Morning Statistics
Critical Values of r in the Runs Test
Two-tailed, α = 0.05 · n₁ (rows) and n₂ (columns) from 2 to 20
How to read each cell: the top number is the lower critical value, the bottom number is the upper critical value.
Reject H₀ if the observed number of runs r ≤ lower or r ≥ upper. A dash (–) means that side can never be significant for those sample sizes.
Reject H₀ if the observed number of runs r ≤ lower or r ≥ upper. A dash (–) means that side can never be significant for those sample sizes.
- The table is symmetric: the cell for (n₁, n₂) equals the cell for (n₂, n₁).
- The lower value is shown as – when it is below 2 (fewer than 2 runs is impossible). The upper value is shown as – when it exceeds the maximum possible runs (2·min(n₁, n₂) + 1, or 2n when n₁ = n₂).
- Source data: G. Sarty & University of Saskatchewan Distance Education Unit (CC BY-NC-SA), reformatted. One typo in the source (n₁ = 16, n₂ = 19) was corrected to 12 / 25 using the symmetric entry.
- For n₁ or n₂ above 20, use the normal approximation instead.
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