An Improved Rank Correlation Effect Size Statistic for Single-Case Designs: Baseline Corrected Tau.
Drop Tau-U and use Baseline Corrected Tau for cleaner single-case effect sizes.
01Research in Context
What this study did
Tarlow (2017) built a new math tool for single-case graphs.
The tool is called Baseline Corrected Tau.
It fixes problems with the older Tau-U formula.
What they found
The new number always stays between -1 and +1.
It removes baseline trend better than Tau-U.
You can plot it right on the graph so parents see the change.
How this fits with other research
Pitchford et al. (2019) warned that Tau-U can look too good when kids hit reading ceilings.
Tarlow (2017) gives you a safer number to report instead.
Morris et al. (2022) showed another way to quantify kid choices with the matching law.
Both papers help BCBAs use clean numbers, not just eyeball graphs.
Why it matters
Next time you run a single-case study, swap the old Tau-U for Baseline Corrected Tau. The number is honest, easy to explain, and keeps ceiling effects from tricking you or the IEP team.
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02At a glance
03Original abstract
Measuring treatment effects when an individual's pretreatment performance is improving poses a challenge for single-case experimental designs. It may be difficult to determine whether improvement is due to the treatment or due to the preexisting baseline trend. Tau- U is a popular single-case effect size statistic that purports to control for baseline trend. However, despite its strengths, Tau- U has substantial limitations: Its values are inflated and not bound between -1 and +1, it cannot be visually graphed, and its relatively weak method of trend control leads to unacceptable levels of Type I error wherein ineffective treatments appear effective. An improved effect size statistic based on rank correlation and robust regression, Baseline Corrected Tau, is proposed and field-tested with both published and simulated single-case time series. A web-based calculator for Baseline Corrected Tau is also introduced for use by single-case investigators.
Behavior modification, 2017 · doi:10.1177/0145445516676750