This study investigates three methods to handle dependency among effect size estimates in meta-analysis arising from studies reporting multiple outcome measures taken on the same sample. The three-level approach is compared with the method of robust variance estimation, and with averaging effects within studies. A simulation study is performed, and the fixed and random effect estimates of the three methods are compared with each other. Both the robust variance estimation and three-level approach result in unbiased estimates of the fixed effects, corresponding standard errors and variances. Averaging effect sizes results in overestimated standard errors when the effect sizes within studies are truly independent. Although the robust variance and three-level approach are more complicated to use, they have the advantage that they do not require an estimate of the correlation between outcomes, and they still result in unbiased parameter estimates.

Single-case experimental designs (SCEDs) have been increasingly used in recent years to inform the development and validation of effective interventions in the behavioral sciences. An important aspect of this work has been the extension of meta-analytic and other statistical innovations to SCED data. Standard practice within SCED methods is to display data graphically, which requires subsequent users to extract the data, either manually or using data extraction programs. Previous research has examined issues of reliability and validity of data extraction programs in the past, but typically at an aggregate level. Little is known, however, about the coding of individual data points. We focused on four different software programs that can be used for this purpose (i.e., Ungraph, DataThief, WebPlotDigitizer, and XYit), and examined the reliability of numeric coding, the validity compared with real data, and overall program usability. This study indicates that the reliability and validity of the retrieved data are independent of the specific software program, but are dependent on the individual single-case study graphs. Differences were found in program usability in terms of user friendliness, data retrieval time, and license costs. Ungraph and WebPlotDigitizer received the highest usability scores. DataThief was perceived as unacceptable and the time needed to retrieve the data was double that of the other three programs. WebPlotDigitizer was the only program free to use. As a consequence, WebPlotDigitizer turned out to be the best option in terms of usability, time to retrieve the data, and costs, although the usability scores of Ungraph were also strong.

A variety of measures have been developed to quantify intervention effects for single-case experimental design studies. Within the family of non-overlap indices, the Tau-U measure is one of the most popular indices. There are several Tau-U variants, each one calculated differently. The appropriateness of each Tau-U variant depends upon the data characteristics present within the study (e.g. number of measurement occasions, the within-case variability, and baseline trend). However, inconsistent terminology is used to refer to the Tau-U variants, and researchers can overlook the attributes of the different Tau-U variants. As a result, the Tau-U variants can be applied inappropriately, and this can result in invalid conclusions of intervention effectiveness. This paper proposes a Tau-U flowchart that can assist the decision-making process when using Tau-U with single-case experimental designs that incorporate baseline-intervention (AB) comparisons (e.g. multiple-baseline designs, withdrawal/reversal designs, etc.). The flowchart can help researchers select the appropriate Tau-U variant to use based on their data and research questions. The flowchart is applied to two single-case experimental studies to demonstrate its use.

In this article, multiple-baseline across participants designs were used to evaluate the impact of a precision teaching (PT) program, within a Tier 2 Response to Intervention framework, targeting fluency in foundational reading skills with at risk kindergarten readers. Thirteen multiple-baseline design experiments that included participation from 35 kindergarten students were included in the current analysis. By combining data from a series of multiple-baseline studies using a multilevel model, we analyzed outcomes to determine an estimated treatment effect. The results indicate that across participants and across studies, PT showed an average increase of 15 correct responses in foundational reading skills per minute. This immediate influence on rates of core reading skills was statistically significant. Moreover, the treatment had a significant positive effect on the time trend indicating that rates in foundational reading skills increased more across time during the treatment phase compared to the baseline phase. The study provides evidence that the obtained rates in foundational reading skills at the end of the intervention were retained after removing the intervention. From the outcomes of the multilevel model, PT can be considered as a promising Tier 2 intervention to increase reading fluency with individuals who are at risk of reading failure.