# Mann-Whitney test

This procedure is available in both the Analyse-it Standard and the Analyse-it Method Evaluation edition

Mann-Whitney test, also known as Wilcoxon-Mann-Whitney test, is a non-parametric test for a difference in central location (median) between two independent samples.

The requirements of the test are:

- Two independent samples measured on an ordinal or continuous scale.
- Samples have similar shape distributions, although the distributions need not be normal.

## Arranging the dataset

Data in existing Excel worksheets can be used and should be arranged in a List dataset layout or Table dataset layout. The dataset must contain a continuous scale variable and a nominal/ordinal scale variable containing two independent groups.

When entering new data we recommend using New Dataset to create a new **2 variables (1 categorical)** dataset ready for data entry.

**Using the test**

To start the test:

- Excel 2007:

Select any cell in the range containing the dataset to analyse, then click**Compare Groups**on the**Analyse-it**tab, then click**Mann Whitney**. - If the dataset is arranged using the table layout:

Click**Variable - Group 1**and**Variable - Group 2**and select the samples to compare.If the dataset is arranged using the list layout:

Click**Variable**and select the dependent variable and click**Factor**and select the independent variable containing the two groups to compare. - Click
**Alternative hypothesis**and select the alternative hypothesis to test. - Click
**OK**to run the test.

Excel 97, 2000, 2002 & 2003:

Select any cell in the range containing the dataset to analyse, then click **Analyse **on the **Analyse-it **toolbar, click **Compare Groups** then click **Mann Whitney**.

X ≠ Y to test if the median(X) is not equal to median(Y). |

X > Y to test if the median(X) is greater than median (Y). |

X < Y to test if the median(X) is less than median (Y). |

The report shows the number of observations analysed, and, if applicable, how many missing values were excluded. Summary statistics for the ranks of each sample are also shown.

The Mann Whitney statistic and hypothesis test are shown. The *p*-value is the probability of rejecting the null hypothesis, that the samples have the same median, when it is in fact true. A significant p-value implies that the two samples have different medians.

**METHOD ** When the number of observations in each sample is ≤15 an exact p-value is calculated, based on the assumption of no ties (see [2]). If a few ties are present (the number of ties is shown next to the p-value) the p-value will be conservative, though if more than 10% of the observations are tied then the p-value is unreliable. For >15 observations a normal approximation, with correction for ties, is used (see [2]).

## Median difference point estimate

If both samples are continuous the median difference and confidence interval can be shown to quantify the difference between the samples in terms that can be practically evaluated.

To show a median difference and confidence interval:

- If the Mann-Whitney dialog box is not visible click
**Edit**on the**Analyse-it**tab/toolbar. - Enter
**Confidence interval**to calculate for the median difference. The level should be entered as a percentage between 50 and 100, without the % sign.**NOTE**The Hodges-Lehman method used to calculate the confidence interval can be extremely time-consuming for large sample sizes. If no confidence interval is required, and when working with large samples, leave the confidence level blank and the calculation will be skipped. - Click
**OK**.

** METHOD ** The median difference and confidence interval are calculated using the Hodges-Lehman method (see [2]).

## Further reading & references

- Handbook of Parametric and Nonparametric Statistical Procedures (3rd edition)

David J. Sheskin, ISBN 1-58488-440-1 2003; 423. - Practical Non-parametric Statistics (3rd edition)

Conover W.J. ISBN 0-471-16068-7 1999; 272-284.

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