Using baseline logic to determine when to change phases within single case experimental designs: Fail safe k values and statistical power

Abstract When using baseline logic with single case experimental designs (SCEDs), one critical step involves collecting enough treatment data points, relative to the number of data points in the previous baseline phase, to set the occasion for relatively equivalent samples of the target behavior across phases. The fail safe k metric for SCED data provides a robust metric to complement visual inspection of graphed data to determine if enough sessions were conducted within a phase of the SCED to adequately predict the level, trend, and stability of the data path if more sessions were conducted in that phase. There was a strong relationship between fail safe k values and statistical power to detect differences in the dependent variable across phases relative to different criteria for estimating treatment effect sizes. Both quantifications suggested that decision rules for changing phases are associated with achieving an acceptable level of statistical power but with varying degrees of sensitivity and specificity for detecting treatment effects.