"A simplified time-series analysis for evaluating treatment interventions": A rejoinder to Blumberg.
The C statistic can call a clear improvement "no effect" when data line up in a straight slope.
01Research in Context
What this study did
Dodd (1984) wrote a short reply to another scientist. The paper did not collect new data. It showed, with math, that the C statistic can fool you.
The C statistic counts how many data points fall above or below a line. If the line is perfectly straight, the count says nothing about change.
What they found
The C statistic equals zero when data line up in a straight slope. Zero looks like "no effect," even if the behavior is clearly improving.
In other words, the tool can say "nothing happened" when something really did.
How this fits with other research
Mulvaney et al. (1974) and Michael (1974) said the same thing ten years earlier: most summary numbers break in single-case work. Dodd (1984) gave a fresh example.
Campbell (2004) later tested four newer effect sizes. All four still disagreed, proving the problem is alive.
Barnard-Brak et al. (2020) offered a fix: use Bayesian N-of-1 models instead of simple counts. Their method sidesteps the straight-line trap that W warned about.
Why it matters
If you plug numbers into a formula without looking at the graph, you can miss real change. Always pair visual analysis with any summary number. If the data look like a perfect ramp, skip the C statistic and pick a tool that measures slope or level, not just overlap.
Want CEUs on This Topic?
The ABA Clubhouse has 60+ free CEUs — live every Wednesday. Ethics, supervision & clinical topics.
Join Free →Before you report any effect size, plot the data and check for a straight ramp — if you see one, pick a different metric.
02At a glance
03Original abstract
first problem with the C statistic is that a condition exists where C is a function only of the number of data points in the series and not the slope of the series. This is the unlikely case where all the data points form an exact linear sequence. This special condition shows that the C statistic is not a measure of effect size.
Journal of applied behavior analysis, 1984 · doi:10.1901/jaba.1984.17-543