High Quality Content by WIKIPEDIA articles! In statistics, Welch's t test is an adaptation of Student's t-test intended for use with two samples having possibly unequal variances. As such, it is an approximate solution to the Behrens–Fisher problem. Welch's t-test defines the statistic t by the following formula: t = {overline{X}_1 - overline{X}_2 over sqrt{ {s_1^2 over N_1} + {s_2^2 over N_2} }}, where overline{X}_{i}, s_{i}^{2} and Ni are the ith sample mean, sample variance and sample size, respectively. Unlike in Student's t-test, the denominator is not based on a pooled variance estimate. The degrees of freedom ? associated with this variance estimate is approximated using the Welch-Satterthwaite equation: nu = {{left( {s_1^2 over N_1} + {s_2^2 over N_2}right)^2 } over {{s_1^4 over N_1^2 cdot nu_1}+{s_2^4 over N_2^2 cdot nu_2}}}={{left( {s_1^2 over N_1} + {s_2^2 over N_2}right)^2 } over {{s_1^4 over N_1^2 cdot left({N_1-1}right)}+{s_2^4 over N_2^2 cdot left({N_2-1}right)}}} ., Here ?i = Ni ? 1, the degrees of freedom associated with the ith variance estimate.

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