Contingency and its two indices within conditional probability analysis.

Holburn (1997) wrote a theory paper. He asked: what is the best way to spot a real contingency?

He said we need two numbers. First, how often does reward come right after the behavior? Second, how often does the behavior come right before the reward?

He claimed these two odds give the full picture. He also guessed that babies learn the first number before the second.

The paper did not test kids or run trials. It is a map for future work.

The main point: always check both odds. If you skip one, you may miss the true contingency.

Cullinan et al. (2001) took the idea into a lab. They used a 10-minute computer game to show how rate, quality, and delay of reward steer choice. Their data echo S’s call to track conditional odds.

Root et al. (2017) seem to push back. They say food is not a reinforcer by default; context and the kid’s state decide. This looks like a clash, but it is not. S tells us how to measure any contingency. R tells us what to measure—first check if the child even wants the food.

Manolov et al. (2025) update the numbers side. They give free web tools to judge nonoverlap in single-case graphs. Their work pairs with S’s old plea: use clear, simple indices instead of fuzzy eye-ball checks.

Next time you run a preference test, log both odds. Note how often the hit leads to the treat, and how often the treat follows the hit. If the numbers drift apart, your “reinforcer” may not be driving the behavior. This quick check can save you from false positives and wasted sessions.