Community applications of instructional technology: teaching writers of instructional packages

A community education program, to develop a variety of performance competencies in large numbers of neighborhood residents, requires a technology for preparing learning units administerable by community members themselves. The effects of a writing manual, designed to teach nonprofessionals to prepare such instructional packages, were analyzed in two experiments. Experiment I employed a multiple-baseline design across three university student trainees. The results showed that appropriate program writing increased by 75% after completion of the manual. The results of Experiment II, with two low-income neighborhood residents serving as trainees, showed that packages produced by trained writers resulted in a greater increase in skill activities than sets of training stimuli produced by untrained writers.     

Time-series analysis in operant research

A time-series method is presented, nontechnically, for analysis of data generated in individual-subject operant studies, and is recommended as a supplement to visual analysis of behavior change in reversal or multiple-baseline experiments. The method can be used to identify three kinds of statistically significant behavior change: (a) changes in score levels from one experimental phase to another, (b) reliable upward or downward trends in scores, and (c) changes in trends between phases. The detection of, and reliance on, serial dependency (autocorrelation among temporally adjacent scores) in individual-subject behavioral scores is emphasized. Examples of published data from the operant literature are used to illustrate the time-series method.     

On rotating to smooth functions

Tucker has outlined an application of principal components analysis to a set of learning curves, for the purpose of identifying meaningful dimensions of individual differences in learning tasks. Since the principal components are defined in terms of a statistical criterion (maximum variance accounted for) rather than a substantive one, it is typically desirable to rotate the components to a more interpretable orientation. Simple structure is not a particularly appealing consideration for such a rotation; it is more reasonable to believe that any meaningful factor should form a (locally) smooth curve when the component loadings are plotted against trial number. Accordingly, this paper develops a procedure for transforming an arbitrary set of component reference curves to a new set which are mutually orthogonal and, subject to orthogonality, are as smooth as possible in a well defined (least squares) sense. Potential applications to learning data, electrophysiological responses, and growth data are indicated.Portions of this research were supported by the National Research Council of Canada, Grant A8615 to the second author. We thank Jagdeth Sheth for supplying his raw data.     

Two-step weighted least squares factor analysis of dichotomized variables

A two-step weighted least squares estimator for multiple factor analysis of dichotomized variables is discussed. The estimator is based on the first and second order joint probabilities. Asymptotic standard errors and a model test are obtained by applying the Jackknife procedure.     

Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A monte carlo study

In order to make the parallel analysis criterion for determining the number of factors easy to use, regression equations for predicting the logarithms of the latent roots of random correlation matrices, with squared multiple correlations on the diagonal, are presented. The correlation matrices were derived from distributions of normally distributed random numbers. The independent variables are log (N–1) and log {[n(n–1)/2]–[(i–1)n]}, whereN is the number of observations;n, the number of variables; andi, the ordinal position of the eigenvalue. The results were excellent, with multiple correlation coefficients ranging from .9948 to .9992.This research was supported by the Office of Naval Research under Contract N00014-67-A-0305-0012, Lloyd G. Humphreys, principal investigator, and by the Department of Computer Science of which Richard G. Montanelli, Jr., is a member.     

Comments on “the measurement of factorial indeterminacy”

Guttman's index of indeterminacy (2² – 1) measures the potential amount of uncertainty in picking the right alternative interpretation for a factor. When alternative solutions for a factor are equally likely to be correct, then the squared multiple correlation ² for predicting the factor from the observed variables is the average correlation _AB between independently selected alternative solutionsA andB, while var ( _AB )=(1 – ²)²/s, wheres is the dimensionality of the space in which unpredicted components of alternative solutions are to be found. When alternative solutions for the factor are not equally likely to be chosen, ² is the lower bound for E( _AB ); however, E( _AB ) need not be a modal value in the distribution of _AB . Guttman's index and E( _AB ) measure different aspects of the same indeterminacy problem.     

A look,by simulation,at the validity of some asymptotic distribution results for rotated loadings

In the last few years, a number of asymptotic results for the distribution of unrotated and rotated factor loadings have been given. This paper investigates the validity of some of these results based on simulation techniques. In particular, it looks at principal component extraction and quartimax rotation on a problem with 13 variables. The indication is that the asymptotic results are quite good.     

Maintenance of Relationship and Individual Functioning Gains Following Online Relationship Programs for Low‐Income Couples

Initial evidence suggests that gains in relationship functioning from brief, web‐based programs are maintained through one year following the intervention; however, whether these results generalize to a low‐income sample is unclear. Furthermore, previous research from in‐person couple therapy suggests there may be different shapes of maintenance slopes for behavioral versus acceptance‐based techniques. This study contacted 668 individuals who enrolled in online behavioral (ePREP) or acceptance‐based (OurRelationship) programs one year following completion of the program. Multilevel modeling was used to examine linear and quadratic rates of change in the year following the online intervention as well as total amount of change from pretreatment to 12‐month follow‐up for both relationship and individual functioning. The majority of couples who responded continued to be in a relationship with the same partner (68.3%). Examinations of relationship functioning indicated couples in both programs maintained their gains over follow‐up (i.e., no significant linear or quadratic changes), with medium‐to‐large within‐group effect sizes from pre‐ to one‐year follow‐up. There were no significant differences in relationship outcomes between OurRelationship and ePREP. Similarly, examinations of individual functioning outcomes indicated couples maintained their gains over follow‐up or continued to improve. In total, couples experienced small‐to‐medium within‐group effect sizes from pretreatment to one‐year follow‐up, with larger effects for individuals who were initially distressed. These results suggest that online programs create lasting change for low‐income couples in relationship and individual functioning, with minimal differences between behavioral and acceptance‐based orientations.