the samples are from populations with the same variance.the samples have paired values from the same population.T.TEST(R1, R2, tails, type) = p-value of the t-test for the difference between the means of two samples R1 and R2, where tails = 1 (one-tailed) or 2 (two-tailed) and type takes the values: m in Theorem 1).Įxcel Function: Excel provides the function T.TEST to handle the various two-sample t-tests. Real Statistics Function: The Real Statistics Resource Pack provides the following function.ĭF_POOLED(R1, R2) = degrees of freedom for the two-sample t-test with unequal variances for samples in ranges R1 and R2 (i.e. When n xand n y are approximately equal, then the degrees of freedom and the value of t in Theorem 1 are approximately the same as those in Theorem 1 of Two Sample t Test with Equal Variances. The resulting test, called, Welch’s t-test, will have a lower number of degrees of freedom than ( n x – 1) + ( n y – 1), which was sufficient for the case where the variances were equal.
Observation: This theorem can be used to test the difference between sample means even when the population variances are unknown and unequal. Observation: The nearest integer to m can be used.Īn alternative calculation ( Satterthwaite’s correction) of m (which has the same value) is as follows If x and y are normal, or n x and n y are sufficiently large for the Central Limit Theorem to hold, then the random variable Theorem 1: Let x̄ and ȳ be the sample means and s x and s y be the sample standard deviations of two sets of data of size n x and n y respectively.
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