Two sample problem

A two-sample problem is a specific type of question in test theory , a branch of mathematical statistics . For two-sample problems, you want to examine the relationship between two samples. Typical examples of this would be the following questions:

• Does the first sample have a lower expected value than the second sample?
• Do the variances of the two samples match?
• Do the samples have the same distribution?

The opposite of a two-sample problem is a one-sample problem . Only one property of a sample is examined. Examples of one-sample problems would be the following questions:

• Does the sample have an expected value smaller than a given threshold value?
• Is the sample normally distributed ?

The tests are named according to this subdivision. There is a one- sample t-test and a two-sample t-test , as well as a one- sample Gaussian test and a two-sample Gaussian test .

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• Ulrich Krengel : Introduction to probability theory and statistics . For studies, professional practice and teaching. 8th edition. Vieweg, Wiesbaden 2005, ISBN 3-8348-0063-5 , p. 179 , doi : 10.1007 / 978-3-663-09885-0 .
• Hans-Otto Georgii: Stochastics . Introduction to probability theory and statistics. 4th edition. Walter de Gruyter, Berlin 2009, ISBN 978-3-11-021526-7 , p. 314 , doi : 10.1515 / 9783110215274 .
• Ludger Rüschendorf: Mathematical Statistics . Springer Verlag, Berlin Heidelberg 2014, ISBN 978-3-642-41996-6 , p. 119 , doi : 10.1007 / 978-3-642-41997-3 .