For each sample, make sure that the final entry in the list is not followed by a carriage return. In importing raw data into the Mann-Whitney test, it is absolutely essential that the numbers of data items for samples A and B are precisely the same as the values of n a and n b that you have specified in setting up this page. Then return to your web browser, click the cursor into the text area for sample A and perform the 'Paste' operation from the 'Edit' menu. Within the spreadsheet application or other source of your data, select and copy the column of data for sample A. Option for Importing Raw Data via Copy & Paste: T Note, however, that the approximation to the normal distribution is best when n a and n b are both equal to or greater than 10. If n a and n b are both equal to or greater than 5, this page will also calculate the value of z, along with the corresponding one- tailed and two- tailed probabilities. As n a and n b increase, the sampling distribution of T A becomes a reasonably close approximation of the unit normal distribution.If either of the samples is of a size smaller than 5, additional instructions will be given below. For cases where n a and n b both fall between 5 and 21, inclusive, the lower and upper limits of the critical intervals of U A are calculated by this page and placed in the designated table below. With relatively small samples, the calculated value of U A can be referred directly to the sampling distribution of U A.Where T A = the observed sum of ranks for sample A, and The value of U reported in this analysis is the one based on sample A, calculated as.There is also an option, below, for importing raw data from a spreadsheet.Īfter data have been entered, click one or the other of the «Calculate» buttons according to whether you are starting out with ranks or raw data. If your data have not yet been rank-ordered in this fashion, they can be entered into the cells labeled «Raw Data» and the ranking will be performed automatically. If this equality is not satisfied, you will receive a message asking you to examine your data entry for errors. In this case, please note that the sum of all ranks for samples A and B combined must be equal to /2. If your data have already been ranked, these ranks can be entered directly into the cells headed by the label «Ranks».
These rankings are then re- sorted into the two separate samples. In order to apply the Mann-Whitney test, the raw data from samples A and B must first be combined into a set of N=n a+n b elements, which are then ranked from lowest to highest, including tied rank values where appropriate. The logic and computational details of the Mann-Whitney testĪre described in Subchapter 11a of Concepts and Applications.
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