Abstract
Recently, there has been an increased interest in developing statistical methodologies for analyzing single case experimental design (SCED) data to supplement visual analysis. Some of these are simulation-driven such as Bayesian methods because Bayesian methods can compensate for small sample sizes, which is a main challenge of SCEDs. Two simulation-driven approaches: Bayesian unknown change-point model (BUCP) and simulation modeling analysis (SMA) were compared in the present study for three real datasets that exhibit “clear” immediacy, “unclear” immediacy, and delayed effects. Although SMA estimates can be used to answer some aspects of functional relationship between the independent and the outcome variables, they cannot address immediacy or provide an effect size estimate that considers autocorrelation as required by the What Works Clearinghouse (WWC) Standards. BUCP overcomes these drawbacks of SMA. In final analysis, it is recommended that both visual and statistical analyses be conducted for a thorough analysis of SCEDs.
Highlights
Single case experimental designs (SCEDs) investigate change within an individual or a sampling unit rather than aggregate change for a group of individuals or units
In Bayesian unknown change-point model (BUCP) analysis, the entire data from all phases are treated as one sequence of points and the BUCP algorithm searches for the change-point(s) in the sequence where there is a substantial change in the relationship between the independent variable and the outcome variable
This way of determining immediacy is highly subjective due to: (a) there being no guideline on how to interpret the magnitude of this difference to establish immediacy; this magnitude depends on the scale of the outcome variable; (b) not taking into account the patterns of all the data points in the phases; and (c) the median computed ignoring the autocorrelations between observations
Summary
Single case experimental designs (SCEDs) investigate change within an individual or a sampling unit rather than aggregate change for a group of individuals or units. SCED studies are interrupted time series designs where an outcome variable is assessed repeatedly for an individual (or unit) over different phases. Single case experimental designs have traditionally relied on visual analysis of graphs from multiple phases for determining the presence and magnitude of a treatment effect. Often visual analysis reports are supplemented with reporting phase means, medians, percentages, and effect sizes such as standardized mean differences or indices based on the amount of data overlap between phases (Parker et al, 2007). Visual analysis has definite advantages with analyzing SCED data, studies have shown that the presence of autocorrelation can confound the results of visual analysis.
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