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Signed rank sum test (one sample)


The Signed rank sum test is a test for symmetry about a test value. This test is the non-parametric alternative for the One sample t-test. It can be used when the observations are not Normally distributed.

Required input

Signed rank sum test (one sample) - dialog box

  • The variable of interest. You can use the Drop-down button button to select variables and filters.
  • The test value you want to compare the sample data with.


Summary statistics

The results windows for the Signed rank sum test first displays summary statistics of the sample.

The statistics include the Hodges-Lehmann location estimator (sometimes called the Hodges-Lehmann median) and its 95% confidence interval (Conover, 1999; CLSI, 2013). The Hodges-Lehmann location estimator of a sample with sample size n is calculated as follows. For each possible set of 2 observations, the average is calculated. The Hodges-Lehmann location estimator is the median of all n × (n+1) / 2 averages. The confidence interval is derived according to Conover (1999, p. 360).

Signed rank sum test (one sample) - statistics

Signed rank sum test results

The Signed rank sum test ranks the absolute values of the differences between the sample data and the test value, and calculates a statistic on the number of negative and positive differences.

  • In the presence of ties, or if the sample size is larger than 25, MedCalc uses the Normal approximation (Hollander et al., 2014) to calculate the P-value.
  • For smaller sample sizes (N≤25) MedCalc calculates the exact probability (Hollander et al., 2014).

If the resulting P-value is small (P<0.05), then the sample data are not symmetrical about the test value and therefore a statistically significant difference can be accepted between the sample median and the test value.

Note that in MedCalc P-values are always two-sided.


  • Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.
  • CLSI (2013) Measurement procedure comparison and bias estimation using patient samples; Approved guideline - 3rd edition. CLSI document EP09-A3. Wayne, PA: Clinical and Laboratory Standards Institute.
  • Conover WJ (1999) Practical nonparametric statistics, 3rd edition. New York: John Wiley & Sons.
  • Hollander M, Wolfe DA, Chicken E (2014). Nonparametric Statistical Methods. 3rd ed. Hoboken NJ: John Wiley & Sons.

See also