MedCalc  # Signed rank sum test (one sample)

 Command: Statistics Rank sum tests Signed rank sum test (one sample)

## Description

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

## Results

### 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 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.

## Literature 