Sign test
Definition taught in Hypothesis tests, part of Statistical inference
Sign test
| Type | Definition |
| Taught in | Hypothesis tests |
| Part | Statistical inference |
| Worked examples | 1 |
| Questions using it | 1 |
For independent pairs (X_i,Y_i), i=1,\ldots,n, let N be the number of pairs with Y_i>X_i, ties discarded. If H_0:\mathbb{P}(Y_i>X_i)=1/2 holds, N\sim\operatorname{Bin}(n,1/2), and H_0 is tested with the binomial test.
Examples
A one-sided sign test
Question page: A one-sided sign test
For the two examiners, the second gave the higher mark on 8 of 12 exams. Find the p-value of the sign test against the one-sided alternative that the second examiner is more generous.
Under H_0, N\sim\operatorname{Bin}(12,1/2), and large N is evidence that the second examiner is more generous. The p-value is
\mathbb{P}(N\ge8)=\frac1{2^{12}}\Bigl[\binom{12}8+\binom{12}9+\binom{12}{10}+\binom{12}{11}+\binom{12}{12}\Bigr]=\frac{495+220+66+12+1}{4096}=\frac{794}{4096}=0.194.
There is still no evidence of a difference.
Used in
- Taught in Hypothesis tests, where the derivation and examples are.
- Questions that use it (1) — A one-sided sign test
- All 6 questions on Hypothesis tests
See also
Binomial test · Null and alternative hypotheses · Critical region · p-value · Type I and type II errors · Neyman–Pearson approach · Power function · One-sample t test