| 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%) |
\[\mu_1-\mu_2\pm\mathtt{T.INV.2T(}0.01,\nu\mathtt{)}\sqrt{s_1^2/n_1+s_2^2/n_2}\] |
|
