Richard I. Parker

An improved effect size for single-case research: nonoverlap of all pairs.

Nonoverlap of All Pairs (NAP), an index of data overlap between phases in single-case research, is demonstrated and field tested with 200 published AB contrasts. NAP is a novel application of an established effect size known in various forms as Area Under the Curve (AUC), the Common Language Effect Size (CL), the Probability of Superiority (PS), the Dominance Statistic (DS), Mann-Whitneys U, and Sommers D, among others. NAP was compared with 3 other non-overlap-based indices: PND (percent of nonoverlapping data), PEM (percent of data points exceeding the median), and PAND (percent of all nonoverlapping data), as well as Pearsons R(2). Five questions were addressed about NAP: (a) typical NAP values, (b) its ability to discriminate among typical single-case research results, (c) its power and precision (confidence interval width), (d) its correlation with the established effect size index, R(2), and (e) its relationship with visual judgments. Results were positive, the new index equaling or outperforming the other overlap indices on most criteria.

Combining Nonoverlap and Trend for Single-Case Research: Tau-U

A new index for analysis of single-case research data was proposed, Tau-U, which combines nonoverlap between phases with trend from within the intervention phase. In addition, it provides the option of controlling undesirable Phase A trend. The derivation of Tau-U from Kendalls Rank Correlation and the Mann-Whitney U test between groups is demonstrated. The equivalence of trend and nonoverlap is also shown, with supportive citations from field leaders. Tau-U calculations are demonstrated for simple AB and ABA designs. Tau-U is then field tested on a sample of 382 published data series. Controlling undesirable Phase A trend caused only a modest change from nonoverlap. The inclusion of Phase B trend yielded more modest results than simple nonoverlap. The Tau-U score distribution did not show the artificial ceiling shown by all other nonoverlap techniques. It performed reasonably well with autocorrelated data. Tau-U shows promise for single-case applications, but further study is desirable.

Effect Size in Single-Case Research: A Review of Nine Nonoverlap Techniques

With rapid advances in the analysis of data from single-case research designs, the various behavior-change indices, that is, effect sizes, can be confusing. To reduce this confusion, nine effect-size indices are described and compared. Each of these indices examines data nonoverlap between phases. Similarities and differences, both conceptual and computational, are highlighted. Seven of the nine indices are applied to a sample of 200 published time series data sets, to examine their distributions. A generic meta-analytic method is presented for combining nonoverlap indices across multiple data series within complex designs.

Percentage of All Non-Overlapping Data (PAND) An Alternative to PND

Although single-case researchers are not accustomed to analyzing data statistically, standards for research and accountability from government and other funding agents are creating pressure for more objective, reliable data. In addition, “evidence-based interventions” movements in special education, clinical psychology, and school psychology imply reliable data summaries. Within special education, two heavily debated single-case research (SCR) statistical indices are “percentage of non-overlapping data” (PND) and the regression effect size, R2 . This article proposes a new index—PAND, the “percentage of all non-overlapping data”—to remedy deficiencies of both PND and R2 . PAND is closely related to the established effect size, Pearsons Phi , the “fourfold point correlation coefficient.” The PAND/ Phi procedure is demonstrated and applied to 75 published multiple baseline designs to answer questions about typical effect sizes, relationships with PND and R2 , statistical power, and time efficiency. Confidence intervals and p values for Phi also are demonstrated. The findings are that PAND/ Phi and PND correlate equally well to R2 . However, only PAND/Phi could show adequate power for most of the multiple baseline designs sampled. The findings suggest that PAND/Phi may meet the requirement for a useful effect size for multiple baseline and other longer designs in SCR.

The Improvement Rate Difference for Single-Case Research

This article describes and field-tests the improvement rate difference (IRD), a new effect size for summarizing single-case research data. Termed “risk difference” in medical research, IRD expresses the difference in successful performance between baseline and intervention phases. IRD can be calculated from visual analysis of nonoverlapping data, and is easily explained to most educators. IRD entails few data assumptions and has confidence intervals. The article applies IRD to 166 published data series, correlates results with three other effect sizes: R2, Kruskal-Wallis W, and percent of nonoverlapping data (PND), and reports interrater reliability of the IRD hand scoring. The major finding is that IRD is a promising effect size for single-case research.

A Meta-Analysis of Single Case Research Studies on Aided Augmentative and Alternative Communication Systems with Individuals with Autism Spectrum Disorders

Many individuals with autism cannot speak or cannot speak intelligibly. A variety of aided augmentative and alternative communication (AAC) approaches have been investigated. Most of the research on these approaches has been single-case research, with small numbers of participants. The purpose of this investigation was to meta-analyze the single case research on the use of aided AAC with individuals with autism spectrum disorders (ASD). Twenty-four single-case studies were analyzed via an effect size measure, the Improvement Rate Difference (IRD). Three research questions were investigated concerning the overall impact of AAC interventions on targeted behavioral outcomes, effects of AAC interventions on individual targeted behavioral outcomes, and effects of three types of AAC interventions. Results indicated that, overall, aided AAC interventions had large effects on targeted behavioral outcomes in individuals with ASD. AAC interventions had positive effects on all of the targeted behavioral outcome; however, effects were greater for communication skills than other categories of skills. Effects of the Picture Exchange Communication System and speech-generating devices were larger than those for other picture-based systems, though picture-based systems did have small effects.

The relationship between visual analysis and five statistical analyses in a simple AB single-case research design.

This study explored some practical issues for single-case researchers who rely on visual analysis of graphed data, but who also may consider supplemental use of promising statistical analysis techniques. The study sought to answer three major questions: (a) What is a typical range of effect sizes from these analytic techniques for data from “effective interventions”? (b) How closely do results from these same analytic techniques concur with visual-analysis-based judgments of effective interventions? and (c) What role does autocorrelation play in interpretation of these analytic results? To answer these questions, five analytic techniques were compared with the judgments of 45 doctoral students and faculty, who rated intervention effectiveness from visual analysis of 35 fabricated AB design graphs. Implications for researchers and practitioners using single-case designs are discussed.

Effects of Two Tutoring Programs on the English Reading Development of Spanish-English Bilingual Students

Spanish-dominant bilingual students in grades 2-5 were tutored 3 times per week for 40 minutes over 10 weeks, using 2 English reading interventions. Tutoring took place from February through April of 1 school year. One, Read Well, combined systematic phonics instruction with practice in decodable text, and the other, a revised version of Read Naturally, consisted of repeated reading, with contextualized vocabulary and comprehension instruction. The progress of tutored students (n = 51) was compared to that of nontutored classmates (n = 42) using subtests of the Woodcock Reading Mastery Tests-Revised. Students who received systematic phonics instruction made significant progress in word identification but not in word attack or passage comprehension. There were no significant effects for students in the repeated reading condition.

Moderating factors of video-modeling with other as model: A meta-analysis of single-case studies

Video modeling with other as model (VMO) is a more practical method for implementing video-based modeling techniques, such as video self-modeling, which requires significantly more editing. Despite this, identification of contextual factors such as participant characteristics and targeted outcomes that moderate the effectiveness of VMO has not previously been explored. The purpose of this study was to meta-analytically evaluate the evidence base of VMO with individuals with disabilities to determine if participant characteristics and targeted outcomes moderate the effectiveness of the intervention. Findings indicate that VMO is highly effective for participants with autism spectrum disorder (IRD=.83) and moderately effective for participants with developmental disabilities (IRD=.68). However, differential effects are indicated across levels of moderators for diagnoses and targeted outcomes. Implications for practice and future research are discussed.

Intensive Intervention in Reading Fluency for At-Risk Beginning Spanish Readers.

Abstract A study was conducted using a single case, multiple baseline (across subjects) design to study an intensive reading intervention among low-achieving at-risk students in first and second grade Spanish/English bilingual classrooms. The intervention, involving three research-supported techniques, was conducted for 45 minutes per day, three days per week, over 12 weeks, with 74 students from four classrooms (analyses included 53 students with complete data). Dependent measures were oral reading fluency scores and comprehension scores from post-reading questions, collected every two weeks from equivalent probes. It was concluded that implementing intensive reading fluency interventions in bilingual classrooms is feasible and valuable if conducted with fidelity, and if students are highly engaged.