Mann-Whitney test (independent samples)

Command:

Statistics Rank sum tests Mann-Whitney test (independent samples)

Description

The Mann-Whitney test is the non-parametric equivalent of the independent samples t-test (it is sometimes - wrongly - called a 'non-parametric t-test').

This test should be used when the sample data are not Normally distributed, and they cannot be transformed to a Normal distribution by means of a logarithmic transformation.

Required input

Select the variables for sample 1 and sample 2. You can use the button to select variables and filters in the variables list.

Caveat: if the two variables are the same, then the two filters must define distinct groups so that the same case is not included in the two samples.

Results

Summary statistics

The results windows for the Mann-Whitney test (independent samples) displays summary statistics of the two samples.

The statistics include the Hodges-Lehmann median difference (the Hodges-Lehmann estimate of location shift) and its 95% confidence interval (Conover, 1999). For two independent samples with sample size m and n, the Hodges-Lehmann median difference is the median of all m × n paired differences between the observations in the two samples. Differences are calculated as sample 2 − sample 1. The confidence interval is derived according to Conover (1999, p. 281).

Note that the Hodges-Lehmann median difference is not necessarily the same as the difference between the two medians.

Mann-Whitney test results

The Mann-Whitney test (independent samples) combines and ranks the data from sample 1 and sample 2 and calculates a statistic on the difference between the sum of the ranks of sample 1 and sample 2.

• In the presence of ties, or when either or both sample sizes are larger than 25, MedCalc uses the Normal approximation (Siegel & Castellan, 1988; Hollander et al., 2014) to calculate the P-value.
• For smaller sample sizes (both N≤25) MedCalc calculates the exact probability (Mann & Whitney, 1947; Dinneen & Blakesley, 1973).

If the resulting P-value is small (P<0.05) then a statistically significant difference between the two samples can be accepted.

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

Literature

• Conover WJ (1999) Practical nonparametric statistics, 3^rd edition. New York: John Wiley & Sons.
• Dinneen LC, Blakesley BC (1973) Algorithm AS 62: A generator for the sampling distribution of the Mann-Whitney U statistic. Journal of the Royal Statistical Society. Series C (Applied Statistics) 22:269-273
• Hollander M, Wolfe DA, Chicken E (2014). Nonparametric Statistical Methods. 3rd ed. Hoboken NJ: John Wiley & Sons.
• Lentner C (ed) (1982) Geigy Scientific Tables, 8^th edition, Volume 2. Basle: Ciba-Geigy Limited.
• Mann HB, Whitney DR (1947) On a test of whether one of two random variables is stochastically larger than the other. The Annals of Mathematical Statistics 18:50-60.
• Siegel S, Castellan NJ Jr (1988) Nonparametric statistics for the behavioral sciences. 2^nd ed. Singapore: McGraw-Hill Book Company.

See also

• To perform different tests in one single procedure, see Comparison of independent samples
• Signed rank sum test (one sample)
• Wilcoxon test (paired samples)

External links

• Mann-Whitney U on Wikipedia.

Recommended book

Practical Nonparametric Statistics
W. J. Conover

Buy from Amazon

This classic text and reference book is intended mainly for one-semester advanced undergraduate and undergrad/graduate introductory courses in nonparametric (or distribution free) statistics. The book will also appeal to applied research workers as a quick reference to the most useful nonparametric methods.