t Test, Independent Samples

An independent samples t test is a hypothesis test for determining whether the population means of two independent groups are the same. The researcher begins by selecting a sample of observations and estimates the population mean of each group from the sample means. The researcher then compares these two sample means via the formula


where x¯1 is the sample mean of group 1, x¯2 is the sample mean of group 2, sp2 is the pooled estimate of variance (formula given in the example problem), n1 is the sample size of group 1, and n2 is the sample size of group 2. This t value can then be used to determine the likelihood that any difference between the two sample means is real versus caused by chance.

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