A two-sample t test
compares the mean of the first sample minus the mean of the second
sample to a given number, the null hypothesis difference.
To compare means from
two independent samples with
n1 and
n2 observations
to a value
m, use
![t equals . fraction open , modified x sub 1 with macron above , minus , x with macron above sub 2 , close minus m , over s . square root of fraction 1 , over n sub 1 end fraction , plus , fraction 1 , over n sub 2 end fraction , end root end fraction. Click image for alternative formats.](images/t_test_two_sample.png)
. In this example,
s2 is
the pooled variance
![s squared , equals . fraction open , n sub 1 , minus 1 close , s sub 1 and super 2 , plus open , n sub 1 , minus 1 close , s sub 2 and super 2 , , over n sub 1 , plus , n sub 2 , minus 2 end fraction. Click image for alternative formats.](images/t_test_pooled_variance.png)
, and
s21 and
s22 are
the sample variances of the two groups. The use of this
t statistic
depends on the assumption that
![sigma sub 1 and super 2 , equals , sigma sub 2 and super 2. Click image for alternative formats.](images/sigma1_equals_sigma2.png)
, where
![sigma sub 1 and super 2. Click image for alternative formats.](images/sigma1.png)
and
![sigma sub 2 and super 2. Click image for alternative formats.](images/sigma2.png)
are the population variances of the two groups.
To run a two-sample t test,
open the t Tests task. From the t test drop-down
list, select Two-sample test.