###### Online Course

# NRSG 795: BIOSTATISTICS FOR EVIDENCE-BASED PRACTICE

## Module 5: Significance Testing/Hypothesis Testing for Two Groups

### Mann-Whitney U and Wilcoxon Signed-Ranks Tests

When you have **data that are not normally distributed** then the assumption of normality is violated and nonparametric tests should be used. To deal with the non normal data, the values are ranked and similar procedures as in the t-test are used on ranked data.

The **Mann-Whitney U** (equivalent to Wilcoxon Rank Sum Test/ Wilcoxon 2-sample t-test) test compares the distributions of ranks in two groups. To perform the Mann-Whitney test, one first ranks all the values from low to high, paying no attention to which group each value belongs. The smallest number gets a rank of 1. The largest number gets a rank of n, where n is the total number of values in the two groups. Then you average the ranks in each group, and report the two averages. It uses the standard normal distributed z-value to test significance-- calculating a two sample z statistic, using the pooled variance estimate. If the means of the ranks in the two groups are very different, the P value will be small. If the P value is large, the data do not give you any reason to reject the null hypothesis. This is not the same as saying that the two populations are the same. You just have no compelling evidence that they differ. If the total sample size is seven or less, the Mann-Whitney test will always give a P value greater than 0.05 no matter how much the groups differ.

The Mann-Whitney U is the nonparametric alternative to the **Independent **t-test.

Here is some information in the event you want to try to run one (not required for class)

Mann-Whitney U

- Click here for an example illustration (calculated by hand)
- Intellectus Statistic: see the Nonparametric choice under Analyses
- Excel: https://www.youtube.com/watch?v=hw3z49QoB1s (9:29)
- Directions of how to do this in EXCEL: http://www.real-statistics.com/non-parametric-tests/mann-whitney-test/
- On line Calculator: http://www.socscistatistics.com/tests/mannwhitney/Default.aspx

The **Wilcoxon signed rank test** is a nonparametric test that compares the median of a set of numbers against a hypothetical median. This test is mathematically similar to conducting a Mann-Whitney U-test. It is also similar to the basic principle of the dependent samples t-test, because just like the dependent samples t-test the Wilcoxon sign test, tests the difference of observations when the observations are matched. This test pools all differences, ranks them and applies a negative sign to all the ranks where the difference between the two observations is negative. It compares the two dependent observations and counts the number of negative and positive differences. It uses the standard normal distributed z-value to test of significance-- the one sample z statistic (mean / standard error of the mean) is calculated from the signed ranks.

The Wilcoxon signed-ranks test is the nonparametric alternative for the **dependent** t-test.

Here is some information in the event you want to try to run a Wilcoxson (not required for class)

Wilcoxson

- Click here for an example illustration
- Intellectus Statistic: see the Nonparametric choice under mode_edit Analyses
- Directions of how to do this in EXCEL: http://www.real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/
- On line Calculator: http://www.graphpad.com/guides/prism/6/statistics/index.htm?how_the_mann-whitney_test_works.htm

#### Required Videos

- Mann-Whitney U: https://www.youtube.com/watch?v=nRAAAp1Bgnw (4:35)
- Wilcoxson signed rank test: https://www.youtube.com/watch?v=mbpGCxYya3M&list=PL568547ACA9211CCA&index=82 (3:47)

#### Learning Activity

- Complete Self test 5

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