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 σ2
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 σ12
and
σ22 are equal, we
can compute a pooled variance sp2. 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,
sp2 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:
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Statistical Tests 
