Saltar al contenido principal

# 12.5: Revisión de la fórmula del capítulo

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$

( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\id}{\mathrm{id}}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\kernel}{\mathrm{null}\,}$$

$$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$

$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$

$$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$

$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$

$$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vectorC}[1]{\textbf{#1}}$$

$$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$

$$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$

$$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

## 12.1 Prueba de dos varianzas

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

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

si$$\delta_{0}=1$$ entonces

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

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

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

## 12.3 La distribución F y la relación F

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

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

$$S S_{\text {within}}=S S_{\text {total}}-S S_{\text {between}}$$

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

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

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

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

$$F=\frac{M S_{\text {between}}}{M S_{\text {within}}}$$

• $$k$$= el número de grupos
• $$n_j$$= el tamaño del jésimo grupo
• $$s_j$$= la suma de los valores en el jésimo grupo
• $$n$$= el número total de todos los valores (observaciones) combinados
• $$x$$= un valor (una observación) a partir de los datos
• $$s_{\overline{x}}^{2}$$= la varianza de las medias de la muestra
• $$s^2_{pooled}$$= la media de las varianzas de la muestra (varianza agrupada)

This page titled 12.5: Revisión de la fórmula del capítulo is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.