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Just a note

This formula is sometimes given in terms of standard errors rather than variances:

  t   =    (1 - 2) -(μ1 - μ2)
[ n1(n1 - 1)[SE1]2 + n2(n2-1)[SE2]2) ]( n1 + n2 )
n1 + n2 - 2 n1n2
Where,

  • t is the estimated value of the t-statistic with n1 + n2 - 2 degrees of freedom,
  • D is the difference between the means 1 and 2 of the two samples,
  • δ is the difference between the true population means under the null hypothesis.
  • sD is the estimated standard error of the difference between the means.
  • n1 & n2 are the number of observations in each sample.
  • SE1 and SE2 are the estimated standard errors of 1 and 2