Runs Test
The Runs Test is a nonparametric statistical test that assesses whether a sequence of binary data (e.g., wins/losses) is random by comparing observed runs to expected runs under independence.
THE IDEA
Runs Test – Cornell Players
The Runs Test (also known as the Wald-Wolfowitz test) is used to determine if a sequence of binary outcomes is random. It counts the number of runs (consecutive identical outcomes) and compares the observed runs to the expected number of runs under the null hypothesis of randomness. A significant result (e.g., p < .01) suggests the sequence is non-random, often indicating streaks or patterns. The excerpt does not include the Cornell players’ data or results.
When to use it
Analyzing the randomness of win/loss sequences in sports to detect streak effects
Evaluating whether a sequence of economic indicators (e.g., up/down days) is consistent with randomness
Testing for non-random patterns in psychological experiments involving binary responses
Quality control: checking if defect patterns in a production line are random
FROM THEORY TO EVERYDAY LIFE
In practice
Cornell Basketball Win/Loss Sequence
A data analyst records the win/loss results for the Cornell basketball team over 30 games: W, W, L, W, L, L, L, W, W, W, L, W, L, L, W, W, L, L, L, W, W, W, W, L, W, L, L, W, L, W. The Runs Test calculates the number of runs (e.g., 18) and compares to the expected runs under randomness. If p < .01, the analyst finds evidence against the randomness model. This alone does not establish a 'hot hand' effect.
A MOMENT TO REFLECT
Put it to work.
What can the Runs Test tell you about a sequence of sports results, and what can it not establish about skill or causes?
In what ways might the gambler's fallacy influence interpretations of a significant Runs Test result?
Can the Runs Test be applied to non-sports data, such as a sequence of daily mood states? Provide an example.
CONTINUE THE CONVERSATION
Source texts
- Heuristics and Biases The Psychology of Intuitive Judgment (Thomas Gilovich, Dale Griffin, Daniel Kahneman)