Molecular and molar analyses of fixed-interval performance.

The team looked at pigeons working on fixed-interval schedules. They wanted to know if averaging many intervals together hides or reveals patterns. They plotted each interval alone, then averaged many intervals together.

They also checked how the chance of responding grows as the interval moves toward food delivery.

Single-interval records looked messy. No smooth scallop appeared. When they averaged many intervals, the classic scallop shape showed up.

Conditional probability also rose as time to food ran out. This matched the averaged curve.

McSweeney et al. (1993) warned that averaging creates fake patterns. They said scallops are artifacts. Davis et al. (1994) reply: averaging uncovers a real pattern you miss in single records. The fight is about whether the scallop lives in the bird or in the math.

Feldman et al. (1999) ran the same test on fixed-ratio schedules. Means hid skewed pause times. Both papers tell us: look at distributions, not just averages.

Shimp (2020) gives a 2020 update. His model lets you see both moment and session views at once. The new tool keeps both grains without forcing you to pick sides.

When you graph a client’s DRL or self-monitoring data, one messy day can hide a trend. Try plotting both single-day lines and a weekly average. If the average shows a curve the single days hide, you may have found a real timing pattern. That tells you the schedule, not the learner, is driving the shape.