| 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 |
\[s=\sqrt{s^2}\] |
|
|
| Mean of Differences |
\[\mu_d=\frac{1}{n}\sum_{i=1}^n(x_{1,i}-x_{2,i})\] |
|
| Unbiased Variance of Differences |
\[s_d^2=\frac{1}{n-1}\sum_{i=1}^n(x_{1,i}-x_{2,i}-\mu_d)^2\] |
|
| Paired t-test |
\[t=\frac{\mu_d}{\sqrt{s_d^2/n}}\] |
|
| \[\nu=n-1\] |
|
| \[p=\mathtt{T.DIST.2T(}|t|,\nu\mathtt{)}\] |
|
| Effect Size |
\[ES_{pairedt}=\frac{\mu_d}{\sqrt{s_d^2}}\] |
|
| Confidence Interval (95%) |
\[\mu_d\pm\mathtt{T.INV.2T(}0.05,\nu\mathtt{)}\sqrt{s_d^2/n}\] |
|
| Confidence Interval (99%) |
\[\mu_d\pm\mathtt{T.INV.2T(}0.01,\nu\mathtt{)}\sqrt{s_d^2/n}\] |
|
