Fork me on GitHub

Unpaired two-tailed t-test

Sample 1

Sample 2

Name Definition Sample 1 Sample 2
Sample Size \[n\]
Mean \[\mu=\frac{1}{n}\sum_{i=1}^n x_i\]
Unbiased Variance \[s^2=\frac{1}{n - 1}\sum_{i=1}^n (x_i - \mu)^2\]
Unbiased Standard Deviation \[s=\sqrt{s^2}\]
Welch's t-test \[t=\frac{\mu_1-\mu_2}{\sqrt{s_1^2/n_1+s_2^2/n_2}}\]
\[\nu=\frac{(s_1^2/n_1+s_2^2/n_2)^2}{\frac{(s_1^2/n_1)^2}{n_1-1}+\frac{(s_2^2/n_2)^2}{n_2-1}}\]
\[p=\mathtt{T.DIST.2T(}|t|,\nu\mathtt{)}\]
Effect Size \[d=\frac{\mu_1-\mu_2}{\sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}}\]
Confidence Interval (95%) \[\mu_1-\mu_2\pm\mathtt{T.INV.2T(}0.05,\nu\mathtt{)}\sqrt{s_1^2/n_1+s_2^2/n_2}\]
Confidence Interval (99%) \[\mu_1-\mu_2\pm\mathtt{T.INV.2T(}0.01,\nu\mathtt{)}\sqrt{s_1^2/n_1+s_2^2/n_2}\]

ToDo

External Links