# I The Cochran and Cox Approximation Pair T test Unequal Variance

#### mertcan

Hi everyone I hope you are well. Maybe as you know according to Behners-Fisher problem (unequal variance case of samples) there are some kind of approximations. I have recently covered the Satterthweiths Approximations and comprehended the logic of it. But I got stuck with the Cochran-Cox approximation which is the following: Approximation of the probability level of the approximate t statistic is the value of p such that $$t^{'} = \frac {\bar x_1-\bar x_2} {\sqrt { s_1^2/n1 + s_2^2/n2}} =(s_1^2/n1*t_1+s_2^2/n2*t_2)/(s_1^2/n1+s_2^2/n2)$$
where t1 and t2 are the critical values of the t distribution corresponding to a significance level of p and sample sizes of n1 and n2, respectively besides s_1 and s_2 are corresponds to sample variances. The number of degrees of freedom is undefined when n1=!n2. Could you help me derive it?

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