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12.5: Revisão da fórmula do capítulo

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    186557

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    12.1 Teste de duas variâncias

    \[H_{0} : \frac{\sigma_{1}^{2}}{\sigma_{2}^{2}}=\delta_{0}\nonumber\]

    \[H_{a} : \frac{\sigma_{1}^{2}}{\sigma_{2}^{2}} \neq \delta_{0}\nonumber\]

    se\(\delta_{0}=1\) então

    \[H_{0} : \sigma_{1}^{2}=\sigma_{2}^{2}\nonumber\]

    \[H_{a} : \sigma_{1}^{2} \neq \sigma_{2}\nonumber\]

    A estatística do teste é:

    \[F_{c}=\frac{S_{1}^{2}}{S_{2}^{2}}\nonumber\]

    12.3 A distribuição F e a razão F

    \(S S_{\mathrm{between}}=\sum\left[\frac{\left(s_{j}\right)^{2}}{n_{j}}\right]-\frac{\left(\sum s_{j}\right)^{2}}{n}\)

    \(S S_{\mathrm{total}}=\sum x^{2}-\frac{\left(\sum x\right)^{2}}{n}\)

    \(S S_{\text {within}}=S S_{\text {total}}-S S_{\text {between}}\)

    \(d f_{\mathrm{between}}=d f(n u m)=k-1\)

    \(d f_{\text {within}}=d f(\text {denom})=n-k\)

    \(M S_{\text {between}}=\frac{S S_{\text {between}}}{d f_{\text {between}}}\)

    \(M S_{\text {within}}=\frac{S S_{\text {within}}}{d f_{\text {within}}}\)

    \(F=\frac{M S_{\text {between}}}{M S_{\text {within}}}\)

    • \(k\)= o número de grupos
    • \(n_j\)= o tamanho do jésimo grupo
    • \(s_j\)= a soma dos valores no jésimo grupo
    • \(n\)= o número total de todos os valores (observações) combinados
    • \(x\)= um valor (uma observação) dos dados
    • \(s_{\overline{x}}^{2}\)= a variância das médias da amostra
    • \(s^2_{pooled}\)= a média das variâncias da amostra (variância combinada)