Assessment & Research

"A simplified time-series analysis for evaluating treatment interventions": A rejoinder to Blumberg.

Tryon (1984) · Journal of applied behavior analysis 1984
★ The Verdict

The C statistic can call a clear improvement "no effect" when data line up in a straight slope.

✓ Read this if BCBAs who use or read single-case meta-analyses.
✗ Skip if Clinicians who rely only on visual inspection and never compute effect sizes.

01Research in Context

01

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.

02

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.

03

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.

04

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.

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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

Intervention
not applicable
Design
theoretical
Finding
not reported

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