On-line statistics

Mann-Whitney and Wilcoxon Matched pairs

 data points should be independent from each other

 data do not have to be normal and variances do not have to be equal

 all individuals must be selected at random from the population

 all individuals must have equal chance of being selected

 sample sizes should be as equal as possible but some differences are allowed

 the distributions do not have to be normal and variances do not have to be equal

 all individuals must be selected at random from the population

 all individuals must have equal chance of being selected

 sample sizes should be equal

 should be used where both data sets have something in common

 if you do not find a significant difference in your data, you cannot say that the samples are the same

 both tests compare medians and, therefore, do not refer to means in the conclusion

Mann-Whitney U and Wilcoxon Matched pairs are basically the same in that they compare between two medians to suggest whether both samples come from the same population or not. If both of your samples are not entirely independent of each other and have some factor in common, i.e. geographical location or before/after treatment, the Wilcoxon Matched pairs test can be applied. If you have two samples that are independent you should use the Mann-Whitney U test.

More and more emphasis is being placed on organic food-crops. Are organic methods as productive as industrial methods? Samples are taken from two fields, one under an organic regime and the other under an intensive regime. Both sets of product are weighed individually, but the resultant data set has a distribution that is very different from normal. All data points must be placed in descending or ascending order and given rank values. The ranks of each datum point are the data that are used in the non-parametric comparison tests.

The statistical packages require the data to be in columns and SPSS requires the sets to be stacked with reference values in a separate column. Excel does not have either of these tests as standard but are not difficult to compute within a spreadsheet.

The output from the Mann-Whitney and Wilcoxon Matched pairs is similar and there are several values you need to look for:

Results are shown from UNISTAT but similar output is given from SPSS.

You can check that the program has used the right data by making sure that the cases (32,32 and 32) and categories (male/female) are correct. The information you then need to use in order to reject or accept your H_O, is the bottom value in both cases. The Mann-Whitney U test is the calculated value and the critical value is based on n 1+n 2 of 30 at your chosen level of confidence. The 2-Tail Probability value is the actual probability of the differences occurring by chance. The two-tail results confirm that the H_O must be rejected and the H_A accepted in both tests.

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