Two-Sample t-test (reminder)

The test statistic t0 that we have to calculate from the samples is:

$t_0=\frac{\bar{y_1}-\bar{y_2}}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

where the y's are sample means, Sp is an estimate of the common variance of both samples

$S_p^2=\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2}$

where S1 and S2 are sample variances.

$\begin{array}{c} H_0:\mu_1=\mu_2 \\ H_1:\mu_1\neq\mu_2 \end{array}$

To decide whether to reject H0 or not, we compare the test statistic (the one calculated with the equation above) t0 with another t, from the t-distribution (with n1 + n2 - 2 dof's). If

$\large |t_0| > t_{\alpha/2,n_1+n_2-2}$

we have to reject H0 (the second term of the equation is the upper probability alpha/2 of the t-distribution). If this happens, H1 holds.

Reference:

Montgomery, D.G. (2001), Design and Analysis of Experiments. 5th Edition. Wiley.

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Two-Sample t-test (reminder)

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