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\[E(SS_{B})=J\sum_{i=1}^{I}\alpha_{i}^{2}+(I-1)\sigma^{2}\] (Bevis (\[E(SS…
\[E(SS_{B})=J\sum_{i=1}^{I}\alpha_{i}^{2}+(I-1)\sigma^{2}\]
Bevis
\[E(SS_{B})=J\sum_{i=1}^{I}E\left((\overline{Y}_{i.}-\overline{Y}_{..})^{2}\right)\]
\[=J\sum_{i=1}^{I}\alpha_{i}^{2}+(I-1)\sigma^{2}\]
\[=J\sum_{i=1}^{I}\left((\underbrace{(\mu+\alpha_{i})}_{\mu_{i}}-\underbrace{\mu}_{\overline{\mu}})^{2}+\underbrace{\frac{I-1}{I}}_{\frac{n-1}{n}}\underbrace{\frac{\sigma^{2}}{J}}_{\sigma^{2}}\right)\]
\(\overline{Y}_i\) tar rollen som \(X_i\)
\(\overline{Y}_{..}\) tar rollen som \(\overline{X}\)
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