The degrees of freedom for this test will be smaller than ( n x – 1) + ( n y – 1), the degrees of freedom for the t-test where the variances are equal. The resulting test is called Welch’s t-test. Property 1 can be used to test the difference between sample means even when the population variances are unknown and unequal. If in addition the variances are equal, then the values of in Property 12.3.1 and 12.3.2 are also equal. If =, then the values of in Property 12.3.1 and 12.3.2 are the same. The nearest integer to df is sometimes used.Īn alternative version ( Satterthwaite’s correction) of df (which has the same value) is calculated as follows Has a t distribution T( df) where the degrees of freedom is expressed as If x and y are normally distributed, or n x and n y are sufficiently large for the Central Limit Theorem to hold, then the random variable Property 1: Let x̄ and ȳ be the sample means and s x and s y be the sample standard deviations of two samples of size n x and n y respectively. This version is based on the following property. When the assumption of equal population variances is not met for the Two-Sample t-Test with Equal Variances (or when you don’t have enough evidence to know whether it holds) you should consider using a modified version of the t-test.
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