervention research studies and literature reviews in the behavioral, educational, and health sciences.