Teach/Me Data Analysis

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Table of Contents Statistical Tests Means Two-Sample t-Test Small Sample Size	Index
See also: large sample size, survey on statistical tests, distribution calculator

Two-Sample t-Test
Small Sample Size

When the sample size is small, the assumption of the central limit theorem does not hold, since the estimates of s² become unreliable. One therefore has to resort to the t-distribution. The t-test requires some constraints to be fulfilled:

the variances have to be equal
the samples have to be independent of each other
the samples have to follow a normal distribution

Since we assume that s₁² and s₂² are equal, we can compute a pooled variance s_p². The rational for pooling the variances is to obtain a better estimate. The pooled variance is a weighted sum of variances. So when n₁ equals n₂, s_p² is just the average of the individual variances. The overall degree of freedom is the sum of the individual degrees of freedom for the two samples: df = df₁ +df₂ = (n₁-1) + (n₂-1) = n₁+ n₂ - 2. In order to apply a two-sample t-test you should follow the scheme shown below:

Last Update: 2005-Jul-16

Two-Sample t-TestSmall Sample Size

Two-Sample t-Test
Small Sample Size