On the analysis of studies of choice.
Stop using the fixed slope window—compute a fresh confidence interval for every matching analysis.
01Research in Context
What this study did
The authors looked at 103 data sets from animal choice studies. They checked how often the strict matching rule held. They also tested the old rule that says a slope between .90 and 1.11 means matching.
What they found
Undermatching showed up almost every time. Animals spread their responses more evenly than the strict rule predicts. The fixed slope window missed many true curves. They say compute your own confidence band instead.
How this fits with other research
Hopkins et al. (1977) first spotted undermatching in four pigeon studies. Tanguay et al. (1982) now shows the same pattern in over one hundred sets, so the trend is robust.
Nasr et al. (2000) looks like a clash. Humans on negative-slope schedules burst and pause, not smooth undermatch. The gap is explained by species and schedule type, not by theory failure.
Jensen (2014) offers a next step. Once you drop the fixed window, use the free compositional tool to get clean estimates with three or more choices.
Why it matters
If you run concurrent schedules in the clinic, expect clients to undermatch. Do not trust the .90-1.11 shortcut. Fit the line, plot the confidence band, and base your clinical call on that range. Better stats mean better decisions about which schedule to pick next.
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Join Free →Graph last week’s concurrent data, add a trend line with 95 % CI, and check if the band crosses 1.0 before you call it a match.
02At a glance
03Original abstract
In a review of 103 sets of data from 23 different studies of choice, Baum (1979) concluded that whereas undermatching was most commonly observed for responses, the time measure generally conformed to the matching relation. A reexamination of the evidence presented by Baum concludes that undermatching is the most commonly observed finding for both measures. Use of the coefficient of determination by both Baum (1979) and de Villiers (1977) for assessing when matching occurs is criticized on statistical grounds. An alternative to the loss-in-predictability criterion used by Baum (1979) is proposed. This alternative statistic has a simple operational meaning and is related to the usual F-ratio test. It can therefore be used as a formal test of the hypothesis that matching occurs. Baum (1979) also suggests that slope values of between .90 and 1.11 can be considered good approximations to matching. It is argued that the establishment of a fixed interval as a criterion for determining when matching occurs, is inappropriate. A confidence interval based on the data from any given experiment is suggested as a more useful method of assessment.
Journal of the experimental analysis of behavior, 1982 · doi:10.1901/jeab.1982.37-323