B.23: Identify ways the matching law can be used to interpret response allocation.
Free practice questions for this part of the BCBA, with an explanation for every option.
A pigeon works on concurrent variable-interval (VI VI) schedules. The left key produces about 120 reinforcers per hour and the right key about 40 per hour. According to the matching law, approximately what proportion of responses should go to the left key?
- A. Nearly 100%Incorrect. Near-exclusive preference is typical of concurrent ratio schedules. On concurrent VI VI schedules, responding is distributed in proportion to relative reinforcement.
- B. About 25%Incorrect. This reverses the proportion. 25% matches the right key's share of reinforcement.
- C. About 75%Correct. The relative rate of responding matches the relative rate of reinforcement: 120 / (120 + 40) = 0.75.
- D. About 50%Incorrect. Equal allocation would be expected only if both alternatives produced equal reinforcement.
A student's calling out produces teacher attention on a rich schedule, while hand raising is acknowledged only occasionally. Based on the matching law, which strategy is most likely to shift the student's responding toward hand raising?
- A. Increase the relative rate (and immediacy) of attention for hand raising while reducing attention for calling outCorrect. Raising the relative reinforcement for the alternative behavior is predicted to shift response allocation toward it.
- B. Nothing, because the matching law applies only to ratio schedulesIncorrect. The matching law was developed mainly with concurrent interval schedules and is widely applied to choice in natural settings.
- C. Require the student to raise a hand and wait 30 seconds before being called onIncorrect. Adding effort or delay to the alternative behavior would likely shift responding toward calling out.
- D. Reduce attention for both calling out and hand raising by the same proportionIncorrect. Allocation depends on relative reinforcement. Reducing both equally leaves the relative proportions unchanged.
In a clinic study on concurrent VI VI schedules, a 12-year-old earns 70% of all reinforcers from the left button. Across sessions, she consistently puts about 90% of her responses on the left button. Compared with the matching law's prediction, her response allocation shows:
- A. Perfect matchingPerfect matching would predict about 70% of responses on the left button, the same as the share of reinforcers.
- B. Bias toward the leaner alternativeThe left button is the richer alternative, and responding is shifted toward it, not toward the leaner one.
- C. UndermatchingUndermatching is when responding is pulled toward indifference, so the richer alternative gets less than its share. Here it gets more.
- D. OvermatchingCorrect. Overmatching is when the share of responses on the richer alternative is larger than the share of reinforcers it produces. Here that is 90% against 70%.