Welch's t test  From Wikipedia, the free encyclopedia Jump to:
navigation, search  In statistics, Welch's t-test (or Welch-
Aspin Test) is a two-sample location test, and is used to check
the hypothesis that two populations have equal means. Welch's
t-test is an adaptation of Student's t-test, and is intended for
use when the two samples have possibly unequal variances.[1]
These tests are often referred to as "unpaired" or "independent
samples" t-tests, as they are typically applied when the
statistical units underlying the two samples being compared are
non-overlapping. Welch's t-test is an approximate solution to
the Behrens–Fisher problem. It is sometimes referred to as the
"Two-sample unpooled t-test for unequal variances" but "Welch's
t-test" is preferred for brevity.   Welch's t-test defines the
statistic t by the following formula:  t \quad = \quad {\;
\overline{X}_1 - \overline{X}_2 \; \over \sqrt{ \; {s_1^2 \over
N_1} \; + \; {s_2^2 \over N_2} \quad }}\,  where
\overline{X}_{i}, s_{i}^{2} and N_{i} ar