Students T-Test

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Definition: Students T-Test

Students T-Test is a test in statistic developed by Student i.e. W. S. Gossett. It uses t-distribution if null hypothesis, H0, is accepted. It is generally used on small samples and is used to compare their means.

When we want to compare the mean values of a measurement variable against a reference or nominal variable, we use Student’s t-test. This test assumes that the standard variances of the statistic groups are equal and the data in the group is normally distributed. Student’s t-tests are of the following types :

  • One sample t-test
  • Independent two sample t-test
  • Dependent t-test


Formula : Null hypothesis : µ = µ0

Alternate hypothesis : µ ≠ µ0

Test statistic for one sample test = (x - µ0 )/(S/√n)


Test statistic for independent 2 sample test = (X1 – X2)/((√(Sx12 Sx22)/2)(√2/n))


Test statistic for dependent t-test = (XD- µ0)/(SD/√n)


Eg–When one is comparing the results of similar analysis performed on 2 samples A and B so as to determine whether these two samples contain the same percentage of a particular component, then this is an example of Student’s t test. Here, the null hypothesis would be that the means of the results on the two samples are same whereas the alternate hypothesis would be that the means are different.


These tests are commonly used in biology, chemistry, economics, etc


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