# 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

- 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 - 3
^{rd}edition. CLSI document EP09-A3. Wayne, PA: Clinical and Laboratory Standards Institute. - Conover WJ (1999) Practical nonparametric statistics, 3
^{rd}edition. New York: John Wiley & Sons. - Hollander M, Wolfe DA, Chicken E (2014). Nonparametric Statistical Methods. 3rd ed. Hoboken NJ: John Wiley & Sons.