Methodology, the matching law, and applied behavior analysis.

Vyse (1986) wrote a think-piece, not an experiment. The paper asked one big question. How can we make fancy math tools help everyday BCBAs?

The author looked at the matching law and other rate equations. He said they are too tidy for real classrooms and clinics. Kids move in and out of seats. Reinforcers vary by the minute. The old formulas ignore that mess.

The paper found a gap. Quantitative models work in labs, but they skip transition states and absolute counts. Without those pieces, a BCBA cannot use the numbers to pick an intervention.

Vyse (1986) urged builders of new methods to track every response and to handle messy, shifting conditions.

St. D'Incal et al. (2025) took the idea into fidelity checks. They tell you to add response-rate lines to your procedural-fidelity graphs. Percent correct can hide drift. Rate shows when staff slow down or speed up.

Spanoudis et al. (2011) gave the tool. They filmed scripted sessions and timed every response. Trained observers hit ±0.1 responses per minute. That accuracy lets you trust small rate changes in the classroom.

Bell (1999) and Branch (1999) sound like they fight. One says add simple stats, the other says drop p-values. Both agree with Vyse (1986) on one point. Eyeballing graphs is not enough. You need a clear rule for deciding an effect is real.

Fingerhut et al. (2023) audited 218 single-case papers. Most used non-overlap indices with no reason given. The review shows the field still needs the guidance Vyse (1986) asked for: pick a metric and justify it.

You no longer have to wait for perfect math. Calibrate your observers with short clips and a timer. Add rate lines next to your fidelity percentages. Use a simple success-rate tally like Faso et al. (2016) to decide when you have enough proof. These steps turn old lab equations into Monday-morning tools you can trust.