Question

How do you cross reference check a two sample t-test hypothesis?

Identify assumptions, cautions, limitations, and generalizations for a two sample t-test hypothesis.

Answer 1

The two-sample t-test is one of the most commonly used hypothesis tests in Six Sigma work. It is applied to compare whether the average difference between two groups is really significant or if it is due instead to random chance. It helps to answer questions like whether the average success rate is higher after implementing a new sales tool than before or whether the test results of patients who received a drug are better than test results of those who received a placebo.

In the two-sample t-test, two sample means are compared to discover whether they come from the same population (meaning there is no difference between the two population means). Now, because the question is whether two populations are actually one and the same, the first step is to obtain the SE mean from the sampling distribution of the difference between two sample means. Again, since the population standard deviations of both of the two populations are unknown, the standard error of the two sample means must be estimated.

In the one-sample t-test, the SE mean was computed as such:

Hence:

However, this is only appropriate when samples are large (both greater than 30). Where samples are smaller, use the following method:

Sp is a pooled estimate of the common population standard deviation. Hence, in this method it can be assumed that variances are equal for both populations. If it cannot be assumed, it cannot be used. (Statistical software can handle unequal variances for the two-sample t-test module, but the actual calculations are complex and beyond the scope of this article).