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When raw data is not available, which normally occurs when we obtain our data from different scientific papers, how is it possible to perform a Mann-Whitney analysis to test whether two samples are statistically different when only median, IQR and sample sizes are available?

I would like to solve this question by using R commander.

For example:

Sample 1: median1=2.5; IQR1=1.25-3.4; n1=4

Sample 2: median2=3.1; IQR2=2.25-6; n2=8

Are they statistically different when a M-W is performed?

cloud91
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    This is a better question for cross validated (stats.stackexchange.com) than here, which is specific to programming related questions. – Brigadeiro Aug 02 '19 at 23:43
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    I agree with the previous comment. To answer your question: No, you can't perform a Mann-Whitney U test on this kind of summary data. To perform the hypothesis test you need to know the ranks of your samples. There already exists a [related question on Cross Validated](https://stats.stackexchange.com/questions/129167/mann-whitney-u-test-when-only-summary-data-mean-sd-sample-size-are-available) that gives a nice example of two datasets with the same summary statistics but different results under the hypothesis test. [...] – Maurits Evers Aug 03 '19 at 00:51
  • [continued] The post demonstrates this based on the mean and sd but the same will hold if you consider the median and IQR instead. You can however calculate the t statistic based on the mean and sd, which then allows you to [perform a t-test based on the mean and sd summary statistics](https://stats.stackexchange.com/questions/30394/how-to-perform-two-sample-t-tests-in-r-by-inputting-sample-statistics-rather-tha). Note that this requires the mean and sd though, not the median and IQR. – Maurits Evers Aug 03 '19 at 00:55
  • thx u all for the comments and the help! next time i’ll be carefull in posting to crossvalidates – cloud91 Aug 03 '19 at 06:57

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