Averaging Effects In The Study Of Fixed-ratio Response Patterns.
Averaged pause data hide skew—look at distributions, not just means, when interpreting fixed-ratio performance.
01Research in Context
What this study did
The team looked at fixed-ratio pauses. They wanted to see if averaging hides the real pattern.
They ran several FR sizes with the same subjects. Then they plotted every single pause, not just the mean.
What they found
Longer upcoming ratios did make pauses longer. But the average line hid two facts.
Most pauses bunched at the short end. A few long pauses pulled the mean up, so the distributions overlapped across conditions.
How this fits with other research
Halpern et al. (1966) first showed the pause-ratio link in pigeons. Their tidy averages looked clean because they never plotted the raw spread.
Crossman et al. (1985) seems to disagree: small FR 1-7 made pauses shorten as ratio grew. The clash disappears when you notice ratio range. Small ratios behave differently; both papers can be right.
MIGLER (1964) warned the same thing for stimulus generalization. Averaging washed out individual curves then; now it hides skewed pause piles.
Why it matters
When you graph pauses for a client on FR 5, 15, 25, do not just compare means. Plot every pause. If the distributions overlap, the child may not feel the difference you think you programmed. Use range or median instead of mean to decide your next ratio step.
Want CEUs on This Topic?
The ABA Clubhouse has 60+ free CEUs — live every Wednesday. Ethics, supervision & clinical topics.
Join Free →Graph every post-reinforcement pause this week; if the bars overlap across ratio sizes, keep the same ratio or drop back.
02At a glance
03Original abstract
Three rats were exposed to multiple fixed‐ratio schedules in which large and small ratios alternated in an irregular order. Over a series of training phases, one ratio was held constant as the second ratio was increased to higher values. On average, postreinforcement pauses increased in duration as the ratio size was increased. Pausing was controlled by the size of the upcoming ratio; the previous ratio had smaller and less consistent effects. However, more detailed consideration of the aggregated data indicated that the pause distributions were positively skewed and that changes in average performances were more a consequence of increased skew rather than shifts of the entire distributions. Moreover, the distributions of pauses from condition to condition overlapped, and brief pauses were common even at the highest ratios. These results demonstrated that depictions of pausing based on aggregated data can be misleading without corresponding information about variations in the distribution on which the averages are based.
Journal of the experimental analysis of behavior, 1999 · doi:10.1901/jeab.1999.71-145