4.4.3—Single-sample sign tests

To test a population median m₀, compare each observation with m₀ and count signs. Under H₀: median=m₀, the positive count has a Bin(n,0.5) distribution after ties are removed.

For H₁: median>m₀ use an upper tail; for median<m₀ use a lower tail; for a two-sided alternative use both tails. State the conclusion in the original units.

If 12 non-tied measurements contain 10 above m₀, calculate P(X≥10) for a one-sided test, then compare with α.

A rejection says the data are inconsistent with the stated median, not that every observation lies on one side or that the effect is practically large.