1.3.5.3. Two-Sample t-Test For Equal Means

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\( T = \frac{\bar{Y_{1}} - \bar{Y_{2}}} {\sqrt{{s^{2}_{1}}/N_{1} + {s^{2}_{2}}/N_{2}}} \)

where N1 and N2 are the sample sizes, \( \bar{Y_{1}} \) and \( \bar{Y_{2}} \) are the sample means, and \( {s^{2}_{1}} \) and \( {s^{2}_{2}} \) are the sample variances.

If equal variances are assumed, then the formula reduces to:

    \( T = \frac{\bar{Y_{1}} - \bar{Y_{2}}} {s_{p}\sqrt{1/N_{1} + 1/N_{2}}} \)
where
    \( s_{p}^{2} = \frac{(N_{1}-1){s^{2}_{1}} + (N_{2}-1){s^{2}_{2}}} {N_{1} + N_{2} - 2} \)

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