A comparison of mean phase difference and generalized least squares for analyzing single-case data

Abstract

The present study focuses on single-case data analysis and specifically on two procedures for quantifying differences between baseline and treatment measurementsThe first technique tested is based on generalized least squares regression analysis and is compared to a proposed non-regression technique, which allows obtaining similar information. The comparison is carried out in the context of generated data representing a variety of patterns (i.e., independent measurements, different serial dependence underlying processes, constant or phase-specific autocorrelation and data variability, different types of trend, and slope and level change). The results suggest that the two techniques perform adequately for a wide range of conditions and researchers can use both of them with certain guarantees. The regression-based procedure offers more efficient estimates, whereas the proposed non-regression procedure is more sensitive to intervention effects. Considering current and previous findings, some tentative recommendations are offered to applied researchers in order to help choosing among the plurality of single-case data analysis techniques.

Single-case experimental designs: Reflections on conduct and analysis

“…Shadish et al, this issue; the unstandardized Mean phase difference; Manolov & Solanas, 2013; see also Swaminathan et al, this issue) or the change in slope (e.g., the Slope and level change procedure [Solanas, Manolov, & Onghena, 2010], also offering unstandardized estimates). Of these, the R-squared and the d statistic are classic parametric effect size indices, though the nonoverlap measures are commonly applied to SCED studies.…”

“…Mean phase difference technique: R code available in the article presenting the procedure (Manolov & Solanas, 2013) and also online at https://dl.dropboxusercontent.com/s/nky75oh40f1gbwh/MPD.R. o Multilevel models: several alternative platforms can be used including two specifically designed programs (HLM, MLwiN), the lme4 and nlme packages in R, proc mixed and proc glimmix in SAS, the mixed option using SPSS syntax, and the gllamm programme in Stata) of which only R is open-source.…”

Further developments in summarising and meta-analysing single-case data: An illustration with neurobehavioural interventions in acquired brain injury

“…All of these analytical options, in contrast to non-overlap indices (e.g., percentage of non-overlapping data: Scruggs & Mastropieri, 2013; Tau-U: Parker, Vannest, Davis, & Sauber, 2011), directly incorporate the option of summarising the results of an MBD by considering all comparisons between a baseline and a subsequent intervention phase. Nevertheless, we consider it necessary to propose a way to provide summary indices for other existing SCED analytical procedures that are applicable to MBD; specifically, we focus on the slope and level change (SLC; Solanas, Manolov, & Onghena, 2010) and the mean phase difference (MPD; Manolov & Solanas, 2013) procedures. The reason for this choice can be found in the desirable features of these indicators, as well as in the limitations of the above-mentioned procedures.…”

“…The joint use of these procedures answers (a) Beretvas and Chung's (2008) call for separate estimation of different effects, as the SLC quantifies change in slope and then the net change in level, something that is also possible with multilevel models (Van den Noortgate & Onghena, 2008) and (b) Swaminathan, Rogers, and Horner's (2014) emphasis on the need for quantification of the overall effect, as the MPD offers single quantification. Moreover, these procedures have shown acceptable performance (Manolov & Solanas, 2013;Manolov, Solanas, Sierra, & Evans, 2011;Solanas et al, 2010) and are accompanied by easy-to-use code in the open-source software R, which makes their use straightforward.…”

The state of the Journal of School Psychology: Promoting science

“…JSP is an excellent source for manuscripts focused on the "how-to" of methodological and statistical techniques that are being used by researchers. Occasionally, these papers stand on their own as general manuscripts such as the following recently published articles focused on (a) mean phase differences and generalized least squares for analyzing single-case design (Manolov & Solanas, 2013); (b) reliability of multi-category ratings scales (Parker, Vannest, & Davis, 2013); (c) single-case effect size calculation (Ross & Begeny, 2014); and (d) a practical guide to generalizability theory (Briesch, Swaminathan, Welsh, & Chafouleas, 2014). As an author, if you are considering submitting a paper focused on methodological and statistical techniques, please feel free to contact me to discuss your idea.…”