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

Variable	PTH

Sample size	285
Lowest value	8.0000
Highest value	73.4000
Arithmetic mean	36.7425
95% CI for the mean	35.1554 to 38.3295
Median	36.6000
95% CI for the median	35.0470 to 38.8651
Hodges-Lehmann location estimator	36.6000
95% Confidence interval	34.9500 to 38.2500

Signed rank sum test

Test value	35
Number of positive differences	159
Number of negative differences	125
Test statistic Z	-1.915179
Two-tailed probability	P = 0.0555

Box-and-Whisker plot

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 non-parametric statistics, 3^rd edition. New York: John Wiley & Sons.
• Hollander M, Wolfe DA, Chicken E (2014). Non-parametric Statistical Methods. 3rd ed. Hoboken NJ: John Wiley & Sons.

See also

• Mann-Whitney test (independent samples)
• Wilcoxon test (paired samples)