Sign Test

The sign test is an exact binomial test of whether a population median equals a specified value, using only whether each observation lies above or below that value.

부호 검정은 각 관측값이 기준값보다 큰지 작은지만 보고 모집단 중앙값이 그 기준값과 같은지를 이항분포로 정확하게 검정하는 방법이다.

How do I test whether the median of my data, or of paired differences, differs from zero with very few assumptions?

사전·사후 점수 차이의 중앙값이 0 과 다른지 가정을 최소한으로 두고 검정하려면 무엇을 써야 하나요?

The sign test counts observations above and below the hypothesized median, drops ties, and compares the count of positive signs with a Binomial(n, 0.5) distribution. For paired data, apply it to the column of differences with a hypothesized median of zero.

When to use Sign Test

• The distribution is strongly skewed or contains outliers.
• Only the direction of a difference is reliable, such as ordinal before-after ratings.
• The sample is small and an exact p-value is wanted.

When to use something else

• The distribution of differences is roughly symmetric; use the Wilcoxon signed-rank test for more power.
• The data are approximately normal; use the one-sample or paired t test instead.

Assumptions and requirements

• Observations (or pairs) are independent.
• The measurement is at least ordinal so that each value can be classed as above or below the hypothesized median.

What the analysis reports

• Counts of positive, negative and tied signs
• Exact binomial p-value
• Sample median
• Order-statistic confidence interval for the median

How to report it

An exact sign test showed that the median (Mdn = [value]) [differed/did not differ] from [m0]; [value] of [value] non-tied observations were above [m0], p = [value].

Related methods

• Wilcoxon Signed Rank Test
• One-Sample t-test
• Exact Binomial Test

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