Suppose the two populations X and Y are independent of each other and obey the normal distribution.
The mean and variance of X areμ_{1},σ_{1}^{2},
The mean and variance of Y areμ_{2},σ_{2}^{2}, that is X~N(μ_{1},σ_{1}^{2}),
Y~N(μ_{2},σ_{2}^{2}),This page is atσ_{1}^{2},σ_{2}^{2}
for known cases mean difference μ_{1}-μ_{2}as hypothetical test，the statistics are

，among them, n_{1},n_{2} are two overall sample sizes.

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