A generalized least squares regression approach for computing effect sizes in single-case research: application examples

A new method for deriving effect sizes from single-case designs is proposed. The strategy is applicable to small-sample time-series data with autoregressive errors. The method uses Generalized Least Squares (GLS) to model the autocorrelation of the data and estimate regression parameters to produce an effect size that represents the magnitude of treatment effect from baseline to treatment phases in standard deviation units. In this paper, the method is applied to two published examples using common single case designs (i.e., withdrawal and multiple-baseline). The results from these studies are described, and the method is compared to ten desirable criteria for single-case effect sizes. Based on the results of this application, we conclude with observations about the use of GLS as a support to visual analysis, provide recommendations for future research, and describe implications for practice.     

An effect size measure and Bayesian analysis of single-case designs

This article describes a linear modeling approach for the analysis of single-case designs (SCDs). Effect size measures in SCDs have been defined and studied for the situation where there is a level change without a time trend. However, when there are level and trend changes, effect size measures are either defined in terms of changes in R² or defined separately for changes in slopes and intercept coefficients. We propose an alternate effect size measure that takes into account changes in slopes and intercepts in the presence of serial dependence and provides an integrated procedure for the analysis of SCDs through estimation and inference based directly on the effect size measure. A Bayesian procedure is described to analyze the data and draw inferences in SCDs. A multilevel model that is appropriate when several subjects are available is integrated into the Bayesian procedure to provide a standardized effect size measure comparable to effect size measures in a between-subjects design. The applicability of the Bayesian approach for the analysis of SCDs is demonstrated through an example.     

Detrended windowed (lag one) autocorrelation: A new method for distinguishing between event-based and emergent timing

Previous research on route directions largely considers the case when a knowledgeable route-giver conveys accurate information. In the real world, however, route information is sometimes inaccurate, and directions can lead navigators astray. We explored how participants respond to route directions containing ambiguities between landmarks and turn directions, forcing reliance on one or the other. In three experiments, participants read route directions (e.g., To get to the metro station, take a right at the pharmacy) and then selected from destinations on a map. Critically, in half of the trials the landmark (pharmacy) and turn (right) directions were conflicting, such that the participant had to make a decision under conditions of uncertainty; under these conditions, we measured whether participants preferentially relied upon landmark- versus direction-based strategies. Across the three experiments, participants were either provided no information regarding the source of directions (Experiment 1), or told that the source of directions was a GPS device (Experiment 2), or a human (Experiment 3). Without information regarding the source of directions, participants generally relied on landmarks or turn information under conditions of ambiguity; in contrast, with a GPS source participants relied primarily on turn information, and with a human source on landmark information. Results were robust across gender and individual differences in spatial preference. We discuss these results within the context of spatial decision-making theory and consider implications for the design and development of landmark-inclusive navigation systems.