Unit 1 - Associazione fra caratteri: definizioni e misure per i caratteri statistici
Aggregazione dei criteri
Visualizzare
33. Correlazione per caratteri qualitativi /6
Numeratore
| \[\begin{eqnarray}\nonumber & & \sum_{k=1}^{n}{r_k\,s_k} - n\left( \frac{n+1}{2} \right)^2\cr &=& \sum_{k=1}^{n}{r_k\,s_k} - 3n\left( \frac{n+1}{12} \right)(n+1)\cr &=& \sum_{k=1}^{n}{r_k\,s_k} + n\left( \frac{n+1}{12} \right)(-3n - 3)\cr &=& \sum_{k=1}^{n}{r_k\,s_k} + n\left( \frac{n+1}{12} \right)[(n-1) - (4n + 2)]\cr &=& \frac{n(n+1)(n-1)}{12} - \frac{(n+1)(2n + 1)}{6} + \sum_{k=1}^{n}{r_k\,s_k}\cr &=& \frac{n(n^2 - 1)}{12} - \frac{1}{2}\sum_{k=1}^{n}(r_k^2 + s_k^2) + \sum_{k=1}^{n}{r_k\,s_k} \cr & \, & \color{brown}{ \boxed{ = \frac{n(n^2 - 1)}{12} - \frac{1}{2}\sum_{k=1}^{n}(r_k - s_k)^2 } } \end{eqnarray} \] | \[ \qquad \] |
Digressioni \[\bar{r} = \bar{s} = \displaystyle{\frac{n+1}{2}}\]\[\sum_{k=1}^{n} r_k = \sum_{k=1}^{n} s_k = \displaystyle{\frac{n(n+1)}{2}}\] |
|---|
