Using the microcomputer as a visual aid in the statistics classroom

A microcomputer running a spreadsheet program makes an excellent visual aid for demonstrating statistical concepts and procedures. Some advantages of this setup over traditional visual aids are described. Several statistical demonstrations that I have found to work well are presented.     

STAZ: Interactive software for undergraduate statistics

STAZ is an interactive computer program that demonstrates statistical concepts, many of which cannot be readily demonstrated using conventional methods. Use of dynamic graphics encourages active engagement with challenging statistical concepts. The program consists of 13 graphical demonstrations, most of which allow for interactive participation by students. A detailed Help file with guided explanations accompanies each demonstration. STAZ is a multiple document interface program that makes full use of Windows features, such as tiling, links, and multitasking. Designed to be used as a supplement for any undergraduate statistics course, STAZ may be used by either instructors in classroom settings or students working independently.     

A simulation laboratory for statistics

In this paper, we describe a general purpose data simulator, Datasim, which is useful for anyone conducting computer-based laboratory assignments in statistics. Simulations illustrating sampling distributions, the central limit theorem, Type I and Type II decision errors, the power of a test, the effects of violating assumptions, and the distinction between orthogonal and non-orthogonal contrasts are discussed. Simulations illustrating other statistical concepts—partial correlation, regression to the mean, heteroscedasticity, the partitioning of error terms in splitplot designs, and so on—can be developed easily. Simulations can be assigned as laboratory exercises, or the instructor can execute the simulations during class, integrate the results into an ongoing lecture, and use the results to initiate class discussion of the relevant statistical concepts.     

Bringing history to life: simulating landmark experiments in psychology

The course in history of psychology can be challenging for students, many of whom enter it with little background in history and faced with unfamiliar names and concepts. The sheer volume of material can encourage passive memorization unless efforts are made to increase student involvement. As part of a trend toward experiential history, historians of science have begun to supplement their lectures with demonstrations of classic physics experiments as a way to bring the history of science to life. Here, the authors report on computer simulations of five landmark experiments from early experimental psychology in the areas of reaction time, span of attention, and apparent motion. The simulations are designed not only to permit hands-on replication of historically important results but also to reproduce the experimental procedures closely enough that students can gain a feel for the nature of early research and the psychological processes being studied.     

Randomization tests for ABAB designs: comparing-data-division- specific and common distributions

Monte Carlo simulations were used to generate data for ABAB designs of different lengths. The points of change in phase are randomly determined before gathering behaviour measurements, which allows the use of a randomization test as an analytic technique. Data simulation and analysis can be based either on data-division-specific or on common distributions. Following one method or another affects the results obtained after the randomization test has been applied. Therefore, the goal of the study was to examine these effects in more detail. The discrepancies in these approaches are obvious when data with zero treatment effect are considered and such approaches have implications for statistical power studies. Data-division-specific distributions provide more detailed information about the performance of the statistical technique.     

Using computers to teach behavior analysis

When it is impractical to provide behavior analysis students with extensive laboratory experience using real organisms, computers can provide effective demonstrations, simulations, and experiments. Furthermore, such computer programs can establish contingency-shaped behavior even in lecture classes, which usually are limited to establishing rule-governed behavior. We describe the development of computerized shaping simulations and the development of software that teaches students to discriminate among reinforcement schedules on the basis of cumulative records.     

A behavioral technology for producing concept formation in university students

Three experiments analyzed the effectiveness of a textbook incorporating "concept programming" in producing concept formation in university students. The concept programming portion of each lesson requires students to determine which concept is illustrated by each of 20 short fictional stories about everyday behavioral situations. The stories are selected to illustrate and contrast the concepts of that lesson. Student responses are heavily prompted during the initial stories of each lesson. The first experiment demonstrated that students generalize to entirely novel examples from the examples in the textbook. The second experiment demonstrated that the concept programming portion of the textbook is a critical component in producing generalization. The third experiment demonstrated that the amount of concept formation produced by the concept programmed textbook is greater than that produced by a widely used standard textbook.     

Overcoming cognitive obstacles in learning fractions: Equal‐partitioning and equal‐whole1

Abstract: The present study was designed to test the hypothesis that acquisition of the concepts of equal‐partitioning and equal‐whole, which constitute implicit knowledge in fractions, promotes understanding of fractions. To test the hypothesis an experimental program based on both the equal‐partitioning and equal‐whole was developed for three third‐grade classrooms in a Japanese elementary school. As a control, conventional teaching based on a Japanese textbook was provided in two third‐grade classrooms. The present study tested the hypothesis that students given such an intervention program would understand order and magnitude as central characteristics of fractions better than those who had been instructed using a traditional textbook. Students in the experimental group showed significantly better understanding of the equal‐partitioning of fractions and the representation of the sizes of fractions than did those in the textbook group. There were, moreover, no differences between the experimental and textbook groups in the performance of routine tasks frequently found in the textbook. These results are discussed in view of the important instructional aims of having students understand fractions.     

Structural modeling and psychometrika: An historical perspective on growth and achievements

The field of linear structural equation modeling with continuous variables is reviewed. Trends in psychometric theory and data analysis across the five decades of publication ofPsychometrika are discussed, especially the clarification of concepts of population and sample, explication of the parametric structure of models, delineation of concepts of exploratory and confirmatory data analysis, expansion of statistical theory in psychometrics, estimation via optimization of an explicit objective function, and implementation of general function minimization methods. Developments in the ideas of factor analysis, latent variables, as well as structural and causal modeling are noted. Some major conceptual achievements involving general covariance structure representations, multiple population models, and moment structures are reviewed. The major statistical achievements of normal theory generalized least squares estimation, elliptical and distribution-free estimation, and higher-moment estimation are discussed. Computer programs that implement some of the theoretical developments are described.This review was supported in part by USPHS grants DA00017 and DA01070.     

Student statistics programs for the Macintosh

This paper reviews 15 statistics programs for the Macintosh. All are intended for student use, often in conjunction with a statistics course, and are available for under $100. Of the general-purpose programs, Data Desk and StatView offer the most appealing combination of features, Macintosh interface, and student-accessible manual. Minitab is also recommended, especially in situations where some students will be using Macs and others using PCs. In addition to the analysis-only programs, two other applications present interesting combinations of statistics and other features. DataSim offers outstanding data generation and experiment simulation along with very complete, and psychology-oriented, statistical analysis. HyperStat combines an entire statistics textbook in hypertext format with a complete data analysis package. Finally, for special situations where simple statistics are all that are required, InStat is recommended because of its tutorial features and very simple interface.     

Perceptual organization of two-dimensional patterns

The perceptual organization of image patterns is considered from 2 standpoints. First, a theoretical framework is presented from which computational models of perceptual organization can be constructed and tested. Second, a specific computational model for perceptual organization of line images is described. In this model, input images are first processed by a dense array of neurons that have properties consistent with recent analyses of single-neuron responses in primary visual cortex. Then, complex image structure is discovered by interleaved pattern-matching and grouping processes constrained by a generalized uniqueness principle. A series of 3-pattern grouping experiments was performed to test a restricted version of the model and to estimate critical parameters. Using the estimated parameters, an extended version of the model was tested by generating predictions for a series of "textbook" perceptual organization demonstrations.     

Reply to Rouder (2014): Good frequentist properties raise confidence

Established psychological results have been called into question by demonstrations that statistical significance is easy to achieve, even in the absence of an effect. One often-warned-against practice, choosing when to stop the experiment on the basis of the results, is guaranteed to produce significant results. In response to these demonstrations, Bayes factors have been proposed as an antidote to this practice, because they are invariant with respect to how an experiment was stopped. Should researchers only care about the resulting Bayes factor, without concern for how it was produced? Yu, Sprenger, Thomas, and Dougherty (2014) and Sanborn and Hills (2014) demonstrated that Bayes factors are sometimes strongly influenced by the stopping rules used. However, Rouder (2014) has provided a compelling demonstration that despite this influence, the evidence supplied by Bayes factors remains correct. Here we address why the ability to influence Bayes factors should still matter to researchers, despite the correctness of the evidence. We argue that good frequentist properties mean that results will more often agree with researchers’ statistical intuitions, and good frequentist properties control the number of studies that will later be refuted. Both help raise confidence in psychological results.     

Statistical power in randomized intervention studies with noncompliance

This study examined various factors that affect statistical power in randomized intervention studies with noncompliance. On the basis of Monte Carlo simulations, this study demonstrates how statistical power changes depending on compliance rate, study design, outcome distributions, and covariate information. It also examines how these factors influence power in different methods of estimating intervention effects. Intent-to-treat analysis and complier average causal effect estimation are compared as 2 alternative ways of estimating intervention effects under noncompliance. The results of this investigation provide practical implications in designing and evaluating intervention studies taking into account noncompliance.     

Authority relationships between obedience and disobedience

Recent episodes of public dissent (such as the demonstrations against G8 policies) raise the issue of the psychological processes triggered in obeying and disobeying the authority. Even if obedience to authority is an important aspect of social life and it plays a key role in maintaining social order, the concept of obedience has been studied in social psychology mainly in terms of its destructive aspects. Besides, most of the studies have overlooked the role of disobedience in the authority relationship. Disobedience may be conceived of as a protest that undermines the legitimacy of the authority or it can represent an instrument for controlling the legitimacy of the authority's demands, becoming a factor protecting against authoritarianism. In this article, a new perspective on the study of the relationship between the individual and the authority is put forward, considering obedience and disobedience as parallel concepts, each having constructive and destructive aspects.     

Love,artificiality and mass identification

How are we to understand the phenomenon of mass identification, epitomised in recent exhibitions of national feeling such as that of South Africa’s 2010 Football World Cup celebrations? Rather than focusing on the concepts of discourse and nationalism, or advancing an analysis of empirical data, this paper outlines a conceptual response to the challenge at hand, drawing on the tools of psychoanalytic theory. Three explanatory perspectives come to the fore. Firstly, such exhibitions of mass emotion might be understood as demonstrations of love, as examples of the libidinal ties that constitute and consolidate mass identification. Secondly, the marked artificiality of such displays of emotion and the fact of the ‘externality’ they entail might be seen, paradoxically, to be essential rather than inauthentic or secondary features of the displays in question. Thirdly, we might advance, via Lacan, that many of our most powerful emotions require not only recourse to the field of the inter-subjective, but reference also to the anonymous, ‘fictional’ framework of available symbolic forms.     

A developmental sequence in preschool children's acquisition of reading readiness skills and print awareness concepts

While various attempts have been made to explain the relationships among preschool children's acquisition of various aspects of print-related knowledge, studies have generally employed statistical procedures appropriate for linear relationships. Yet the relationships among measures of print-related knowledge may not be linear. One technique that has not been employed in this area but which provides a means for identifying nonlinear hierarchical relationships among measures is order analysis. The purpose of this paper was to examine empirically the acquisition of preschool children's print-related knowledge through order analysis. A data set that consisted of 60 preschool children's performances on five measures which assessed concepts about the purposes and processes of reading and the reading readiness skills of letter naming and visual and auditory discrimination was reanalyzed using ordering procedure. A multivariate analysis indicated a multidimensional relationship among the three reading readiness and two print awareness measures that differed across the three age groups. The hierarchical orderings of the five measures indicated that mastery of the reading readiness skills occurred prior to the mastery of the print awareness concepts.     

Specificity of task constraints and effects of visual demonstrations and verbal instructions in directing learners' search during skill acquisition

In the present study, the efficacy of visual demonstrations and verbal instructions as instructional constraints on the acquisition of movement coordination was investigated. Fifteen participants performed an aiming task on 100 acquisition and 20 retention trials, under 1 of 3 conditions: a modeling group (MG), a verbally directed group (VDG), and a control group (CG). The MG observed a model intermittently throughout acquisition, whereas the VDG was verbally instructed to use the model's movement pattern. Participants in the CG received neither form of instruction. Kinematic analysis revealed that compared with verbal instructions or no instructions, visual demonstrations significantly improved participants' approximation of the model's coordination pattern. No differences were found in movement outcomes. Coordination data supported the visual perception perspective on observational learning, whereas outcome data suggested that the modeling effect is mainly a function of task constraints, that is, the novelty of a movement pattern.     

The critical role of group studies in neuropsychology: comprehension regularities in Broca's aphasia

We reexamine the empirical record of the comprehension abilities of Broca's aphasic patients. We establish clear, commonly accepted, selection criteria and obtain a pool of results. We then subject these results to a detailed statistical analysis and show that these patients comprehend certain canonical sentences (actives, subject relatives, and clefts with agentive predicates) at above-chance levels, whereas comprehension of sentences that contain deviations from canonicity (passives, object-gap relatives, and clefts) is distinct and is at chance. That the latter is the case, and patients indeed guess at such structures, we show by comparing the distribution of individual results in passive comprehension to that of a model for such guessing-an analogous series of tosses of an unbiased coin. The two distributions are virtually identical. We conclude that the group's performance is stable, and well-delineated, despite intersubject variation whose source is now identified. This means that certain comprehension tests may not always be used for the diagnosis of individual patients, but they do characterize the group. It also means that group studies are not just a valid option in neuropsychology; they are a must, since demonstrations like ours indiciate very clearly that single-case studies may be misleading. As we show, the findings from any one patient, without the context of a group, may give a distorted picture of the pathological reality. Our conclusions thus promote studies of groups of brain-damaged patients as a central tool for the investigation of brain/behavior relations.