Wald–Wolfowitz Run Test
The Wald–Wolfowitz runs test examines whether a binary sequence has more alternation or clustering than expected under a randomness model.
THE IDEA
The Wald–Wolfowitz run test, applied to each player's performance record, assesses whether observed streaks of consecutive hits or misses (runs) differ significantly from the number of runs expected under randomness. The test compares the observed number of runs (column 4) to the expected number (column 5). In the analysis, 14 players had slightly more runs than expected and 12 had slightly fewer, but only player 9 showed significantly fewer runs (more clustering) than expected by chance, as indicated by the Z statistic (column 6). The referenced table is not included in this excerpt.
When to use it
Analyzing athletes' performance streaks (e.g., hitting streaks in baseball, shooting streaks in basketball).
Testing randomness in coin toss sequences or other binary outcome experiments.
Evaluating process control in manufacturing to detect non-random patterns in defect sequences.
Assessing the randomness of binary data in psychological experiments (e.g., responses in a guessing task).
FROM THEORY TO EVERYDAY LIFE
In practice
Basketball Shooting Streaks
A basketball player’s sequence of made and missed shots over a game can be analyzed using the run test. If the player makes three consecutive shots then misses two, that creates runs—here, two runs (one of makes, one of misses). The test compares the total number of such runs to what would be expected if each shot were independent. A significantly low number of runs suggests clustering (e.g., a 'hot hand').
Quality Control in Manufacturing
A factory records inspection outcomes as pass or fail. A runs test can examine whether failures cluster more than expected under independence. Further investigation is needed to identify the cause of a pattern.
A MOMENT TO REFLECT
Put it to work.
How does the run test help distinguish between true streakiness in performance and mere random variation?
Can you think of a situation where observing a long run of successes might be misleading without a run test?
Why is it important to use a statistical test like the Wald–Wolfowitz run test rather than just eyeballing streaks?
References
- Nonparametric Statistics for the Behavioral Sciences — Siegel, S. (1956)
CONTINUE THE CONVERSATION
Source texts
- Heuristics and Biases The Psychology of Intuitive Judgment (Thomas Gilovich, Dale Griffin, Daniel Kahneman)