Diseño de Experimentos con Statgraphics, R y Python Cloud
Profe: Julio Hurtado Marquez
31/01/2023
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CURSO DE DISEÑO DE EXPERIMENTOS - 2023
Profe: Julio Hurtado Marquez
Email: juliohur@gmail.com
(a) Presentación
(b) Bienvenida a la U
(c) Presentación del Docente y Estudiantes
(d) Presentación del curso
(e) Contenidos en Savio
(f) Evaluaciones: Talleres en google drive y Savio
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1.0. Introducción al DOE: Generalidades
1.1. Video 1: Introducción al DOE
embed_youtube("h9nY-1iM0dY")2.0. Diseños Completos Aleatorizados (DCA): Generalidades
2.1. Video 2: Diseños Completos Aleatorizados (DCA): Generalidades
embed_youtube("bQdvpi6WZYc")2.2. Video 3: DCA Ejemplos prácticos usando Statgraphics
embed_youtube("F_KEL5IPS0s")2.3 Tema 1: Diseños Completos Aleatorizados - DCA usando RStudio
Ejemplo 2.3. (Texto Analisis y Diseno de Experimentos_Humberto-Roman_2da Ed_McGrawHill, pág. 63)
Problema: Un fabricante de calzado desea mejorar la calidad de las suelas, las cuales se pueden hacer con uno de los cuatro tipos de cuero A, B, C y D disponibles en el mercado. Para ello, prueba los cueros con una máquina que hace pasar los zapatos por una superficie abrasiva. La suela de los zapatos se desgasta al pasarla por dicha superficie. Como criterio de desgaste se usa la pérrdida de peso después de un número fijo de ciclos. Se prueban en orden aleatorio 24 zapatos, seis de cada tipo de cuero. Al hacer las pruebas en orden completamente al azar se evitan sesgos y las mediciones en un tipo de cuero resultan independiente de las demás. Los datos (en mg) sobre el desgaste de cada tipo de cuero se muestran en la tabla siguiente:.
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Tabla de datos
| Tipos de Cuero | Desgaste | |||||
|---|---|---|---|---|---|---|
| A | 264 | 260 | 258 | 241 | 262 | 255 |
| B | 208 | 220 | 216 | 200 | 213 | 206 |
| C | 220 | 263 | 219 | 225 | 230 | 228 |
| D | 217 | 226 | 215 | 224 | 220 | 222 |
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2.4 Usando RStudio - DCA
(a) Vector de Datos en R
# Datos del Problema Tipos de Cuero T.CUERO
A<-c(264, 260, 258, 241, 262, 255)
B<-c(208, 220, 216, 200, 213, 206)
C<-c(220, 263, 219, 225, 230, 228)
D<-c(217, 226, 215, 224, 220, 222)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(b) Creando matriz a partir de los vectores
T.CUERO <-matrix(c(A, B, C, D),nrow = 6,ncol = 4)
T.CUERO## [,1] [,2] [,3] [,4]
## [1,] 264 208 220 217
## [2,] 260 220 263 226
## [3,] 258 216 219 215
## [4,] 241 200 225 224
## [5,] 262 213 230 220
## [6,] 255 206 228 222%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(c) Agregar nombres de columnas
colnames(T.CUERO)<-c("A", "B", "C", "D")
T.CUERO## A B C D
## [1,] 264 208 220 217
## [2,] 260 220 263 226
## [3,] 258 216 219 215
## [4,] 241 200 225 224
## [5,] 262 213 230 220
## [6,] 255 206 228 222%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(d) agregar nombres de filas/renglones
rownames(T.CUERO)<-c("1","2","3","4","5","6")
T.CUERO## A B C D
## 1 264 208 220 217
## 2 260 220 263 226
## 3 258 216 219 215
## 4 241 200 225 224
## 5 262 213 230 220
## 6 255 206 228 222summary(T.CUERO)## A B C D
## Min. :241.0 Min. :200.0 Min. :219.0 Min. :215.0
## 1st Qu.:255.8 1st Qu.:206.5 1st Qu.:221.2 1st Qu.:217.8
## Median :259.0 Median :210.5 Median :226.5 Median :221.0
## Mean :256.7 Mean :210.5 Mean :230.8 Mean :220.7
## 3rd Qu.:261.5 3rd Qu.:215.2 3rd Qu.:229.5 3rd Qu.:223.5
## Max. :264.0 Max. :220.0 Max. :263.0 Max. :226.0%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(e) El primer paso es graficar los datos; los diagramas de caja son útiles:
boxplot(T.CUERO, col=c("red", "blue", "yellow", "orange"))
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2.5 Usando RStudio forma 2 - DCA
(a) DCA de una mejor forma :Creando el data.frame
set.seed(7638)
T.CUERO2 <- factor( rep( c("A", "B", "C","D" ), each = 6))
Desgaste <- c(264, 260, 258, 241, 262, 255, 208, 220, 216, 200, 213, 206, 220, 263, 219, 225, 230, 228, 217, 226, 215, 224, 220, 222)
DCA <- data.frame( T.CUERO2, Desgaste )
DCA%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(b) Resumen estadístico
summary(DCA, f=TRUE)## T.CUERO2 Desgaste
## A:6 Min. :200.0
## B:6 1st Qu.:216.8
## C:6 Median :223.0
## D:6 Mean :229.7
## 3rd Qu.:244.5
## Max. :264.0%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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span style=“color:red”>(c) El primer paso es graficar los datos; los diagramas de caja son útiles:
plot(Desgaste ~ T.CUERO2, data=DCA, col=c("red", "blue", "yellow", "orange"))
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2.6. Modelo Lineal - DCA
(a) Ahora ajustemos el modelo lineal (lm en R).
\[lm: y_{ij} = \mu+\tau_i+\epsilon_{ij}= \mu_i+\epsilon_{ij}\] donde \(\mu\) es la media real del desgaste con los diferentes tipos de cuero, \(\tau_i\) es el efecto medio sobre el desgaste de los tipos de cuero y \(\epsilon_ij\) es el arror aleatorio
g <- lm(Desgaste ~ T.CUERO2, data=DCA)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(b) Resumen estadístico: el modelo lineal (lm en R). Anote las conclusiones
summary(g)##
## Call:
## lm(formula = Desgaste ~ T.CUERO2, data = DCA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.667 -4.792 -0.750 3.833 32.167
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 256.667 4.112 62.419 < 2e-16 ***
## T.CUERO2B -46.167 5.815 -7.939 1.31e-07 ***
## T.CUERO2C -25.833 5.815 -4.442 0.00025 ***
## T.CUERO2D -36.000 5.815 -6.191 4.78e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.07 on 20 degrees of freedom
## Multiple R-squared: 0.7771, Adjusted R-squared: 0.7436
## F-statistic: 23.24 on 3 and 20 DF, p-value: 1.002e-06(c) Anova: el modelo lineal (lm en R). Anote las conclusiones*
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anova(g)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(d) Examinemos la matriz del diseño para comprender la codificación
model.matrix(g)## (Intercept) T.CUERO2B T.CUERO2C T.CUERO2D
## 1 1 0 0 0
## 2 1 0 0 0
## 3 1 0 0 0
## 4 1 0 0 0
## 5 1 0 0 0
## 6 1 0 0 0
## 7 1 1 0 0
## 8 1 1 0 0
## 9 1 1 0 0
## 10 1 1 0 0
## 11 1 1 0 0
## 12 1 1 0 0
## 13 1 0 1 0
## 14 1 0 1 0
## 15 1 0 1 0
## 16 1 0 1 0
## 17 1 0 1 0
## 18 1 0 1 0
## 19 1 0 0 1
## 20 1 0 0 1
## 21 1 0 0 1
## 22 1 0 0 1
## 23 1 0 0 1
## 24 1 0 0 1
## attr(,"assign")
## [1] 0 1 1 1
## attr(,"contrasts")
## attr(,"contrasts")$T.CUERO2
## [1] "contr.treatment"%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(e) Examinemos la matriz del diseño para comprender la codificación: Podemos ajustar el modelo sin el término de intersección
gi <- lm(Desgaste ~ T.CUERO2 -1, data=DCA)
model.matrix(gi)## T.CUERO2A T.CUERO2B T.CUERO2C T.CUERO2D
## 1 1 0 0 0
## 2 1 0 0 0
## 3 1 0 0 0
## 4 1 0 0 0
## 5 1 0 0 0
## 6 1 0 0 0
## 7 0 1 0 0
## 8 0 1 0 0
## 9 0 1 0 0
## 10 0 1 0 0
## 11 0 1 0 0
## 12 0 1 0 0
## 13 0 0 1 0
## 14 0 0 1 0
## 15 0 0 1 0
## 16 0 0 1 0
## 17 0 0 1 0
## 18 0 0 1 0
## 19 0 0 0 1
## 20 0 0 0 1
## 21 0 0 0 1
## 22 0 0 0 1
## 23 0 0 0 1
## 24 0 0 0 1
## attr(,"assign")
## [1] 1 1 1 1
## attr(,"contrasts")
## attr(,"contrasts")$T.CUERO2
## [1] "contr.treatment"summary(gi)##
## Call:
## lm(formula = Desgaste ~ T.CUERO2 - 1, data = DCA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.667 -4.792 -0.750 3.833 32.167
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## T.CUERO2A 256.667 4.112 62.42 <2e-16 ***
## T.CUERO2B 210.500 4.112 51.19 <2e-16 ***
## T.CUERO2C 230.833 4.112 56.14 <2e-16 ***
## T.CUERO2D 220.667 4.112 53.66 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.07 on 20 degrees of freedom
## Multiple R-squared: 0.9984, Adjusted R-squared: 0.9981
## F-statistic: 3137 on 4 and 20 DF, p-value: < 2.2e-16- Podemos leer directamente las medias de nivel pero las pruebas no son útiles ya que implican comparaciones con cero. Tenga en cuenta el error de cálculo de \(R^2\).
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f) Variables que contiene nuestro modelo: usando names(g)
names(g)## [1] "coefficients" "residuals" "effects" "rank"
## [5] "fitted.values" "assign" "qr" "df.residual"
## [9] "contrasts" "xlevels" "call" "terms"
## [13] "model"%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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2.7. Supuestos del Modelo Lineal - DCA
(a) Examinando la normalidad de los datos: Gráfico QQ
qqnorm(g$res, main = "Distribución de residuos para la variable Desgaste",col="red", lwd=3)
qqline(g$res, col="blue", lwd=3)
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(b) Media y desviación de los residuos
mean(g$res)## [1] 3.330669e-16sd(g$res)## [1] 9.392411%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(c) Tabla de residuos
g$res## 1 2 3 4 5 6
## 7.3333333 3.3333333 1.3333333 -15.6666667 5.3333333 -1.6666667
## 7 8 9 10 11 12
## -2.5000000 9.5000000 5.5000000 -10.5000000 2.5000000 -4.5000000
## 13 14 15 16 17 18
## -10.8333333 32.1666667 -11.8333333 -5.8333333 -0.8333333 -2.8333333
## 19 20 21 22 23 24
## -3.6666667 5.3333333 -5.6666667 3.3333333 -0.6666667 1.3333333%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(d) Examinando la Homocedasticidad de los datos: Residuos vs Predichos
plot(g$fit,g$res,xlab="Predichos",ylab="Residuos",
main="Gráfico Residuos-Predichos", col="blue", lwd=3)
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(e) Examinando la Homocedasticidad de los datos: Residuos vs Predichos
plot(jitter(g$fit),g$res,xlab="Predichos",ylab="Residuos",
main="Jittered plot", col="blue", lwd=3)
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2.8. Comparaciones Múltiples - DCA
(a) Comparaciones multiples
g <- lm(Desgaste ~ T.CUERO2, data=DCA)
summary(g)##
## Call:
## lm(formula = Desgaste ~ T.CUERO2, data = DCA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.667 -4.792 -0.750 3.833 32.167
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 256.667 4.112 62.419 < 2e-16 ***
## T.CUERO2B -46.167 5.815 -7.939 1.31e-07 ***
## T.CUERO2C -25.833 5.815 -4.442 0.00025 ***
## T.CUERO2D -36.000 5.815 -6.191 4.78e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.07 on 20 degrees of freedom
## Multiple R-squared: 0.7771, Adjusted R-squared: 0.7436
## F-statistic: 23.24 on 3 and 20 DF, p-value: 1.002e-06%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(b) Una forma alternativa en la que podemos hacer el mismo cálculo es recodificar el factor con B como nivel de referencia y reajustar el modelo:
DCA$T.CUERO2 <- relevel(DCA$T.CUERO2,ref="B")
g <- lm(Desgaste ~ T.CUERO2, data=DCA)
summary(g)##
## Call:
## lm(formula = Desgaste ~ T.CUERO2, data = DCA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.667 -4.792 -0.750 3.833 32.167
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 210.500 4.112 51.192 < 2e-16 ***
## T.CUERO2A 46.167 5.815 7.939 1.31e-07 ***
## T.CUERO2C 20.333 5.815 3.497 0.00227 **
## T.CUERO2D 10.167 5.815 1.748 0.09575 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.07 on 20 degrees of freedom
## Multiple R-squared: 0.7771, Adjusted R-squared: 0.7436
## F-statistic: 23.24 on 3 and 20 DF, p-value: 1.002e-06%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(c) Anova del modelo
anova(g)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(d) Tukey: Rangos múltiples
z = TukeyHSD(aov(Desgaste ~ T.CUERO2, data=DCA))
z## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Desgaste ~ T.CUERO2, data = DCA)
##
## $T.CUERO2
## diff lwr upr p adj
## A-B 46.16667 29.890265 62.443068 0.0000007
## C-B 20.33333 4.056932 36.609735 0.0112174
## D-B 10.16667 -6.109735 26.443068 0.3263417
## C-A -25.83333 -42.109735 -9.556932 0.0013189
## D-A -36.00000 -52.276401 -19.723599 0.0000265
## D-C -10.16667 -26.443068 6.109735 0.3263417plot(z)
El método de Tukey supone lo peor centrándose en la diferencia más grande. Hay otros competidores como el Newman-Keuls, el rango múltiple de Duncan y el procedimiento de Waller-Duncan. Para una descripción detallada de las muchas alternativas disponibles ver Hsu (1996).
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2.9. Prueba de homogeneidad de varianza - DCA
(z) Resumen estadístico
summary(lm( abs(g$res) ~ DCA$T.CUERO2))##
## Call:
## lm(formula = abs(g$res) ~ DCA$T.CUERO2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.8889 -3.3333 -0.3889 1.6667 21.4444
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.83333 2.68960 2.169 0.0423 *
## DCA$T.CUERO2A -0.05556 3.80367 -0.015 0.9885
## DCA$T.CUERO2C 4.88889 3.80367 1.285 0.2134
## DCA$T.CUERO2D -2.50000 3.80367 -0.657 0.5185
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.588 on 20 degrees of freedom
## Multiple R-squared: 0.166, Adjusted R-squared: 0.04088
## F-statistic: 1.327 on 3 and 20 DF, p-value: 0.2936Dado que el valor p es grande, concluimos que no hay evidencia de una varianza no constante.
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2.10. Ejemplo de Diseño de Experimentos con Python
https://github.com/JSEFERINO/JSEFERINO/blob/main/DOEJH.ipynb
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2.11. DCA con Python
https://github.com/JSEFERINO/JSEFERINO/blob/main/DOEJH2Cipynb.ipynb
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2.12. DCA-2 con Python
https://github.com/JSEFERINO/JSEFERINO/blob/main/DOEJH0.ipynb
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2.13. DCA-3 con Python
https://github.com/JSEFERINO/JSEFERINO/blob/main/DOEJH7.ipynb
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2.14. Evaluación 1. DCA - PARTE I
https://forms.gle/hSNWpv8EiRGFRdqL8
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2.15. Evaluación 2. DCA - PARTE II
https://forms.gle/Guicic1XUFHH7oPNA
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3.0 Tema 3: Diseños en Bloques Completos al Azar DBCA: Generalidades
3.1 Video 3: Diseños en Bloques Completos al Azar DBCA: Generalidades**
embed_youtube("--GzYcmlk5o")3.2 Tema 3: Diseños en Bloques Completos al Azar DBCA
Ejemplo 3.2. (Texto Analisis y Diseno de Experimentos_Humberto-Roman_2da Ed_McGrawHill, pág. 63)
Se evalúa la eficacia de sulfato ferroso a 4 diferentes concentraciones A=2, B=2.5, C=3, y D=4 mg/kg/día para combatir la anemia en personas con desnutrición. Dada la variabilidad de pesos y sexos, se decidió agrupar en bloque de personas por pesos lo más semejantes posibles. Se les dio el tratamiento durante 4 meses y se procedió a determinar su volumen sanguíneo dando los siguientes resultados:
| Tratamientos | A | B | C | D | ||
|---|---|---|---|---|---|---|
| I | 4.1 | 6.5 | 4.1 | 4.9 | ||
| II | 4.1 | 5.3 | 4.0 | 6.2 | ||
| Bloques | III | 6.5 | 6.9 | 4.5 | 4.8 | |
| IV | 4.3 | 6.8 | 4.3 | 4.2 | ||
| V | 6.0 | 6.5 | 4.1 | 6.9 |
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3.3 Ingresando los datos en RStudio
(a) Primero creamos los vectores teniendo en cuenta que los factores se deben crear como factor.
V.sanguíneo =c(4.1, 6.5,4.1, 4.9,
4.1, 5.3, 4.0, 6.2,
6.5, 6.9, 4.5, 4.8,
4.3, 6.8, 4.3,4.2,
6.0, 6.5,4.1, 6.9)
Tratamientos =factor( c(rep("A",1),
rep("B",1),
rep("C",1),
rep("D",1)))
Bloques = factor(c(rep("I",4),
rep("II",4),
rep("III",4),
rep("IV",4),
rep("V",4))) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(b) Se obtiene ahora la nueva tabla de datos del modelo
DBCA1 = data.frame(Bloques,Tratamientos, V.sanguíneo)
DBCA1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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3.4 Analizando los datos en RStudio
(a) Para el próximo paso debemos descargar los siguientes paquetes (gridExtra) y (ggplot2)
library(gridExtra)
library(ggplot2)## Warning: replacing previous import 'ellipsis::check_dots_unnamed' by
## 'rlang::check_dots_unnamed' when loading 'tibble'## Warning: replacing previous import 'ellipsis::check_dots_used' by
## 'rlang::check_dots_used' when loading 'tibble'## Warning: replacing previous import 'ellipsis::check_dots_empty' by
## 'rlang::check_dots_empty' when loading 'tibble'## Warning: replacing previous import 'ellipsis::check_dots_unnamed' by
## 'rlang::check_dots_unnamed' when loading 'pillar'## Warning: replacing previous import 'ellipsis::check_dots_used' by
## 'rlang::check_dots_used' when loading 'pillar'## Warning: replacing previous import 'ellipsis::check_dots_empty' by
## 'rlang::check_dots_empty' when loading 'pillar'%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(b) Diagramas de caja: Los siguientes son gráficos descriptivos de los factores con la variable respuesta
Tratamientos2 <- ggplot(DBCA1, aes(x = Tratamientos, y = V.sanguíneo, fill=Tratamientos)) +
geom_boxplot() + theme(legend.position = "none")
Bloques2 <- ggplot(DBCA1, aes(x = Bloques, y = V.sanguíneo, fill=Bloques)) +
geom_boxplot() + theme(legend.position = "none")
grid.arrange(Tratamientos2,Bloques2, nrow=1, ncol=2)
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(c) El Modelo linal y tabla ANOVA
modeloDBCA1= lm(V.sanguíneo ~ Tratamientos + Bloques, DBCA1)
anovaDBCA1=aov(modeloDBCA1)
anovaDBCA1## Call:
## aov(formula = modeloDBCA1)
##
## Terms:
## Tratamientos Bloques Residuals
## Sum of Squares 12.550 3.755 8.345
## Deg. of Freedom 3 4 12
##
## Residual standard error: 0.8339165
## Estimated effects may be unbalancedsummary(anovaDBCA1)## Df Sum Sq Mean Sq F value Pr(>F)
## Tratamientos 3 12.550 4.183 6.016 0.00964 **
## Bloques 4 3.755 0.939 1.350 0.30797
## Residuals 12 8.345 0.695
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(d) Comparaciones múltiples: HSD de Tukey
TukeyHSD(anovaDBCA1)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = modeloDBCA1)
##
## $Tratamientos
## diff lwr upr p adj
## B-A 1.4 -0.1658432 2.9658432 0.0854565
## C-A -0.8 -2.3658432 0.7658432 0.4580868
## D-A 0.4 -1.1658432 1.9658432 0.8713824
## C-B -2.2 -3.7658432 -0.6341568 0.0061420
## D-B -1.0 -2.5658432 0.5658432 0.2800111
## D-C 1.2 -0.3658432 2.7658432 0.1586223
##
## $Bloques
## diff lwr upr p adj
## II-I 0.000000e+00 -1.8795268 1.879527 1.0000000
## III-I 7.750000e-01 -1.1045268 2.654527 0.6881671
## IV-I -8.881784e-16 -1.8795268 1.879527 1.0000000
## V-I 9.750000e-01 -0.9045268 2.854527 0.4944147
## III-II 7.750000e-01 -1.1045268 2.654527 0.6881671
## IV-II -8.881784e-16 -1.8795268 1.879527 1.0000000
## V-II 9.750000e-01 -0.9045268 2.854527 0.4944147
## IV-III -7.750000e-01 -2.6545268 1.104527 0.6881671
## V-III 2.000000e-01 -1.6795268 2.079527 0.9967411
## V-IV 9.750000e-01 -0.9045268 2.854527 0.4944147%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(e) Comparaciones múltiples: gráfico HSD de Tukey
plot(TukeyHSD(anovaDBCA1))
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3.5 Pruebas de Medias por comparaciones Múltiples
(a) (Prueba LSD). Instale el paquete “agricolae
library(agricolae)## Warning: replacing previous import 'ellipsis::check_dots_unnamed' by
## 'rlang::check_dots_unnamed' when loading 'hms'## Warning: replacing previous import 'ellipsis::check_dots_used' by
## 'rlang::check_dots_used' when loading 'hms'## Warning: replacing previous import 'ellipsis::check_dots_empty' by
## 'rlang::check_dots_empty' when loading 'hms'%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) Prueba LSD para Tratamientos
LSD.test(anovaDBCA1,"Tratamientos",console=TRUE)##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## LSD t Test for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means and individual ( 95 %) CI
##
## V.sanguíneo std r LCL UCL Min Max
## A 5.0 1.1575837 5 4.187436 5.812564 4.1 6.5
## B 6.4 0.6403124 5 5.587436 7.212564 5.3 6.9
## C 4.2 0.2000000 5 3.387436 5.012564 4.0 4.5
## D 5.4 1.1113055 5 4.587436 6.212564 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of t: 2.178813
##
## least Significant Difference: 1.149139
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 bc
## C 4.2 cplot(LSD.test(anovaDBCA1,"Tratamientos",console=TRUE))##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## LSD t Test for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means and individual ( 95 %) CI
##
## V.sanguíneo std r LCL UCL Min Max
## A 5.0 1.1575837 5 4.187436 5.812564 4.1 6.5
## B 6.4 0.6403124 5 5.587436 7.212564 5.3 6.9
## C 4.2 0.2000000 5 3.387436 5.012564 4.0 4.5
## D 5.4 1.1113055 5 4.587436 6.212564 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of t: 2.178813
##
## least Significant Difference: 1.149139
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 bc
## C 4.2 c
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(c) Prueba LSD para Bloques
LSD.test(anovaDBCA1,"Bloques",console=TRUE)##
## Study: anovaDBCA1 ~ "Bloques"
##
## LSD t Test for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Bloques, means and individual ( 95 %) CI
##
## V.sanguíneo std r LCL UCL Min Max
## I 4.900 1.131371 4 3.991526 5.808474 4.1 6.5
## II 4.900 1.048809 4 3.991526 5.808474 4.0 6.2
## III 5.675 1.201041 4 4.766526 6.583474 4.5 6.9
## IV 4.900 1.267544 4 3.991526 5.808474 4.2 6.8
## V 5.875 1.239287 4 4.966526 6.783474 4.1 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of t: 2.178813
##
## least Significant Difference: 1.284776
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## V 5.875 a
## III 5.675 a
## I 4.900 a
## II 4.900 a
## IV 4.900 aplot(LSD.test(anovaDBCA1,"Bloques",console=TRUE))##
## Study: anovaDBCA1 ~ "Bloques"
##
## LSD t Test for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Bloques, means and individual ( 95 %) CI
##
## V.sanguíneo std r LCL UCL Min Max
## I 4.900 1.131371 4 3.991526 5.808474 4.1 6.5
## II 4.900 1.048809 4 3.991526 5.808474 4.0 6.2
## III 5.675 1.201041 4 4.766526 6.583474 4.5 6.9
## IV 4.900 1.267544 4 3.991526 5.808474 4.2 6.8
## V 5.875 1.239287 4 4.966526 6.783474 4.1 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of t: 2.178813
##
## least Significant Difference: 1.284776
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## V 5.875 a
## III 5.675 a
## I 4.900 a
## II 4.900 a
## IV 4.900 a
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(f) Prueba de Tukey: Tratamientos
HSD.test(anovaDBCA1, "Tratamientos",console=TRUE)##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## HSD Test for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means
##
## V.sanguíneo std r Min Max
## A 5.0 1.1575837 5 4.1 6.5
## B 6.4 0.6403124 5 5.3 6.9
## C 4.2 0.2000000 5 4.0 4.5
## D 5.4 1.1113055 5 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of Studentized Range: 4.19866
##
## Minimun Significant Difference: 1.565843
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 ab
## C 4.2 bplot(HSD.test(anovaDBCA1, "Tratamientos",console=TRUE))##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## HSD Test for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means
##
## V.sanguíneo std r Min Max
## A 5.0 1.1575837 5 4.1 6.5
## B 6.4 0.6403124 5 5.3 6.9
## C 4.2 0.2000000 5 4.0 4.5
## D 5.4 1.1113055 5 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of Studentized Range: 4.19866
##
## Minimun Significant Difference: 1.565843
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 ab
## C 4.2 b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(g) Prueba de Tukey: Bloques
HSD.test(anovaDBCA1, "Bloques",console=TRUE)##
## Study: anovaDBCA1 ~ "Bloques"
##
## HSD Test for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Bloques, means
##
## V.sanguíneo std r Min Max
## I 4.900 1.131371 4 4.1 6.5
## II 4.900 1.048809 4 4.0 6.2
## III 5.675 1.201041 4 4.5 6.9
## IV 4.900 1.267544 4 4.2 6.8
## V 5.875 1.239287 4 4.1 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of Studentized Range: 4.50771
##
## Minimun Significant Difference: 1.879527
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## V 5.875 a
## III 5.675 a
## I 4.900 a
## II 4.900 a
## IV 4.900 a%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(h) Prueba de Student-Newman-Keuls (SNK)
SNK.test(anovaDBCA1, "Tratamientos",console=TRUE)##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## Student Newman Keuls Test
## for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means
##
## V.sanguíneo std r Min Max
## A 5.0 1.1575837 5 4.1 6.5
## B 6.4 0.6403124 5 5.3 6.9
## C 4.2 0.2000000 5 4.0 4.5
## D 5.4 1.1113055 5 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
##
## Critical Range
## 2 3 4
## 1.149139 1.407072 1.565843
##
## Means with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 ab
## C 4.2 bplot(SNK.test(anovaDBCA1, "Tratamientos",console=TRUE))##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## Student Newman Keuls Test
## for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means
##
## V.sanguíneo std r Min Max
## A 5.0 1.1575837 5 4.1 6.5
## B 6.4 0.6403124 5 5.3 6.9
## C 4.2 0.2000000 5 4.0 4.5
## D 5.4 1.1113055 5 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
##
## Critical Range
## 2 3 4
## 1.149139 1.407072 1.565843
##
## Means with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 ab
## C 4.2 b
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(i) Prueba de Scheffé
scheffe.test(anovaDBCA1, "Bloques",console=TRUE)##
## Study: anovaDBCA1 ~ "Bloques"
##
## Scheffe Test for V.sanguíneo
##
## Mean Square Error : 0.6954167
##
## Bloques, means
##
## V.sanguíneo std r Min Max
## I 4.900 1.131371 4 4.1 6.5
## II 4.900 1.048809 4 4.0 6.2
## III 5.675 1.201041 4 4.5 6.9
## IV 4.900 1.267544 4 4.2 6.8
## V 5.875 1.239287 4 4.1 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of F: 3.259167
##
## Minimum Significant Difference: 2.129074
##
## Means with the same letter are not significantly different.
##
## V.sanguíneo groups
## V 5.875 a
## III 5.675 a
## I 4.900 a
## II 4.900 a
## IV 4.900 aplot(scheffe.test(anovaDBCA1, "Bloques",console=TRUE))##
## Study: anovaDBCA1 ~ "Bloques"
##
## Scheffe Test for V.sanguíneo
##
## Mean Square Error : 0.6954167
##
## Bloques, means
##
## V.sanguíneo std r Min Max
## I 4.900 1.131371 4 4.1 6.5
## II 4.900 1.048809 4 4.0 6.2
## III 5.675 1.201041 4 4.5 6.9
## IV 4.900 1.267544 4 4.2 6.8
## V 5.875 1.239287 4 4.1 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of F: 3.259167
##
## Minimum Significant Difference: 2.129074
##
## Means with the same letter are not significantly different.
##
## V.sanguíneo groups
## V 5.875 a
## III 5.675 a
## I 4.900 a
## II 4.900 a
## IV 4.900 a
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(j) Prueba de Duncan
duncan.test(anovaDBCA1, "Tratamientos",console=TRUE)##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## Duncan's new multiple range test
## for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means
##
## V.sanguíneo std r Min Max
## A 5.0 1.1575837 5 4.1 6.5
## B 6.4 0.6403124 5 5.3 6.9
## C 4.2 0.2000000 5 4.0 4.5
## D 5.4 1.1113055 5 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
##
## Critical Range
## 2 3 4
## 1.149139 1.202818 1.235342
##
## Means with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 b
## C 4.2 bplot(duncan.test(anovaDBCA1, "Tratamientos",console=TRUE))##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## Duncan's new multiple range test
## for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means
##
## V.sanguíneo std r Min Max
## A 5.0 1.1575837 5 4.1 6.5
## B 6.4 0.6403124 5 5.3 6.9
## C 4.2 0.2000000 5 4.0 4.5
## D 5.4 1.1113055 5 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
##
## Critical Range
## 2 3 4
## 1.149139 1.202818 1.235342
##
## Means with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 b
## C 4.2 b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(k) Prueba de Bonferroni
LSD.test(anovaDBCA1, "Tratamientos", p.adj= "bon",console=TRUE)##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## LSD t Test for V.sanguíneo
## P value adjustment method: bonferroni
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means and individual ( 95 %) CI
##
## V.sanguíneo std r LCL UCL Min Max
## A 5.0 1.1575837 5 4.187436 5.812564 4.1 6.5
## B 6.4 0.6403124 5 5.587436 7.212564 5.3 6.9
## C 4.2 0.2000000 5 3.387436 5.012564 4.0 4.5
## D 5.4 1.1113055 5 4.587436 6.212564 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of t: 3.152681
##
## Minimum Significant Difference: 1.662772
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 ab
## C 4.2 bplot(LSD.test(anovaDBCA1, "Tratamientos", p.adj= "bon",console=TRUE))##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## LSD t Test for V.sanguíneo
## P value adjustment method: bonferroni
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means and individual ( 95 %) CI
##
## V.sanguíneo std r LCL UCL Min Max
## A 5.0 1.1575837 5 4.187436 5.812564 4.1 6.5
## B 6.4 0.6403124 5 5.587436 7.212564 5.3 6.9
## C 4.2 0.2000000 5 3.387436 5.012564 4.0 4.5
## D 5.4 1.1113055 5 4.587436 6.212564 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of t: 3.152681
##
## Minimum Significant Difference: 1.662772
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 ab
## C 4.2 b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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3.6 Supuestos del Modelo en RStudio: Normalidad
(a) Normalidad de los residuos
shapiro.test(anovaDBCA1$res)##
## Shapiro-Wilk normality test
##
## data: anovaDBCA1$res
## W = 0.95529, p-value = 0.4545%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(b) Supuesto del modelo:Normalidad de los residuos
summary(anovaDBCA1$residuals)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -1.025 -0.550 -0.025 0.000 0.450 1.150sd((anovaDBCA1$residuals))## [1] 0.6627296%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(c) Supuesto del modelo:Normalidad de los residuos
boxplot(anovaDBCA1$residuals,col="lightblue") 
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(d) Supuesto del modelo:Normalidad de los residuos
hist(anovaDBCA1$residuals, col="lightgreen", main = "Histograma de los Residuos",
freq = F, xlab="Residuos",ylab="Densidad")
lines(density(anovaDBCA1$residuals), col="red", lwd=3)
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(e) ** Prueba de Normalidad con Q-Q Plot**
qqnorm(anovaDBCA1$residuals,col="blue", lwd=3)
qqline(anovaDBCA1$residuals,col="red", lwd=3)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ## 3.7. Supuestos del Modelo en RStudio: Supuesto de Independencia
(a) Supuesto de Independencia
plot(anovaDBCA1$residuals,main = "Residuos vs Observaciones",col="red", lwd=3) 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ## 3.8. Supuestos del Modelo en RStudio: Supuesto de Homocedasticidad
(a) Homocedasticidad
boxplot(anovaDBCA1$residuals~Bloques, xlab="Bloques",ylab="Residuos",
col = c("yellow", "blue", "white","green", "red")) 
names(anovaDBCA1)## [1] "coefficients" "residuals" "effects" "rank"
## [5] "fitted.values" "assign" "qr" "df.residual"
## [9] "contrasts" "xlevels" "call" "terms"
## [13] "model"%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(d) Homocedasticidad: Gráfico de predichos contra residuos estandarizados
pred=fitted(anovaDBCA1)
resid=rstandard(anovaDBCA1)
plot(pred,resid,xlab="Valores predichos", ylab="Residuos estandarizados",abline(h=0),col="red", lwd=3)
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(e) Homocedasticidad: Prueba de Bartlett para Lisina
bartlett.test(anovaDBCA1$residuals ~ Bloques)##
## Bartlett test of homogeneity of variances
##
## data: anovaDBCA1$residuals by Bloques
## Bartlett's K-squared = 1.2802, df = 4, p-value = 0.8647%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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3.9. Evaluación 3. DBCA
https://forms.gle/m2CFT2heKXeskHe28
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4.0 Tema 4: Diseños en Cuadrados Latino - DCL: Generalidades
4.1 Video 4. Diseños en Cuadrados Latino - DCL: Generalidades
embed_youtube("-7Yh4KTkDoo")4.2. Tema 4: Diseños en Cuadrados Latino - DCL: Usando RStudio
Ejemplo 4.2 (Texto Analisis y Diseno de Experimentos_Humberto-Roman_2da Ed_McGrawHill, pág. 63)
Ejemplo 4.2 Se desea evaluar el funcionamiento hepático en perros con diferentes patologías hepáticas que se encuentran con tratamiento de vitaminas B a 4 diferentes concentraciones. Por lo que se hace un doble arreglo en base a las patologías y razas, y se procedió a la medición de la Transaminasa Glutámico Pirúvica (TGP)
| Razas Patologias | 1:Isquemia | 2:Tumor | 3:Hepatitis | 4:Hemocromatosis |
|---|---|---|---|---|
| 1:Cocker | A=10 | B=9 | C=25 | D=8 |
| 2:Pastor | D=9 | A=5 | B=17 | C=26 |
| 3:Boxer | C=24 | D=9 | A=8 | B=19 |
| 4:Schnauzer | B=20 | C=22 | D=8 | A=5 |
¿Existen diferencias en la diferentes concentraciones de vitamina B con respecto a TGP?
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4.3 Ingresando los datos en RStudio
(a) Usando RSTUDIO
set.seed(7638)
PATOLOGIAS <- factor( rep( c("P1", "P2", "P3","P4" ), each = 1))
RAZAS <- factor( rep( c("R1", "R2", "R3", "R4" ), each = 4))
VITAMINAS <- factor(c("A", "B", "C","D","D", "A", "B", "C","C", "D", "A", "B", "B", "C", "D", "A" ))
f = TGP <- c(10, 9, 25, 8, 9, 5, 17, 26, 24, 9, 8, 19, 20, 22, 8 ,5)
DCL <- data.frame( RAZAS, PATOLOGIAS, VITAMINAS, f)
DCL%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) Acerca del Diseño
Factor de interés: Concentraciones de Vitamina B
####Niveles del Factor: A, B, C y D (cuatro niveles I=4).
Otros factores:
Patologias con cuatro niveles (J=4)
Razas con cuatro niveles (K=4)
Variable de interés: Y= Medicion de la TGP.
Replicas por nivel: n=1.
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4.4 Analizando los datos en RStudio
(a) DCL Diagrama de cajas
plot(f ~RAZAS + PATOLOGIAS +VITAMINAS, data=DCL, col=c("red2", "blue2", "yellow2", "orange2"))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(b) Anova
g <- lm(f ~RAZAS + PATOLOGIAS +VITAMINAS, data=DCL)
summary(g)##
## Call:
## lm(formula = f ~ RAZAS + PATOLOGIAS + VITAMINAS, data = DCL)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5000 -0.9375 0.2500 1.2500 2.2500
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.750 2.271 3.413 0.014266 *
## RAZASR2 1.250 2.031 0.615 0.560856
## RAZASR3 2.000 2.031 0.985 0.362784
## RAZASR4 0.750 2.031 0.369 0.724605
## PATOLOGIASP2 -4.500 2.031 -2.216 0.068608 .
## PATOLOGIASP3 -1.250 2.031 -0.615 0.560856
## PATOLOGIASP4 -1.250 2.031 -0.615 0.560856
## VITAMINASB 9.250 2.031 4.554 0.003874 **
## VITAMINASC 17.250 2.031 8.493 0.000146 ***
## VITAMINASD 1.500 2.031 0.739 0.488053
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.872 on 6 degrees of freedom
## Multiple R-squared: 0.9424, Adjusted R-squared: 0.8561
## F-statistic: 10.92 on 9 and 6 DF, p-value: 0.004384anova(g)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(c) Anova del modelo
g2<-aov(f ~RAZAS + PATOLOGIAS +VITAMINAS, data=DCL)
g2## Call:
## aov(formula = f ~ RAZAS + PATOLOGIAS + VITAMINAS, data = DCL)
##
## Terms:
## RAZAS PATOLOGIAS VITAMINAS Residuals
## Sum of Squares 8.5 44.5 757.5 49.5
## Deg. of Freedom 3 3 3 6
##
## Residual standard error: 2.872281
## Estimated effects may be unbalanced%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(d) Anova
summary(g2)## Df Sum Sq Mean Sq F value Pr(>F)
## RAZAS 3 8.5 2.83 0.343 0.795455
## PATOLOGIAS 3 44.5 14.83 1.798 0.247633
## VITAMINAS 3 757.5 252.50 30.606 0.000493 ***
## Residuals 6 49.5 8.25
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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4.5 Pruebas de Medias por comparaciones Múltiples
(a) HSD Tukey
TukeyHSD(g2)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = f ~ RAZAS + PATOLOGIAS + VITAMINAS, data = DCL)
##
## $RAZAS
## diff lwr upr p adj
## R2-R1 1.25 -5.780769 8.280769 0.9234780
## R3-R1 2.00 -5.030769 9.030769 0.7632815
## R4-R1 0.75 -6.280769 7.780769 0.9812251
## R3-R2 0.75 -6.280769 7.780769 0.9812251
## R4-R2 -0.50 -7.530769 6.530769 0.9942013
## R4-R3 -1.25 -8.280769 5.780769 0.9234780
##
## $PATOLOGIAS
## diff lwr upr p adj
## P2-P1 -4.500000e+00 -11.530769 2.530769 0.221112
## P3-P1 -1.250000e+00 -8.280769 5.780769 0.923478
## P4-P1 -1.250000e+00 -8.280769 5.780769 0.923478
## P3-P2 3.250000e+00 -3.780769 10.280769 0.443965
## P4-P2 3.250000e+00 -3.780769 10.280769 0.443965
## P4-P3 1.776357e-15 -7.030769 7.030769 1.000000
##
## $VITAMINAS
## diff lwr upr p adj
## B-A 9.25 2.2192309 16.2807691 0.0151908
## C-A 17.25 10.2192309 24.2807691 0.0006054
## D-A 1.50 -5.5307691 8.5307691 0.8783266
## C-B 8.00 0.9692309 15.0307691 0.0291977
## D-B -7.75 -14.7807691 -0.7192309 0.0334590
## D-C -15.75 -22.7807691 -8.7192309 0.0009991%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) HSD Tukey
plot(TukeyHSD(g2))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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4.6 Supuestos del Modelo en RStudio
(a) Supuestos del Modelo
Los cuatro gráficos usados para verificar las suposiciones del modelo lineal se pueden hacer fácilmente usando R. El siguiente código produce estos gráficos.
par( mfrow = c(2,2) )
plot(g2, which=5)
plot(g2, which=1)
plot(g2, which=2)
plot(residuals(g2) ~ f, main="Residuals vs corridas", font.main=1, DCL)
abline(h = 0, lty = 2)
par(mfrow=c(2,2)) divide la región en cuatro subregiones.
plot(g2, which=5) produce un gráfico de los residuos estandarizados vs niveles de los factores
plot(g2, which=1) produce la gráfica de residuos vs valores predichos
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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4.7 Supuestos del Modelo en RStudio: Homocedasticidad
(j) DCL Homogeneidad de la Varianza Prueba de Levene
summary(lm( abs(g$res) ~DCL$PATOLOGIAS))##
## Call:
## lm(formula = abs(g$res) ~ DCL$PATOLOGIAS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.2500 -0.6562 0.0000 0.5312 1.7500
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.2500 0.4649 4.840 0.000405 ***
## DCL$PATOLOGIASP2 -0.5000 0.6575 -0.760 0.461656
## DCL$PATOLOGIASP3 -1.6250 0.6575 -2.472 0.029411 *
## DCL$PATOLOGIASP4 -1.1250 0.6575 -1.711 0.112772
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9298 on 12 degrees of freedom
## Multiple R-squared: 0.3688, Adjusted R-squared: 0.211
## F-statistic: 2.337 on 3 and 12 DF, p-value: 0.1252%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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4.8. Evaluación 4. DCL
https://forms.gle/Nr16va6hK9q5UAGx9
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5.0 Tema 5: Diseños en Cuadrados Greco Latino - DCGL: Generalidades
5.1 Video 5: Diseños en Cuadrados Greco Latino - DCGL: Generalidades
embed_youtube("H9MfiJVrDK0")5.2 Ejemplo 4. (Texto Analisis y Diseno de Experimentos_Humberto-Roman_2da Ed_McGrawHill, pág. 63)
Ejemplo 5.2. Un investigador está interesado en el efecto del porcentaje de lisina y del porcentaje de proteína en la producción de vacas lecheras. Se consideran siete niveles en cada factor.
% de lisina: 0.0 (A), 0.1 (B), 0.2 (C), 0.3 (D), 0.4 (E), 0.5 (F ), 0.6 (G).
% de proteína: 2 (\(\alpha\)), 4(\(\beta\)), 6( \(\chi\)), 8(\(\delta\)), 10(\(\epsilon\)), 12(\(\phi\)), 14(\(\gamma\)).
Para el estudio, se seleccionan siete vacas al azar, a las cuales se les da un seguimiento de siete periodos de tres meses. Los datos en galones de leche fueron los siguientes:
| Cows Period | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| 1 | 304 | 436 | 350 | 504 | 417 | 519 | 432 |
| (A\(\alpha\)) | (B\(\epsilon\)) | (C\(\beta\)) | (D\(\phi\)) | (E\(\chi\)) | (F\(\gamma\)) | (G\(\delta\)) | |
| 2 | 381 | 505 | 425 | 564 | 494 | 350 | 413 |
| (B\(\beta\)) | (C\(\phi\)) | (D\(\chi\)) | (E\(\gamma\)) | (F\(\delta\)) | (G\(\alpha\)) | (A\(\epsilon\)) | |
| 3 | 432 | 566 | 479 | 357 | 461 | 340 | 502 |
| (C\(\chi\)) | (D\(\gamma\)) | (E\(\delta\)) | (F\(\alpha\)) | (G\(\epsilon\)) | (A\(\beta\)) | (B\(\phi\)) | |
| 4 | 442 | 372 | 536 | 366 | 495 | 425 | 507 |
| (D\(\delta\)) | (E\(\alpha\)) | (F\(\epsilon\)) | (G\(\beta\)) | (A\(\phi\)) | (B\(\chi\)) | (C\(\gamma\)) | |
| 5 | 496 | 449 | 493 | 345 | 509 | 481 | 380 |
| (E\(\epsilon\)) | (F\(\beta\)) | (G\(\phi\)) | (A\(\chi\)) | (B\(\gamma\)) | (C\(\delta\)) | (D\(\alpha\)) | |
| 6 | 534 | 421 | 452 | 427 | 346 | 478 | 397 |
| (F\(\phi\)) | (G\(\chi\)) | (A\(\gamma\)) | (B\(\delta\)) | (C\(\alpha\)) | (D\(\epsilon\)) | (E\(\beta\)) | |
| 7 | 543 | 386 | 435 | 485 | 406 | 554 | 410 |
| (G\(\gamma\)) | (A\(\delta\)) | (B\(\alpha\)) | (C\(\epsilon\)) | (D\(\beta\)) | (E\(\phi\)) | (F\(\chi\)) |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ## 5.3 Ingresando los datos en RStudio
(a) Primero creamos los vectores teniendo en cuenta que los factores se deben crear como factor.
Lisina = factor(c("A","B","C","D","E","F","G",
"B","C","D","E","F","G","A",
"C","D","E","F","G","A","B",
"D","E","F","G","A","B","C",
"E","F","G","A","B","C","D",
"F","G","A","B","C","D", "E",
"G","A","B","C","D", "E","F"))
Producción =c(304, 381, 432, 442, 496, 534, 543,
436, 505, 566, 372, 449, 421, 386,
350, 425, 479, 536, 493, 452, 435,
504, 564, 357, 366, 345, 427, 485,
417, 494, 461, 495, 509, 346, 406,
519, 350, 340, 425, 481, 478, 554,
432, 413, 502, 507, 380, 397, 410)
Vaca =factor( c(rep("1",1),
rep("2",1),
rep("3",1),
rep("4",1),
rep("5",1),
rep("6",1),
rep("7",1)))
Periodo = factor(c(rep("1",7),
rep("2",7),
rep("3",7),
rep("4",7),
rep("5",7),
rep("6",7),
rep("7",7)))
Proteína =factor(c("a","b","c","d","e", "f", "g",
"e","f","g","a","b", "c", "d",
"b","c","d","e","f", "g", "a",
"f", "g", "a","b","c","d","e",
"c","d","e", "f", "g","a","b",
"g","a","b","c","d","e", "f",
"d","e", "f", "g","a","b","c")) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) Se obtiene ahora la nueva tabla de datos del modelo
dataGreco = data.frame(Vaca,Periodo, Lisina, Proteína, Producción)
dataGreco%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5.4 Analizando los datos en RStudio
(a) Para el próximo paso debemos descargar los siguientes paquetes (gridExtra) y (ggplot2)
library(gridExtra)
library(ggplot2)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) Diagramas de caja: Los siguientes son gráficos descriptivos de los factores con la variable respuesta
Lisina2 <- ggplot(dataGreco, aes(x = Lisina, y = Producción, fill=Lisina)) +
geom_boxplot() + theme(legend.position = "none")
Proteína2 <- ggplot(dataGreco, aes(x = Proteína, y = Producción, fill=Proteína)) +
geom_boxplot() + theme(legend.position = "none")
Vaca2 <- ggplot(dataGreco, aes(x = Vaca, y = Producción, fill=Vaca)) +
geom_boxplot() + theme(legend.position = "none")
Periodo2 <- ggplot(dataGreco, aes(x = Periodo, y = Producción, fill=Periodo)) +
geom_boxplot() + theme(legend.position = "none")
grid.arrange(Lisina2,Proteína2,Vaca2,Periodo2, nrow=2,ncol=2)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(c) El Modelo linal y tabla ANOVA
modeloGreco= lm(Producción ~ Lisina + Vaca + Periodo + Proteína, dataGreco)
anovaGreco=aov(modeloGreco)
anovaGreco## Call:
## aov(formula = modeloGreco)
##
## Terms:
## Lisina Vaca Periodo Proteína Residuals
## Sum of Squares 30718.24 5831.96 2124.24 160242.82 15544.41
## Deg. of Freedom 6 6 6 6 24
##
## Residual standard error: 25.44963
## Estimated effects may be unbalancedsummary(anovaGreco)## Df Sum Sq Mean Sq F value Pr(>F)
## Lisina 6 30718 5120 7.905 8.98e-05 ***
## Vaca 6 5832 972 1.501 0.220
## Periodo 6 2124 354 0.547 0.768
## Proteína 6 160243 26707 41.235 1.75e-11 ***
## Residuals 24 15544 648
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(d) Comparaciones múltiples: HSD de Tukey
TukeyHSD(anovaGreco)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = modeloGreco)
##
## $Lisina
## diff lwr upr p adj
## B-A 54.285714 10.602565 97.96886 0.0084334
## C-A 53.000000 9.316850 96.68315 0.0105520
## D-A 66.571429 22.888279 110.25458 0.0009375
## E-A 77.714286 34.031136 121.39744 0.0001255
## F-A 80.571429 36.888279 124.25458 0.0000753
## G-A 47.285714 3.602565 90.96886 0.0278698
## C-B -1.285714 -44.968864 42.39744 0.9999999
## D-B 12.285714 -31.397435 55.96886 0.9685039
## E-B 23.428571 -20.254578 67.11172 0.6087189
## F-B 26.285714 -17.397435 69.96886 0.4798768
## G-B -7.000000 -50.683150 36.68315 0.9983751
## D-C 13.571429 -30.111721 57.25458 0.9496240
## E-C 24.714286 -18.968864 68.39744 0.5501792
## F-C 27.571429 -16.111721 71.25458 0.4246848
## G-C -5.714286 -49.397435 37.96886 0.9994849
## E-D 11.142857 -32.540293 54.82601 0.9805282
## F-D 14.000000 -29.683150 57.68315 0.9419417
## G-D -19.285714 -62.968864 24.39744 0.7872452
## F-E 2.857143 -40.826007 46.54029 0.9999911
## G-E -30.428571 -74.111721 13.25458 0.3137926
## G-F -33.285714 -76.968864 10.39744 0.2230055
##
## $Vaca
## diff lwr upr p adj
## 2-1 24.2857143 -19.397435 67.96886 0.5696607
## 3-1 25.0000000 -18.683150 68.68315 0.5372409
## 4-1 25.8571429 -17.826007 69.54029 0.4988057
## 5-1 27.2857143 -16.397435 70.96886 0.4367144
## 6-1 13.2857143 -30.397435 56.96886 0.9543493
## 7-1 36.7142857 -6.968864 80.39744 0.1415911
## 3-2 0.7142857 -42.968864 44.39744 1.0000000
## 4-2 1.5714286 -42.111721 45.25458 0.9999997
## 5-2 3.0000000 -40.683150 46.68315 0.9999881
## 6-2 -11.0000000 -54.683150 32.68315 0.9817515
## 7-2 12.4285714 -31.254578 56.11172 0.9667006
## 4-3 0.8571429 -42.826007 44.54029 1.0000000
## 5-3 2.2857143 -41.397435 45.96886 0.9999976
## 6-3 -11.7142857 -55.397435 31.96886 0.9750321
## 7-3 11.7142857 -31.968864 55.39744 0.9750321
## 5-4 1.4285714 -42.254578 45.11172 0.9999999
## 6-4 -12.5714286 -56.254578 31.11172 0.9648262
## 7-4 10.8571429 -32.826007 54.54029 0.9829176
## 6-5 -14.0000000 -57.683150 29.68315 0.9419417
## 7-5 9.4285714 -34.254578 53.11172 0.9917682
## 7-6 23.4285714 -20.254578 67.11172 0.6087189
##
## $Periodo
## diff lwr upr p adj
## 2-1 0.4285714 -43.25458 44.11172 1.0000000
## 3-1 5.4285714 -38.25458 49.11172 0.9996162
## 4-1 -12.0000000 -55.68315 31.68315 0.9719025
## 5-1 -0.5714286 -44.25458 43.11172 1.0000000
## 6-1 2.1428571 -41.54029 45.82601 0.9999984
## 7-1 -13.0000000 -56.68315 30.68315 0.9587653
## 3-2 5.0000000 -38.68315 48.68315 0.9997612
## 4-2 -12.4285714 -56.11172 31.25458 0.9667006
## 5-2 -1.0000000 -44.68315 42.68315 1.0000000
## 6-2 1.7142857 -41.96886 45.39744 0.9999996
## 7-2 -13.4285714 -57.11172 30.25458 0.9520258
## 4-3 -17.4285714 -61.11172 26.25458 0.8537421
## 5-3 -6.0000000 -49.68315 37.68315 0.9993194
## 6-3 -3.2857143 -46.96886 40.39744 0.9999796
## 7-3 -18.4285714 -62.11172 25.25458 0.8193780
## 5-4 11.4285714 -32.25458 55.11172 0.9779036
## 6-4 14.1428571 -29.54029 57.82601 0.9392195
## 7-4 -1.0000000 -44.68315 42.68315 1.0000000
## 6-5 2.7142857 -40.96886 46.39744 0.9999934
## 7-5 -12.4285714 -56.11172 31.25458 0.9667006
## 7-6 -15.1428571 -58.82601 28.54029 0.9178534
##
## $Proteína
## diff lwr upr p adj
## b-a 20.71429 -22.968864 64.39744 0.7291166
## c-a 47.28571 3.602565 90.96886 0.0278698
## d-a 85.28571 41.602565 128.96886 0.0000326
## e-a 108.71429 65.031136 152.39744 0.0000006
## f-a 149.00000 105.316850 192.68315 0.0000000
## g-a 159.42857 115.745422 203.11172 0.0000000
## c-b 26.57143 -17.111721 70.25458 0.4673904
## d-b 64.57143 20.888279 108.25458 0.0013458
## e-b 88.00000 44.316850 131.68315 0.0000203
## f-b 128.28571 84.602565 171.96886 0.0000000
## g-b 138.71429 95.031136 182.39744 0.0000000
## d-c 38.00000 -5.683150 81.68315 0.1181175
## e-c 61.42857 17.745422 105.11172 0.0023709
## f-c 101.71429 58.031136 145.39744 0.0000020
## g-c 112.14286 68.459707 155.82601 0.0000004
## e-d 23.42857 -20.254578 67.11172 0.6087189
## f-d 63.71429 20.031136 107.39744 0.0015710
## g-d 74.14286 30.459707 117.82601 0.0002385
## f-e 40.28571 -3.397435 83.96886 0.0844845
## g-e 50.71429 7.031136 94.39744 0.0156454
## g-f 10.42857 -33.254578 54.11172 0.9860875%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(e) Comparaciones múltiples: gráfico HSD de Tukey
plot(TukeyHSD(anovaGreco))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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5.5. Pruebas de Medias por comparaciones Múltiples
(a) (Prueba LSD). Instale el paquete “agricolae
library(agricolae)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) Prueba LSD para Lisina
LSD.test(anovaGreco,"Lisina",console=TRUE)##
## Study: anovaGreco ~ "Lisina"
##
## LSD t Test for Producción
##
## Mean Square Error: 647.6837
##
## Lisina, means and individual ( 95 %) CI
##
## Producción std r LCL UCL Min Max
## A 390.7143 67.49250 7 370.8615 410.5670 304 495
## B 445.0000 45.36151 7 425.1472 464.8528 381 509
## C 443.7143 69.90878 7 423.8615 463.5670 346 507
## D 457.2857 63.65196 7 437.4330 477.1385 380 566
## E 468.4286 75.68984 7 448.5758 488.2813 372 564
## F 471.2857 68.58988 7 451.4330 491.1385 357 536
## G 438.0000 68.10776 7 418.1472 457.8528 350 543
##
## Alpha: 0.05 ; DF Error: 24
## Critical Value of t: 2.063899
##
## least Significant Difference: 28.07604
##
## Treatments with the same letter are not significantly different.
##
## Producción groups
## F 471.2857 a
## E 468.4286 a
## D 457.2857 ab
## B 445.0000 ab
## C 443.7143 ab
## G 438.0000 b
## A 390.7143 c%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(c) Prueba LSD para Proteína
LSD.test(anovaGreco,"Proteína",console=TRUE)##
## Study: anovaGreco ~ "Proteína"
##
## LSD t Test for Producción
##
## Mean Square Error: 647.6837
##
## Proteína, means and individual ( 95 %) CI
##
## Producción std r LCL UCL Min Max
## a 363.4286 39.84912 7 343.5758 383.2813 304 435
## b 384.1429 37.19959 7 364.2901 403.9956 340 449
## c 410.7143 29.79214 7 390.8615 430.5670 345 432
## d 448.7143 38.16506 7 428.8615 468.5670 386 494
## e 472.1429 40.36264 7 452.2901 491.9956 413 536
## f 512.4286 22.76589 7 492.5758 532.2813 493 554
## g 522.8571 39.66286 7 503.0044 542.7099 452 566
##
## Alpha: 0.05 ; DF Error: 24
## Critical Value of t: 2.063899
##
## least Significant Difference: 28.07604
##
## Treatments with the same letter are not significantly different.
##
## Producción groups
## g 522.8571 a
## f 512.4286 a
## e 472.1429 b
## d 448.7143 b
## c 410.7143 c
## b 384.1429 cd
## a 363.4286 d%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(d) Prueba LSD para vaca
LSD.test(anovaGreco,"Vaca",console=TRUE)##
## Study: anovaGreco ~ "Vaca"
##
## LSD t Test for Producción
##
## Mean Square Error: 647.6837
##
## Vaca, means and individual ( 95 %) CI
##
## Producción std r LCL UCL Min Max
## 1 423.1429 76.97711 7 403.2901 442.9956 304 519
## 2 447.4286 76.01065 7 427.5758 467.2813 350 564
## 3 448.1429 79.76095 7 428.2901 467.9956 340 566
## 4 449.0000 66.44797 7 429.1472 468.8528 366 536
## 5 450.4286 63.68113 7 430.5758 470.2813 345 509
## 6 436.4286 59.93012 7 416.5758 456.2813 346 534
## 7 459.8571 68.15039 7 440.0044 479.7099 386 554
##
## Alpha: 0.05 ; DF Error: 24
## Critical Value of t: 2.063899
##
## least Significant Difference: 28.07604
##
## Treatments with the same letter are not significantly different.
##
## Producción groups
## 7 459.8571 a
## 5 450.4286 ab
## 4 449.0000 ab
## 3 448.1429 ab
## 2 447.4286 ab
## 6 436.4286 ab
## 1 423.1429 b%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(e) Prueba LSD para Periodo
LSD.test(anovaGreco,"Periodo",console=TRUE)##
## Study: anovaGreco ~ "Periodo"
##
## LSD t Test for Producción
##
## Mean Square Error: 647.6837
##
## Periodo, means and individual ( 95 %) CI
##
## Producción std r LCL UCL Min Max
## 1 447.4286 85.86784 7 427.5758 467.2813 304 543
## 2 447.8571 67.90540 7 428.0044 467.7099 372 566
## 3 452.8571 58.99556 7 433.0044 472.7099 350 536
## 4 435.4286 84.56725 7 415.5758 455.2813 345 564
## 5 446.8571 59.63061 7 427.0044 466.7099 346 509
## 6 449.5714 81.69630 7 429.7187 469.4242 340 554
## 7 434.4286 50.42769 7 414.5758 454.2813 380 507
##
## Alpha: 0.05 ; DF Error: 24
## Critical Value of t: 2.063899
##
## least Significant Difference: 28.07604
##
## Treatments with the same letter are not significantly different.
##
## Producción groups
## 3 452.8571 a
## 6 449.5714 a
## 2 447.8571 a
## 1 447.4286 a
## 5 446.8571 a
## 4 435.4286 a
## 7 434.4286 a%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(f) Prueba de Tukey: Lisina
HSD.test(anovaGreco, "Lisina",console=TRUE)##
## Study: anovaGreco ~ "Lisina"
##
## HSD Test for Producción
##
## Mean Square Error: 647.6837
##
## Lisina, means
##
## Producción std r Min Max
## A 390.7143 67.49250 7 304 495
## B 445.0000 45.36151 7 381 509
## C 443.7143 69.90878 7 346 507
## D 457.2857 63.65196 7 380 566
## E 468.4286 75.68984 7 372 564
## F 471.2857 68.58988 7 357 536
## G 438.0000 68.10776 7 350 543
##
## Alpha: 0.05 ; DF Error: 24
## Critical Value of Studentized Range: 4.541314
##
## Minimun Significant Difference: 43.68315
##
## Treatments with the same letter are not significantly different.
##
## Producción groups
## F 471.2857 a
## E 468.4286 a
## D 457.2857 a
## B 445.0000 a
## C 443.7143 a
## G 438.0000 a
## A 390.7143 b%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(g) Prueba de Tukey: Proteína
HSD.test(anovaGreco, "Proteína",console=TRUE)##
## Study: anovaGreco ~ "Proteína"
##
## HSD Test for Producción
##
## Mean Square Error: 647.6837
##
## Proteína, means
##
## Producción std r Min Max
## a 363.4286 39.84912 7 304 435
## b 384.1429 37.19959 7 340 449
## c 410.7143 29.79214 7 345 432
## d 448.7143 38.16506 7 386 494
## e 472.1429 40.36264 7 413 536
## f 512.4286 22.76589 7 493 554
## g 522.8571 39.66286 7 452 566
##
## Alpha: 0.05 ; DF Error: 24
## Critical Value of Studentized Range: 4.541314
##
## Minimun Significant Difference: 43.68315
##
## Treatments with the same letter are not significantly different.
##
## Producción groups
## g 522.8571 a
## f 512.4286 ab
## e 472.1429 bc
## d 448.7143 cd
## c 410.7143 de
## b 384.1429 ef
## a 363.4286 f%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(h) Prueba de Student-Newman-Keuls (SNK)
SNK.test(anovaGreco, "Lisina",console=TRUE)##
## Study: anovaGreco ~ "Lisina"
##
## Student Newman Keuls Test
## for Producción
##
## Mean Square Error: 647.6837
##
## Lisina, means
##
## Producción std r Min Max
## A 390.7143 67.49250 7 304 495
## B 445.0000 45.36151 7 381 509
## C 443.7143 69.90878 7 346 507
## D 457.2857 63.65196 7 380 566
## E 468.4286 75.68984 7 372 564
## F 471.2857 68.58988 7 357 536
## G 438.0000 68.10776 7 350 543
##
## Alpha: 0.05 ; DF Error: 24
##
## Critical Range
## 2 3 4 5 6 7
## 28.07603 33.97159 37.52646 40.07601 42.06077 43.68315
##
## Means with the same letter are not significantly different.
##
## Producción groups
## F 471.2857 a
## E 468.4286 a
## D 457.2857 a
## B 445.0000 a
## C 443.7143 a
## G 438.0000 a
## A 390.7143 b%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(i) Prueba de Scheffé
scheffe.test(anovaGreco, "Lisina",console=TRUE)##
## Study: anovaGreco ~ "Lisina"
##
## Scheffe Test for Producción
##
## Mean Square Error : 647.6837
##
## Lisina, means
##
## Producción std r Min Max
## A 390.7143 67.49250 7 304 495
## B 445.0000 45.36151 7 381 509
## C 443.7143 69.90878 7 346 507
## D 457.2857 63.65196 7 380 566
## E 468.4286 75.68984 7 372 564
## F 471.2857 68.58988 7 357 536
## G 438.0000 68.10776 7 350 543
##
## Alpha: 0.05 ; DF Error: 24
## Critical Value of F: 2.508189
##
## Minimum Significant Difference: 52.77196
##
## Means with the same letter are not significantly different.
##
## Producción groups
## F 471.2857 a
## E 468.4286 a
## D 457.2857 a
## B 445.0000 a
## C 443.7143 a
## G 438.0000 ab
## A 390.7143 b%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(j) Prueba de Duncan
duncan.test(anovaGreco, "Lisina",console=TRUE)##
## Study: anovaGreco ~ "Lisina"
##
## Duncan's new multiple range test
## for Producción
##
## Mean Square Error: 647.6837
##
## Lisina, means
##
## Producción std r Min Max
## A 390.7143 67.49250 7 304 495
## B 445.0000 45.36151 7 381 509
## C 443.7143 69.90878 7 346 507
## D 457.2857 63.65196 7 380 566
## E 468.4286 75.68984 7 372 564
## F 471.2857 68.58988 7 357 536
## G 438.0000 68.10776 7 350 543
##
## Alpha: 0.05 ; DF Error: 24
##
## Critical Range
## 2 3 4 5 6 7
## 28.07603 29.48828 30.39500 31.03545 31.51352 31.88335
##
## Means with the same letter are not significantly different.
##
## Producción groups
## F 471.2857 a
## E 468.4286 ab
## D 457.2857 ab
## B 445.0000 ab
## C 443.7143 ab
## G 438.0000 b
## A 390.7143 c%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(k) Prueba de Bonferroni
LSD.test(anovaGreco, "Lisina", p.adj= "bon",console=TRUE)##
## Study: anovaGreco ~ "Lisina"
##
## LSD t Test for Producción
## P value adjustment method: bonferroni
##
## Mean Square Error: 647.6837
##
## Lisina, means and individual ( 95 %) CI
##
## Producción std r LCL UCL Min Max
## A 390.7143 67.49250 7 370.8615 410.5670 304 495
## B 445.0000 45.36151 7 425.1472 464.8528 381 509
## C 443.7143 69.90878 7 423.8615 463.5670 346 507
## D 457.2857 63.65196 7 437.4330 477.1385 380 566
## E 468.4286 75.68984 7 448.5758 488.2813 372 564
## F 471.2857 68.58988 7 451.4330 491.1385 357 536
## G 438.0000 68.10776 7 418.1472 457.8528 350 543
##
## Alpha: 0.05 ; DF Error: 24
## Critical Value of t: 3.395988
##
## Minimum Significant Difference: 46.19699
##
## Treatments with the same letter are not significantly different.
##
## Producción groups
## F 471.2857 a
## E 468.4286 a
## D 457.2857 a
## B 445.0000 a
## C 443.7143 a
## G 438.0000 a
## A 390.7143 b%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5.6 Supuestos del Modelo en RStudio: Normalidad
(a) Normalidad de los residuos
shapiro.test(anovaGreco$res)##
## Shapiro-Wilk normality test
##
## data: anovaGreco$res
## W = 0.97204, p-value = 0.2915%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) Supuesto del modelo:Normalidad de los residuos
summary(anovaGreco$residuals)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -31.531 -11.673 -3.245 0.000 10.469 48.612sd((anovaGreco$residuals))## [1] 17.99561%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(c) Supuesto del modelo:Normalidad de los residuos
boxplot(anovaGreco$residuals,col="lightblue") 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(d) Supuesto del modelo:Normalidad de los residuos
hist(anovaGreco$residuals, col="lightgreen", main = "Histograma de los Residuos",
freq = F, xlab="Residuos",ylab="Densidad")
lines(density(anovaGreco$residuals), col="red", lwd=3)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(e) ** Prueba de Normalidad con Q-Q Plot**
qqnorm(anovaGreco$residuals,col="blue", lwd=3)
qqline(anovaGreco$residuals,col="red", lwd=3)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5.7. Supuestos del Modelo en RStudio: Supuesto de Independencia
(y) Supuesto de Independencia
plot(anovaGreco$residuals,main = "Residuos vs Observaciones",col="red", lwd=3) 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5.8. Supuestos del Modelo en RStudio: Supuesto de Homocedasticidad
(a) Homocedasticidad
boxplot(anovaGreco$residuals~Lisina, xlab="Lisina",ylab="Residuos",
col = c("yellow", "blue", "white","green", "red")) # Homocedasticidad
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) Homocedasticidad
boxplot(anovaGreco$residuals~Proteína, xlab="Proteína",ylab="Residuos",
col = c("yellow", "blue", "white","green", "red")) # Homocedasticidad
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(c) Homocedasticidad
boxplot(anovaGreco$residuals~Periodo, xlab="Periodo",ylab="Residuos",
col = c("yellow", "blue", "white","green", "red")) # Homocedasticidad
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(d) Homocedasticidad: Gráfico de predichos contra residuos estandarizados
pred=fitted(anovaGreco)
resid=rstandard(anovaGreco)
plot(pred,resid,xlab="Valores predichos", ylab="Residuos estandarizados",abline(h=0),col="red", lwd=3)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(e) Homocedasticidad: Prueba de Bartlett para Lisina
bartlett.test(anovaGreco$residuals ~ Lisina)##
## Bartlett test of homogeneity of variances
##
## data: anovaGreco$residuals by Lisina
## Bartlett's K-squared = 2.6611, df = 6, p-value = 0.85%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(f) Homocedasticidad: Prueba de Bartlett para Proteína
bartlett.test(anovaGreco$residuals ~ Proteína)##
## Bartlett test of homogeneity of variances
##
## data: anovaGreco$residuals by Proteína
## Bartlett's K-squared = 2.8279, df = 6, p-value = 0.8301%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(g) Homocedasticidad: Prueba de Bartlett para Proteína
bartlett.test(anovaGreco$residuals ~ Periodo)##
## Bartlett test of homogeneity of variances
##
## data: anovaGreco$residuals by Periodo
## Bartlett's K-squared = 5.1728, df = 6, p-value = 0.5218%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5.9. Evaluación 5. DCGL
https://forms.gle/ierbMiggJX3P7Ze29
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6.0 Tema 6: Diseño en Bloques Incompletos Balanceados - DBIB
6.1 Ejemplo 6. (Texto Analisis y Diseno de Experimentos_Humberto-Roman_2da Ed_McGrawHill, pág. 63)
Supongase que un ingeniero químico cree que el tiempo de reacción en un proceso químico es función del catalizador empleado. De hecho 4 catalizadores estan siendo investigados. El procedimiento experimental consiste en seleccionar un lote de materia prima, cargar una planta piloto, aplicar cada catalizador a ensayos separados de dicha planta y observar el tiempo de reacción. Debido a que las variaciones en los lotes de materia prima pueden afectar el comportamiento del catalizador, el ingeniero decide controlar este factor por medio de bloques. Sin embargo, cada lote es lo suficientemente grande para permitir el ensayo de 3 catalizadores únicamente. Por lo tanto, es necesario utilizar un diseño aleatoriazado por bloques incompletos. El diseño BIBD, junto con las observaciones recopiladas aparecen en la siguiente tabla:
| BLOQUE | 1 | 2 | 3 | 4 | ||
|---|---|---|---|---|---|---|
| A | 73 | 74 | – | 71 | ||
| CATALIZADOR | B | – | 75 | 67 | 72 | |
| C | 73 | 75 | 68 | – | ||
| D | 75 | – | 72 | 75 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ## 6.2 Ingresando los datos en RStudio
(a) Primero creamos los vectores teniendo en cuenta que los factores se deben crear como factor.
set.seed(7638)
CATALIZADOR <- factor( rep( c("A", "A", "A","B","B","B","C","C","C","D" ,"D","D"), each = 1))
BLOQUE <- factor( rep( c("1", "2", "4", "2", "3", "4","1", "2", "3", "1", "3", "4"), each = 1))
f = PRODUCCION <- c(73, 74, 71, 75, 67, 72, 73, 75, 68, 75, 72, 75)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) Se obtiene ahora la nueva tabla de datos del modelo
DBIB <- data.frame( BLOQUE, CATALIZADOR, f)
DBIB%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
6.3 Analizando los datos en RStudio
(a) Para el próximo paso debemos descargar los siguientes paquetes (gridExtra) y (ggplot2)
library(gridExtra)
library(ggplot2)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) Diagramas de caja: Los siguientes son gráficos descriptivos de los factores con la variable respuesta
CATALIZADOR2 <- ggplot(DBIB, aes(x = CATALIZADOR, y = f, fill=CATALIZADOR)) +
geom_boxplot() + theme(legend.position = "none")
BLOQUE2 <- ggplot(DBIB, aes(x = BLOQUE, y = f, fill=BLOQUE)) +
geom_boxplot() + theme(legend.position = "none")
grid.arrange(CATALIZADOR2,BLOQUE2, nrow=1,ncol=2)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(c) El Modelo linal y tabla ANOVA
modeloDBIB= lm(f ~ BLOQUE+CATALIZADOR, DBIB)
anovaDBIB=aov(modeloDBIB)
anovaDBIB## Call:
## aov(formula = modeloDBIB)
##
## Terms:
## BLOQUE CATALIZADOR Residuals
## Sum of Squares 55.00 22.75 3.25
## Deg. of Freedom 3 3 5
##
## Residual standard error: 0.8062258
## Estimated effects may be unbalancedsummary(anovaDBIB)## Df Sum Sq Mean Sq F value Pr(>F)
## BLOQUE 3 55.00 18.333 28.20 0.00147 **
## CATALIZADOR 3 22.75 7.583 11.67 0.01074 *
## Residuals 5 3.25 0.650
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(d) Comparaciones múltiples: HSD de Tukey
TukeyHSD(anovaDBIB)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = modeloDBIB)
##
## $BLOQUE
## diff lwr upr p adj
## 2-1 1.000000 -1.428998 3.428998 0.4917130
## 3-1 -4.666667 -7.095665 -2.237669 0.0032954
## 4-1 -1.000000 -3.428998 1.428998 0.4917130
## 3-2 -5.666667 -8.095665 -3.237669 0.0013433
## 4-2 -2.000000 -4.428998 0.428998 0.0975482
## 4-3 3.666667 1.237669 6.095665 0.0096068
##
## $CATALIZADOR
## diff lwr upr p adj
## B-A 0.2222222 -2.2067758 2.651220 0.9852477
## C-A 0.5555556 -1.8734425 2.984554 0.8323947
## D-A 3.2222222 0.7932242 5.651220 0.0165827
## C-B 0.3333333 -2.0956647 2.762331 0.9540767
## D-B 3.0000000 0.5710020 5.428998 0.0222012
## D-C 2.6666667 0.2376686 5.095665 0.0352698%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(e) Comparaciones múltiples: gráfico HSD de Tukey
plot(TukeyHSD(anovaDBIB))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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6.4 Pruebas de Medias por comparaciones Múltiples
(a) (Prueba LSD). Instale el paquete “agricolae
library(agricolae)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) Prueba LSD para CATALIZADOR
LSD.test(anovaDBIB,"CATALIZADOR",console=TRUE)##
## Study: anovaDBIB ~ "CATALIZADOR"
##
## LSD t Test for f
##
## Mean Square Error: 0.65
##
## CATALIZADOR, means and individual ( 95 %) CI
##
## f std r LCL UCL Min Max
## A 72.66667 1.527525 3 71.47013 73.86321 71 74
## B 71.33333 4.041452 3 70.13679 72.52987 67 75
## C 72.00000 3.605551 3 70.80346 73.19654 68 75
## D 74.00000 1.732051 3 72.80346 75.19654 72 75
##
## Alpha: 0.05 ; DF Error: 5
## Critical Value of t: 2.570582
##
## least Significant Difference: 1.692164
##
## Treatments with the same letter are not significantly different.
##
## f groups
## D 74.00000 a
## A 72.66667 ab
## C 72.00000 b
## B 71.33333 bplot(LSD.test(anovaDBIB,"CATALIZADOR",console=TRUE))##
## Study: anovaDBIB ~ "CATALIZADOR"
##
## LSD t Test for f
##
## Mean Square Error: 0.65
##
## CATALIZADOR, means and individual ( 95 %) CI
##
## f std r LCL UCL Min Max
## A 72.66667 1.527525 3 71.47013 73.86321 71 74
## B 71.33333 4.041452 3 70.13679 72.52987 67 75
## C 72.00000 3.605551 3 70.80346 73.19654 68 75
## D 74.00000 1.732051 3 72.80346 75.19654 72 75
##
## Alpha: 0.05 ; DF Error: 5
## Critical Value of t: 2.570582
##
## least Significant Difference: 1.692164
##
## Treatments with the same letter are not significantly different.
##
## f groups
## D 74.00000 a
## A 72.66667 ab
## C 72.00000 b
## B 71.33333 b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(c) Prueba LSD para Proteína
LSD.test(anovaDBIB,"BLOQUE",console=TRUE)##
## Study: anovaDBIB ~ "BLOQUE"
##
## LSD t Test for f
##
## Mean Square Error: 0.65
##
## BLOQUE, means and individual ( 95 %) CI
##
## f std r LCL UCL Min Max
## 1 73.66667 1.1547005 3 72.47013 74.86321 73 75
## 2 74.66667 0.5773503 3 73.47013 75.86321 74 75
## 3 69.00000 2.6457513 3 67.80346 70.19654 67 72
## 4 72.66667 2.0816660 3 71.47013 73.86321 71 75
##
## Alpha: 0.05 ; DF Error: 5
## Critical Value of t: 2.570582
##
## least Significant Difference: 1.692164
##
## Treatments with the same letter are not significantly different.
##
## f groups
## 2 74.66667 a
## 1 73.66667 ab
## 4 72.66667 b
## 3 69.00000 cplot(LSD.test(anovaDBIB,"BLOQUE",console=TRUE))##
## Study: anovaDBIB ~ "BLOQUE"
##
## LSD t Test for f
##
## Mean Square Error: 0.65
##
## BLOQUE, means and individual ( 95 %) CI
##
## f std r LCL UCL Min Max
## 1 73.66667 1.1547005 3 72.47013 74.86321 73 75
## 2 74.66667 0.5773503 3 73.47013 75.86321 74 75
## 3 69.00000 2.6457513 3 67.80346 70.19654 67 72
## 4 72.66667 2.0816660 3 71.47013 73.86321 71 75
##
## Alpha: 0.05 ; DF Error: 5
## Critical Value of t: 2.570582
##
## least Significant Difference: 1.692164
##
## Treatments with the same letter are not significantly different.
##
## f groups
## 2 74.66667 a
## 1 73.66667 ab
## 4 72.66667 b
## 3 69.00000 c
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(d) Prueba de Tukey: Lisina
HSD.test(anovaDBIB, "CATALIZADOR",console=TRUE)##
## Study: anovaDBIB ~ "CATALIZADOR"
##
## HSD Test for f
##
## Mean Square Error: 0.65
##
## CATALIZADOR, means
##
## f std r Min Max
## A 72.66667 1.527525 3 71 74
## B 71.33333 4.041452 3 67 75
## C 72.00000 3.605551 3 68 75
## D 74.00000 1.732051 3 72 75
##
## Alpha: 0.05 ; DF Error: 5
## Critical Value of Studentized Range: 5.218325
##
## Minimun Significant Difference: 2.428998
##
## Treatments with the same letter are not significantly different.
##
## f groups
## D 74.00000 a
## A 72.66667 ab
## C 72.00000 ab
## B 71.33333 bplot(HSD.test(anovaDBIB, "CATALIZADOR",console=TRUE))##
## Study: anovaDBIB ~ "CATALIZADOR"
##
## HSD Test for f
##
## Mean Square Error: 0.65
##
## CATALIZADOR, means
##
## f std r Min Max
## A 72.66667 1.527525 3 71 74
## B 71.33333 4.041452 3 67 75
## C 72.00000 3.605551 3 68 75
## D 74.00000 1.732051 3 72 75
##
## Alpha: 0.05 ; DF Error: 5
## Critical Value of Studentized Range: 5.218325
##
## Minimun Significant Difference: 2.428998
##
## Treatments with the same letter are not significantly different.
##
## f groups
## D 74.00000 a
## A 72.66667 ab
## C 72.00000 ab
## B 71.33333 b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(e) Prueba de Tukey: Proteína
HSD.test(anovaDBIB, "BLOQUE",console=TRUE)##
## Study: anovaDBIB ~ "BLOQUE"
##
## HSD Test for f
##
## Mean Square Error: 0.65
##
## BLOQUE, means
##
## f std r Min Max
## 1 73.66667 1.1547005 3 73 75
## 2 74.66667 0.5773503 3 74 75
## 3 69.00000 2.6457513 3 67 72
## 4 72.66667 2.0816660 3 71 75
##
## Alpha: 0.05 ; DF Error: 5
## Critical Value of Studentized Range: 5.218325
##
## Minimun Significant Difference: 2.428998
##
## Treatments with the same letter are not significantly different.
##
## f groups
## 2 74.66667 a
## 1 73.66667 a
## 4 72.66667 a
## 3 69.00000 bplot(HSD.test(anovaDBIB, "BLOQUE",console=TRUE))##
## Study: anovaDBIB ~ "BLOQUE"
##
## HSD Test for f
##
## Mean Square Error: 0.65
##
## BLOQUE, means
##
## f std r Min Max
## 1 73.66667 1.1547005 3 73 75
## 2 74.66667 0.5773503 3 74 75
## 3 69.00000 2.6457513 3 67 72
## 4 72.66667 2.0816660 3 71 75
##
## Alpha: 0.05 ; DF Error: 5
## Critical Value of Studentized Range: 5.218325
##
## Minimun Significant Difference: 2.428998
##
## Treatments with the same letter are not significantly different.
##
## f groups
## 2 74.66667 a
## 1 73.66667 a
## 4 72.66667 a
## 3 69.00000 b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(f) Prueba de Student-Newman-Keuls (SNK)
SNK.test(anovaDBIB, "CATALIZADOR",console=TRUE)##
## Study: anovaDBIB ~ "CATALIZADOR"
##
## Student Newman Keuls Test
## for f
##
## Mean Square Error: 0.65
##
## CATALIZADOR, means
##
## f std r Min Max
## A 72.66667 1.527525 3 71 74
## B 71.33333 4.041452 3 67 75
## C 72.00000 3.605551 3 68 75
## D 74.00000 1.732051 3 72 75
##
## Alpha: 0.05 ; DF Error: 5
##
## Critical Range
## 2 3 4
## 1.692164 2.141987 2.428998
##
## Means with the same letter are not significantly different.
##
## f groups
## D 74.00000 a
## A 72.66667 ab
## C 72.00000 ab
## B 71.33333 bplot(SNK.test(anovaDBIB, "CATALIZADOR",console=TRUE))##
## Study: anovaDBIB ~ "CATALIZADOR"
##
## Student Newman Keuls Test
## for f
##
## Mean Square Error: 0.65
##
## CATALIZADOR, means
##
## f std r Min Max
## A 72.66667 1.527525 3 71 74
## B 71.33333 4.041452 3 67 75
## C 72.00000 3.605551 3 68 75
## D 74.00000 1.732051 3 72 75
##
## Alpha: 0.05 ; DF Error: 5
##
## Critical Range
## 2 3 4
## 1.692164 2.141987 2.428998
##
## Means with the same letter are not significantly different.
##
## f groups
## D 74.00000 a
## A 72.66667 ab
## C 72.00000 ab
## B 71.33333 b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(g) Prueba de Student-Newman-Keuls (SNK)
SNK.test(anovaDBIB, "BLOQUE",console=TRUE)##
## Study: anovaDBIB ~ "BLOQUE"
##
## Student Newman Keuls Test
## for f
##
## Mean Square Error: 0.65
##
## BLOQUE, means
##
## f std r Min Max
## 1 73.66667 1.1547005 3 73 75
## 2 74.66667 0.5773503 3 74 75
## 3 69.00000 2.6457513 3 67 72
## 4 72.66667 2.0816660 3 71 75
##
## Alpha: 0.05 ; DF Error: 5
##
## Critical Range
## 2 3 4
## 1.692164 2.141987 2.428998
##
## Means with the same letter are not significantly different.
##
## f groups
## 2 74.66667 a
## 1 73.66667 a
## 4 72.66667 a
## 3 69.00000 bplot(SNK.test(anovaDBIB, "BLOQUE",console=TRUE))##
## Study: anovaDBIB ~ "BLOQUE"
##
## Student Newman Keuls Test
## for f
##
## Mean Square Error: 0.65
##
## BLOQUE, means
##
## f std r Min Max
## 1 73.66667 1.1547005 3 73 75
## 2 74.66667 0.5773503 3 74 75
## 3 69.00000 2.6457513 3 67 72
## 4 72.66667 2.0816660 3 71 75
##
## Alpha: 0.05 ; DF Error: 5
##
## Critical Range
## 2 3 4
## 1.692164 2.141987 2.428998
##
## Means with the same letter are not significantly different.
##
## f groups
## 2 74.66667 a
## 1 73.66667 a
## 4 72.66667 a
## 3 69.00000 b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(h) Prueba de Scheffé
scheffe.test(anovaDBIB, "CATALIZADOR",console=TRUE)##
## Study: anovaDBIB ~ "CATALIZADOR"
##
## Scheffe Test for f
##
## Mean Square Error : 0.65
##
## CATALIZADOR, means
##
## f std r Min Max
## A 72.66667 1.527525 3 71 74
## B 71.33333 4.041452 3 67 75
## C 72.00000 3.605551 3 68 75
## D 74.00000 1.732051 3 72 75
##
## Alpha: 0.05 ; DF Error: 5
## Critical Value of F: 5.409451
##
## Minimum Significant Difference: 2.651846
##
## Means with the same letter are not significantly different.
##
## f groups
## D 74.00000 a
## A 72.66667 ab
## C 72.00000 ab
## B 71.33333 bplot(scheffe.test(anovaDBIB, "CATALIZADOR",console=TRUE))##
## Study: anovaDBIB ~ "CATALIZADOR"
##
## Scheffe Test for f
##
## Mean Square Error : 0.65
##
## CATALIZADOR, means
##
## f std r Min Max
## A 72.66667 1.527525 3 71 74
## B 71.33333 4.041452 3 67 75
## C 72.00000 3.605551 3 68 75
## D 74.00000 1.732051 3 72 75
##
## Alpha: 0.05 ; DF Error: 5
## Critical Value of F: 5.409451
##
## Minimum Significant Difference: 2.651846
##
## Means with the same letter are not significantly different.
##
## f groups
## D 74.00000 a
## A 72.66667 ab
## C 72.00000 ab
## B 71.33333 b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(i) Prueba de Scheffé
scheffe.test(anovaDBIB, "BLOQUE",console=TRUE)##
## Study: anovaDBIB ~ "BLOQUE"
##
## Scheffe Test for f
##
## Mean Square Error : 0.65
##
## BLOQUE, means
##
## f std r Min Max
## 1 73.66667 1.1547005 3 73 75
## 2 74.66667 0.5773503 3 74 75
## 3 69.00000 2.6457513 3 67 72
## 4 72.66667 2.0816660 3 71 75
##
## Alpha: 0.05 ; DF Error: 5
## Critical Value of F: 5.409451
##
## Minimum Significant Difference: 2.651846
##
## Means with the same letter are not significantly different.
##
## f groups
## 2 74.66667 a
## 1 73.66667 a
## 4 72.66667 a
## 3 69.00000 bplot(scheffe.test(anovaDBIB, "BLOQUE",console=TRUE))##
## Study: anovaDBIB ~ "BLOQUE"
##
## Scheffe Test for f
##
## Mean Square Error : 0.65
##
## BLOQUE, means
##
## f std r Min Max
## 1 73.66667 1.1547005 3 73 75
## 2 74.66667 0.5773503 3 74 75
## 3 69.00000 2.6457513 3 67 72
## 4 72.66667 2.0816660 3 71 75
##
## Alpha: 0.05 ; DF Error: 5
## Critical Value of F: 5.409451
##
## Minimum Significant Difference: 2.651846
##
## Means with the same letter are not significantly different.
##
## f groups
## 2 74.66667 a
## 1 73.66667 a
## 4 72.66667 a
## 3 69.00000 b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(j) Prueba de Duncan
duncan.test(anovaDBIB, "CATALIZADOR",console=TRUE)##
## Study: anovaDBIB ~ "CATALIZADOR"
##
## Duncan's new multiple range test
## for f
##
## Mean Square Error: 0.65
##
## CATALIZADOR, means
##
## f std r Min Max
## A 72.66667 1.527525 3 71 74
## B 71.33333 4.041452 3 67 75
## C 72.00000 3.605551 3 68 75
## D 74.00000 1.732051 3 72 75
##
## Alpha: 0.05 ; DF Error: 5
##
## Critical Range
## 2 3 4
## 1.692164 1.744832 1.767154
##
## Means with the same letter are not significantly different.
##
## f groups
## D 74.00000 a
## A 72.66667 ab
## C 72.00000 b
## B 71.33333 bplot(duncan.test(anovaDBIB, "CATALIZADOR",console=TRUE))##
## Study: anovaDBIB ~ "CATALIZADOR"
##
## Duncan's new multiple range test
## for f
##
## Mean Square Error: 0.65
##
## CATALIZADOR, means
##
## f std r Min Max
## A 72.66667 1.527525 3 71 74
## B 71.33333 4.041452 3 67 75
## C 72.00000 3.605551 3 68 75
## D 74.00000 1.732051 3 72 75
##
## Alpha: 0.05 ; DF Error: 5
##
## Critical Range
## 2 3 4
## 1.692164 1.744832 1.767154
##
## Means with the same letter are not significantly different.
##
## f groups
## D 74.00000 a
## A 72.66667 ab
## C 72.00000 b
## B 71.33333 b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(k) Prueba de Duncan
duncan.test(anovaDBIB, "BLOQUE",console=TRUE)##
## Study: anovaDBIB ~ "BLOQUE"
##
## Duncan's new multiple range test
## for f
##
## Mean Square Error: 0.65
##
## BLOQUE, means
##
## f std r Min Max
## 1 73.66667 1.1547005 3 73 75
## 2 74.66667 0.5773503 3 74 75
## 3 69.00000 2.6457513 3 67 72
## 4 72.66667 2.0816660 3 71 75
##
## Alpha: 0.05 ; DF Error: 5
##
## Critical Range
## 2 3 4
## 1.692164 1.744832 1.767154
##
## Means with the same letter are not significantly different.
##
## f groups
## 2 74.66667 a
## 1 73.66667 ab
## 4 72.66667 b
## 3 69.00000 cplot(duncan.test(anovaDBIB, "BLOQUE",console=TRUE))##
## Study: anovaDBIB ~ "BLOQUE"
##
## Duncan's new multiple range test
## for f
##
## Mean Square Error: 0.65
##
## BLOQUE, means
##
## f std r Min Max
## 1 73.66667 1.1547005 3 73 75
## 2 74.66667 0.5773503 3 74 75
## 3 69.00000 2.6457513 3 67 72
## 4 72.66667 2.0816660 3 71 75
##
## Alpha: 0.05 ; DF Error: 5
##
## Critical Range
## 2 3 4
## 1.692164 1.744832 1.767154
##
## Means with the same letter are not significantly different.
##
## f groups
## 2 74.66667 a
## 1 73.66667 ab
## 4 72.66667 b
## 3 69.00000 c
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(k) Prueba de Bonferroni
LSD.test(anovaDBIB, "CATALIZADOR", p.adj= "bon",console=TRUE)##
## Study: anovaDBIB ~ "CATALIZADOR"
##
## LSD t Test for f
## P value adjustment method: bonferroni
##
## Mean Square Error: 0.65
##
## CATALIZADOR, means and individual ( 95 %) CI
##
## f std r LCL UCL Min Max
## A 72.66667 1.527525 3 71.47013 73.86321 71 74
## B 71.33333 4.041452 3 70.13679 72.52987 67 75
## C 72.00000 3.605551 3 70.80346 73.19654 68 75
## D 74.00000 1.732051 3 72.80346 75.19654 72 75
##
## Alpha: 0.05 ; DF Error: 5
## Critical Value of t: 4.219309
##
## Minimum Significant Difference: 2.777489
##
## Treatments with the same letter are not significantly different.
##
## f groups
## D 74.00000 a
## A 72.66667 a
## C 72.00000 a
## B 71.33333 aplot(LSD.test(anovaDBIB, "CATALIZADOR", p.adj= "bon",console=TRUE))##
## Study: anovaDBIB ~ "CATALIZADOR"
##
## LSD t Test for f
## P value adjustment method: bonferroni
##
## Mean Square Error: 0.65
##
## CATALIZADOR, means and individual ( 95 %) CI
##
## f std r LCL UCL Min Max
## A 72.66667 1.527525 3 71.47013 73.86321 71 74
## B 71.33333 4.041452 3 70.13679 72.52987 67 75
## C 72.00000 3.605551 3 70.80346 73.19654 68 75
## D 74.00000 1.732051 3 72.80346 75.19654 72 75
##
## Alpha: 0.05 ; DF Error: 5
## Critical Value of t: 4.219309
##
## Minimum Significant Difference: 2.777489
##
## Treatments with the same letter are not significantly different.
##
## f groups
## D 74.00000 a
## A 72.66667 a
## C 72.00000 a
## B 71.33333 a
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(l) Prueba de Bonferroni
LSD.test(anovaDBIB, "BLOQUE", p.adj= "bon",console=TRUE)##
## Study: anovaDBIB ~ "BLOQUE"
##
## LSD t Test for f
## P value adjustment method: bonferroni
##
## Mean Square Error: 0.65
##
## BLOQUE, means and individual ( 95 %) CI
##
## f std r LCL UCL Min Max
## 1 73.66667 1.1547005 3 72.47013 74.86321 73 75
## 2 74.66667 0.5773503 3 73.47013 75.86321 74 75
## 3 69.00000 2.6457513 3 67.80346 70.19654 67 72
## 4 72.66667 2.0816660 3 71.47013 73.86321 71 75
##
## Alpha: 0.05 ; DF Error: 5
## Critical Value of t: 4.219309
##
## Minimum Significant Difference: 2.777489
##
## Treatments with the same letter are not significantly different.
##
## f groups
## 2 74.66667 a
## 1 73.66667 a
## 4 72.66667 a
## 3 69.00000 bplot(LSD.test(anovaDBIB, "BLOQUE", p.adj= "bon",console=TRUE))##
## Study: anovaDBIB ~ "BLOQUE"
##
## LSD t Test for f
## P value adjustment method: bonferroni
##
## Mean Square Error: 0.65
##
## BLOQUE, means and individual ( 95 %) CI
##
## f std r LCL UCL Min Max
## 1 73.66667 1.1547005 3 72.47013 74.86321 73 75
## 2 74.66667 0.5773503 3 73.47013 75.86321 74 75
## 3 69.00000 2.6457513 3 67.80346 70.19654 67 72
## 4 72.66667 2.0816660 3 71.47013 73.86321 71 75
##
## Alpha: 0.05 ; DF Error: 5
## Critical Value of t: 4.219309
##
## Minimum Significant Difference: 2.777489
##
## Treatments with the same letter are not significantly different.
##
## f groups
## 2 74.66667 a
## 1 73.66667 a
## 4 72.66667 a
## 3 69.00000 b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
6.5 Supuestos del Modelo en RStudio: Normalidad
(a) Normalidad de los residuos
shapiro.test(anovaDBIB$res)##
## Shapiro-Wilk normality test
##
## data: anovaDBIB$res
## W = 0.96945, p-value = 0.905%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) Supuesto del modelo:Normalidad de los residuos
summary(anovaDBIB$residuals)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.875 -0.375 0.000 0.000 0.375 0.875sd((anovaDBIB$residuals))## [1] 0.5435573%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(c) Supuesto del modelo:Normalidad de los residuos
boxplot(anovaDBIB$residuals,col="lightblue") 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(d) Supuesto del modelo:Normalidad de los residuos
hist(anovaDBIB$residuals, col="lightgreen", main = "Histograma de los Residuos",
freq = F, xlab="Residuos",ylab="Densidad")
lines(density(anovaDBIB$residuals), col="red", lwd=3)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(e) ** Prueba de Normalidad con Q-Q Plot**
qqnorm(anovaDBIB$residuals,col="blue", lwd=3)
qqline(anovaDBIB$residuals,col="red", lwd=3)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ## 6.6 Supuestos del Modelo en RStudio: Supuesto de Independencia
(y) Supuesto de Independencia
plot(anovaDBIB$residuals,main = "Residuos vs Observaciones",col="red", lwd=3) 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
6.7 Supuestos del Modelo en RStudio: Supuesto de Homocedasticidad
(a) Homocedasticidad
boxplot(anovaDBIB$residuals~CATALIZADOR, xlab="CATALIZADOR",ylab="Residuos",
col = c("yellow", "blue", "white","green", "red"))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) Homocedasticidad
boxplot(anovaDBIB$residuals~BLOQUE, xlab="BLOQUE",ylab="Residuos",
col = c("yellow", "blue", "white","green", "red")) 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(c) Homocedasticidad: Gráfico de predichos contra residuos estandarizados
pred=fitted(anovaDBIB)
resid=rstandard(anovaDBIB)
plot(pred,resid,xlab="Valores predichos", ylab="Residuos estandarizados",abline(h=0),col="red", lwd=3)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(f) Homocedasticidad: Prueba de Bartlett para Proteína
bartlett.test(anovaDBIB$residuals ~ CATALIZADOR)##
## Bartlett test of homogeneity of variances
##
## data: anovaDBIB$residuals by CATALIZADOR
## Bartlett's K-squared = 4.2189, df = 3, p-value = 0.2388%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(g) Homocedasticidad: Prueba de Bartlett para Proteína
bartlett.test(anovaDBIB$residuals ~ BLOQUE)##
## Bartlett test of homogeneity of variances
##
## data: anovaDBIB$residuals by BLOQUE
## Bartlett's K-squared = 1.8464, df = 3, p-value = 0.6049%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
7.0 Tema 6: Diseños Factorial - Dos Factores: Generalidades y Ejemplo en Statgraphics
7.1 Video: Diseños Factorial - Dos Factores: Generalidades y Ejemplo en Statgraphics
embed_youtube("_5-L0gFtEdQ")7.2 Ejemplo 6. (Texto Analisis y Diseno de Experimentos_Humberto-Roman_2da Ed_McGrawHill, pág. 134)
Problema: Consideremos un experimento en el que se quiere estudiar el efecto de los factores velocidad de alimentación y profundidad de corte sobre el acabado de un metal. Aunque los factores son de naturaleza continua, en este proceso sólo se pueden trabajar en 3 y 4 niveles, respectivamente. Por ello, se decide correr un factorial completo \(4x3\) con tres réplicas, que permitirá obtener toda la información relevante en relación al efecto de estos factores sobre el acabado. El acabado (Y) está en unidades de gramos e interesa minimizar su valor
| B: vel // A: Pro (pulg.) | 0.15 | 0.18 | 0.21 | 0.24 |
|---|---|---|---|---|
| 74 | 79 | 82 | 99 | |
| 0.20 | 64 | 68 | 88 | 104 |
| 60 | 73 | 92 | 96 | |
| 92 | 98 | 99 | 104 | |
| 0.25 | 86 | 104 | 108 | 110 |
| 88 | 88 | 95 | 99 | |
| 99 | 104 | 108 | 114 | |
| 0.30 | 98 | 99 | 110 | 111 |
| 102 | 95 | 99 | 107 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
7.3 Construyamos el diseño en R
(a) Construyamos el diseño en R
D2F <- expand.grid( A = c(0.15, 0.18, 0.21, 0.24), B = c(0.20, 0.25, 0.30) )
D2F<- rbind(D2F, D2F, D2F )
D2Ff = ACABADO <- c(74, 79, 82, 99, 92, 98, 99, 104, 99, 104, 108, 114, 64, 68, 88, 104, 86, 104, 108, 110, 98, 99, 110, 111, 60, 73, 92, 96, 88, 88, 95, 99, 102, 95, 99, 107)
D2F1 <- data.frame( D2F, f)
D2F1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) Diagrama de Caja
plot(f ~ factor(A) * factor(B), data = D2F1, col=c("red", "blue", "yellow", "orange"))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
7.4 Anova para el modelo bifactorial
(a) Anova para el modelo bifactorial
mod1 <- aov( f ~ factor(A) * factor(B), data = D2F1 )
summary(mod1)## Df Sum Sq Mean Sq F value Pr(>F)
## factor(A) 3 2125.1 708.4 24.663 1.65e-07 ***
## factor(B) 2 3160.5 1580.3 55.018 1.09e-09 ***
## factor(A):factor(B) 6 557.1 92.8 3.232 0.018 *
## Residuals 24 689.3 28.7
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) Anova para el modelo bifactorial2 más completo
g <- lm(f ~ factor(A) * factor(B), data = D2F1)
anova(g)summary(g)##
## Call:
## lm(formula = f ~ factor(A) * factor(B), data = D2F1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.6667 -3.6667 -0.3333 3.5833 8.0000
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 66.0000 3.0942 21.330 < 2e-16 ***
## factor(A)0.18 7.3333 4.3759 1.676 0.10675
## factor(A)0.21 21.3333 4.3759 4.875 5.70e-05 ***
## factor(A)0.24 33.6667 4.3759 7.694 6.25e-08 ***
## factor(B)0.25 22.6667 4.3759 5.180 2.64e-05 ***
## factor(B)0.3 33.6667 4.3759 7.694 6.25e-08 ***
## factor(A)0.18:factor(B)0.25 0.6667 6.1884 0.108 0.91511
## factor(A)0.21:factor(B)0.25 -9.3333 6.1884 -1.508 0.14456
## factor(A)0.24:factor(B)0.25 -18.0000 6.1884 -2.909 0.00770 **
## factor(A)0.18:factor(B)0.3 -7.6667 6.1884 -1.239 0.22737
## factor(A)0.21:factor(B)0.3 -15.3333 6.1884 -2.478 0.02065 *
## factor(A)0.24:factor(B)0.3 -22.6667 6.1884 -3.663 0.00123 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.359 on 24 degrees of freedom
## Multiple R-squared: 0.8945, Adjusted R-squared: 0.8461
## F-statistic: 18.49 on 11 and 24 DF, p-value: 4.111e-09%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
7.5 Gráficos de Interacción
(a) Gráficos de Interacción
with(D2F1, (interaction.plot(factor(A), factor(B), f, type = "b",pch = c(18,24,22), leg.bty = "o", main = "Gráfico de interacción de Velocidad y Profundidad",xlab = "Profundidad",ylab = "f acabado", col=c("red", "blue", "yellow", "orange"))))
## NULL%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) Gráficos de Interacción
with(D2F1, (interaction.plot(factor(B), factor(A), f, type = "b",pch = c(18,24,22), leg.bty = "o", main = "Gráficos de Interacción Velocidad y Profundidad",xlab = "Velocidad",ylab = "f acabado", col=c("darkred", "darkblue", "yellow", "darkorange"))))
## NULL%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
7.6 Prueba de Rangos Múltiples: Prueba HSD de Tukey
(g) Prueba HSD de Tukey
TukeyHSD(mod1)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = f ~ factor(A) * factor(B), data = D2F1)
##
## $`factor(A)`
## diff lwr upr p adj
## 0.18-0.15 5.000000 -1.96935966 11.96936 0.2236177
## 0.21-0.15 13.111111 6.14175145 20.08047 0.0001427
## 0.24-0.15 20.111111 13.14175145 27.08047 0.0000002
## 0.21-0.18 8.111111 1.14175145 15.08047 0.0183181
## 0.24-0.18 15.111111 8.14175145 22.08047 0.0000202
## 0.24-0.21 7.000000 0.03064034 13.96936 0.0487217
##
## $`factor(B)`
## diff lwr upr p adj
## 0.25-0.2 16.00 10.536111 21.46389 0.0000004
## 0.3-0.2 22.25 16.786111 27.71389 0.0000000
## 0.3-0.25 6.25 0.786111 11.71389 0.0228257
##
## $`factor(A):factor(B)`
## diff lwr upr p adj
## 0.18:0.2-0.15:0.2 7.3333333 -8.4443944 23.111061 0.8621754
## 0.21:0.2-0.15:0.2 21.3333333 5.5556056 37.111061 0.0026516
## 0.24:0.2-0.15:0.2 33.6666667 17.8889389 49.444394 0.0000035
## 0.15:0.25-0.15:0.2 22.6666667 6.8889389 38.444394 0.0012723
## 0.18:0.25-0.15:0.2 30.6666667 14.8889389 46.444394 0.0000165
## 0.21:0.25-0.15:0.2 34.6666667 18.8889389 50.444394 0.0000021
## 0.24:0.25-0.15:0.2 38.3333333 22.5556056 54.111061 0.0000004
## 0.15:0.3-0.15:0.2 33.6666667 17.8889389 49.444394 0.0000035
## 0.18:0.3-0.15:0.2 33.3333333 17.5556056 49.111061 0.0000041
## 0.21:0.3-0.15:0.2 39.6666667 23.8889389 55.444394 0.0000002
## 0.24:0.3-0.15:0.2 44.6666667 28.8889389 60.444394 0.0000000
## 0.21:0.2-0.18:0.2 14.0000000 -1.7777277 29.777728 0.1156484
## 0.24:0.2-0.18:0.2 26.3333333 10.5556056 42.111061 0.0001693
## 0.15:0.25-0.18:0.2 15.3333333 -0.4443944 31.111061 0.0620975
## 0.18:0.25-0.18:0.2 23.3333333 7.5556056 39.111061 0.0008807
## 0.21:0.25-0.18:0.2 27.3333333 11.5556056 43.111061 0.0000982
## 0.24:0.25-0.18:0.2 31.0000000 15.2222723 46.777728 0.0000139
## 0.15:0.3-0.18:0.2 26.3333333 10.5556056 42.111061 0.0001693
## 0.18:0.3-0.18:0.2 26.0000000 10.2222723 41.777728 0.0002031
## 0.21:0.3-0.18:0.2 32.3333333 16.5556056 48.111061 0.0000069
## 0.24:0.3-0.18:0.2 37.3333333 21.5556056 53.111061 0.0000006
## 0.24:0.2-0.21:0.2 12.3333333 -3.4443944 28.111061 0.2331919
## 0.15:0.25-0.21:0.2 1.3333333 -14.4443944 17.111061 1.0000000
## 0.18:0.25-0.21:0.2 9.3333333 -6.4443944 25.111061 0.6067268
## 0.21:0.25-0.21:0.2 13.3333333 -2.4443944 29.111061 0.1548689
## 0.24:0.25-0.21:0.2 17.0000000 1.2222723 32.777728 0.0270232
## 0.15:0.3-0.21:0.2 12.3333333 -3.4443944 28.111061 0.2331919
## 0.18:0.3-0.21:0.2 12.0000000 -3.7777277 27.777728 0.2649724
## 0.21:0.3-0.21:0.2 18.3333333 2.5556056 34.111061 0.0134649
## 0.24:0.3-0.21:0.2 23.3333333 7.5556056 39.111061 0.0008807
## 0.15:0.25-0.24:0.2 -11.0000000 -26.7777277 4.777728 0.3773797
## 0.18:0.25-0.24:0.2 -3.0000000 -18.7777277 12.777728 0.9998762
## 0.21:0.25-0.24:0.2 1.0000000 -14.7777277 16.777728 1.0000000
## 0.24:0.25-0.24:0.2 4.6666667 -11.1110611 20.444394 0.9935407
## 0.15:0.3-0.24:0.2 0.0000000 -15.7777277 15.777728 1.0000000
## 0.18:0.3-0.24:0.2 -0.3333333 -16.1110611 15.444394 1.0000000
## 0.21:0.3-0.24:0.2 6.0000000 -9.7777277 21.777728 0.9585056
## 0.24:0.3-0.24:0.2 11.0000000 -4.7777277 26.777728 0.3773797
## 0.18:0.25-0.15:0.25 8.0000000 -7.7777277 23.777728 0.7881462
## 0.21:0.25-0.15:0.25 12.0000000 -3.7777277 27.777728 0.2649724
## 0.24:0.25-0.15:0.25 15.6666667 -0.1110611 31.444394 0.0528028
## 0.15:0.3-0.15:0.25 11.0000000 -4.7777277 26.777728 0.3773797
## 0.18:0.3-0.15:0.25 10.6666667 -5.1110611 26.444394 0.4200394
## 0.21:0.3-0.15:0.25 17.0000000 1.2222723 32.777728 0.0270232
## 0.24:0.3-0.15:0.25 22.0000000 6.2222723 37.777728 0.0018375
## 0.21:0.25-0.18:0.25 4.0000000 -11.7777277 19.777728 0.9982365
## 0.24:0.25-0.18:0.25 7.6666667 -8.1110611 23.444394 0.8270901
## 0.15:0.3-0.18:0.25 3.0000000 -12.7777277 18.777728 0.9998762
## 0.18:0.3-0.18:0.25 2.6666667 -13.1110611 18.444394 0.9999609
## 0.21:0.3-0.18:0.25 9.0000000 -6.7777277 24.777728 0.6544316
## 0.24:0.3-0.18:0.25 14.0000000 -1.7777277 29.777728 0.1156484
## 0.24:0.25-0.21:0.25 3.6666667 -12.1110611 19.444394 0.9991877
## 0.15:0.3-0.21:0.25 -1.0000000 -16.7777277 14.777728 1.0000000
## 0.18:0.3-0.21:0.25 -1.3333333 -17.1110611 14.444394 1.0000000
## 0.21:0.3-0.21:0.25 5.0000000 -10.7777277 20.777728 0.9888577
## 0.24:0.3-0.21:0.25 10.0000000 -5.7777277 25.777728 0.5112272
## 0.15:0.3-0.24:0.25 -4.6666667 -20.4443944 11.111061 0.9935407
## 0.18:0.3-0.24:0.25 -5.0000000 -20.7777277 10.777728 0.9888577
## 0.21:0.3-0.24:0.25 1.3333333 -14.4443944 17.111061 1.0000000
## 0.24:0.3-0.24:0.25 6.3333333 -9.4443944 22.111061 0.9410768
## 0.18:0.3-0.15:0.3 -0.3333333 -16.1110611 15.444394 1.0000000
## 0.21:0.3-0.15:0.3 6.0000000 -9.7777277 21.777728 0.9585056
## 0.24:0.3-0.15:0.3 11.0000000 -4.7777277 26.777728 0.3773797
## 0.21:0.3-0.18:0.3 6.3333333 -9.4443944 22.111061 0.9410768
## 0.24:0.3-0.18:0.3 11.3333333 -4.4443944 27.111061 0.3371703
## 0.24:0.3-0.21:0.3 5.0000000 -10.7777277 20.777728 0.9888577%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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7.7 Diseños Factorial - Dos Factores con Python
7.8 Diseños Factorial - 2x3 con Python
8.0 Tema 8: Diseños Factorial - Tres Factores
8.1. *Video: Diseños Factorial - Tres Factores: Generalidades y Ejemplo en Statgraphics**
embed_youtube("UxVEHWf-Fdw")8.2 Tema 6: Diseños Factorial - Tres Factores: Usando RStudio
Ejemplo 8.2. (Texto Analisis y Diseno de Experimentos_Humberto-Roman_2da Ed_McGrawHill, pág. 143)
El experimento Se desea investigar el efecto del tipo de suspensión (A), abertura de malla (B) y temperatura de ciclaje (C) en el volumen de sedimentación Y(%) de una suspensión. Para ello se decide correr un experimento factorial 322 con seis réplicas, y las observaciones obtenidas en las 72 corridas experimentales se muestran en la siguiente tabla
| : A1 // B: | B1 | B1 | B1 | B2 | B2 | B2 |
|---|---|---|---|---|---|---|
| 60 | 75 | 75 | 67 | 73 | 73 | |
| C1 | 86 | 70 | 70 | 67 | 68 | 68 |
| 55 | 53 | 53 | 52 | 52 | 57 | |
| C2 | 55 | 55 | 55 | 52 | 54 | 54 |
| : A2 // B: | B1 | B1 | B1 | B2 | B2 | B2 |
|---|---|---|---|---|---|---|
| 62 | 68 | 65 | 71 | 80 | 80 | |
| C1 | 76 | 65 | 65 | 72 | 80 | 80 |
| 44 | 44 | 45 | 60 | 60 | 60 | |
| C2 | 48 | 48 | 45 | 67 | 67 | 65 |
| : A3 // B: | B1 | B1 | B1 | B2 | B2 | B2 |
|---|---|---|---|---|---|---|
| 70 | 71 | 75 | 75 | 75 | 75 | |
| C1 | 76 | 68 | 73 | 75 | 75 | 77 |
| 52 | 51 | 50 | 56 | 55 | 57 | |
| C2 | 52 | 48 | 54 | 59 | 50 | 55 |
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8.3 Ingresando los datos en RStudio
(a) (Ingresando los datos a R)
D3F <- expand.grid( A = c("A1", "A2", "A3"), B = c("B1", "B2"), C = c("C1", "C2") )
D3FD3F<- rbind(D3F, D3F, D3F, D3F,D3F, D3F )
D3Ff = volumen <- c(60,62,70,67,71,75,55,44,54,52,60,55,86,68,71,73,80,75,53,48,48,52,60,57,75,65,75,73,80,75,53,44,52,57,60,50,75,76,76,67,72,75,55,45,50,52,67,55,70,65,68,68,80,75,55,48,51,54,67,56,70,65,73,68,80,77,55,45,52,54,65, 59)
D3F1 <- data.frame( D3F, f)
D3F1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(b) Diagrama de Caja
plot(f ~ factor(A) * factor(B)* factor(C), data = D3F1, col=c("red", "blue", "yellow", "orange"))
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8.4 Analizando los datos en RStudio
(a) Anova para el volumen de sedimentación
mod1 <- aov( f ~ factor(A) * factor(B)* factor(C), data = D3F1 )
summary(mod1)## Df Sum Sq Mean Sq F value Pr(>F)
## factor(A) 2 14 7 0.494 0.6126
## factor(B) 1 480 480 34.253 2.16e-07 ***
## factor(C) 1 6087 6087 433.905 < 2e-16 ***
## factor(A):factor(B) 2 788 394 28.096 2.45e-09 ***
## factor(A):factor(C) 2 41 20 1.456 0.2412
## factor(B):factor(C) 1 57 57 4.055 0.0485 *
## factor(A):factor(B):factor(C) 2 31 16 1.106 0.3375
## Residuals 60 842 14
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(b) Anova para el volumen de sedimentación completa
g <- lm(f ~ factor(A) * factor(B)* factor(C), data = D3F1)
anova(g)summary(g)##
## Call:
## lm(formula = f ~ factor(A) * factor(B) * factor(C), data = D3F1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.6667 -1.7083 -0.3333 2.3333 13.3333
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 72.667 1.529 47.524 < 2e-16 ***
## factor(A)A2 -5.833 2.162 -2.698 0.00905 **
## factor(A)A3 -0.500 2.162 -0.231 0.81793
## factor(B)B2 -3.333 2.162 -1.542 0.12845
## factor(C)C2 -18.333 2.162 -8.478 7.52e-12 ***
## factor(A)A2:factor(B)B2 13.667 3.058 4.469 3.55e-05 ***
## factor(A)A3:factor(B)B2 6.500 3.058 2.126 0.03767 *
## factor(A)A2:factor(C)C2 -2.833 3.058 -0.927 0.35789
## factor(A)A3:factor(C)C2 -2.667 3.058 -0.872 0.38668
## factor(B)B2:factor(C)C2 2.500 3.058 0.818 0.41687
## factor(A)A2:factor(B)B2:factor(C)C2 4.667 4.325 1.079 0.28488
## factor(A)A3:factor(B)B2:factor(C)C2 -1.500 4.325 -0.347 0.72993
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.745 on 60 degrees of freedom
## Multiple R-squared: 0.8991, Adjusted R-squared: 0.8806
## F-statistic: 48.59 on 11 and 60 DF, p-value: < 2.2e-16%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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8.5 Analizando los datos en RStudio: Gráficos de Interacción
(a) Gráficos de Interacción
with(D3F1, (interaction.plot(factor(A), factor(B), f, type = "b",pch = c(18,24,22), leg.bty = "o", main = "Gráficos de Interacción Suspensión y Abertura",xlab = "Suspensión",ylab = "f Volumen", col=c("red", "blue", "yellow", "orange"))))
## NULL%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b)Gráficos de Interacción
with(D3F1, (interaction.plot(factor(A), factor(C), f, type = "b",pch = c(18,24,22), leg.bty = "o", main = "Gráficos de Interacción Suspensión y Temperatura",xlab = "Suspensión",ylab = "f Volumen", col=c("red", "blue", "yellow", "orange"))))
## NULL%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(c)Gráficos de Interacción
with(D3F1, (interaction.plot(factor(B), factor(C), f, type = "b",pch = c(18,24,22), leg.bty = "o", main = "Gráficos de Interacción Abertura y Temperatura",xlab = "Abertura",ylab = "f Volumen", col=c("red", "blue", "yellow", "orange"))))
## NULL%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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8.6 Pruebas de Medias por comparaciones Múltiples
(a)Prueba HSD de Tukey
TukeyHSD(mod1)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = f ~ factor(A) * factor(B) * factor(C), data = D3F1)
##
## $`factor(A)`
## diff lwr upr p adj
## A2-A1 0.7500000 -1.848344 3.348344 0.7680852
## A3-A1 1.0416667 -1.556678 3.640011 0.6026331
## A3-A2 0.2916667 -2.306678 2.890011 0.9607046
##
## $`factor(B)`
## diff lwr upr p adj
## B2-B1 5.166667 3.400821 6.932513 2e-07
##
## $`factor(C)`
## diff lwr upr p adj
## C2-C1 -18.38889 -20.15473 -16.62304 0
##
## $`factor(A):factor(B)`
## diff lwr upr p adj
## A2:B1-A1:B1 -7.250000 -11.7511865 -2.7488135 0.0001895
## A3:B1-A1:B1 -1.833333 -6.3345198 2.6678531 0.8356078
## A1:B2-A1:B1 -2.083333 -6.5845198 2.4178531 0.7488090
## A2:B2-A1:B1 6.666667 2.1654802 11.1678531 0.0007097
## A3:B2-A1:B1 1.833333 -2.6678531 6.3345198 0.8356078
## A3:B1-A2:B1 5.416667 0.9154802 9.9178531 0.0096192
## A1:B2-A2:B1 5.166667 0.6654802 9.6678531 0.0154752
## A2:B2-A2:B1 13.916667 9.4154802 18.4178531 0.0000000
## A3:B2-A2:B1 9.083333 4.5821469 13.5845198 0.0000023
## A1:B2-A3:B1 -0.250000 -4.7511865 4.2511865 0.9999829
## A2:B2-A3:B1 8.500000 3.9988135 13.0011865 0.0000096
## A3:B2-A3:B1 3.666667 -0.8345198 8.1678531 0.1734453
## A2:B2-A1:B2 8.750000 4.2488135 13.2511865 0.0000052
## A3:B2-A1:B2 3.916667 -0.5845198 8.4178531 0.1230911
## A3:B2-A2:B2 -4.833333 -9.3345198 -0.3321469 0.0283481
##
## $`factor(A):factor(C)`
## diff lwr upr p adj
## A2:C1-A1:C1 1.0000000 -3.501186 5.501186 0.9861601
## A3:C1-A1:C1 2.7500000 -1.751186 7.251186 0.4744663
## A1:C2-A1:C1 -17.0833333 -21.584520 -12.582147 0.0000000
## A2:C2-A1:C1 -16.5833333 -21.084520 -12.082147 0.0000000
## A3:C2-A1:C1 -17.7500000 -22.251186 -13.248814 0.0000000
## A3:C1-A2:C1 1.7500000 -2.751186 6.251186 0.8606445
## A1:C2-A2:C1 -18.0833333 -22.584520 -13.582147 0.0000000
## A2:C2-A2:C1 -17.5833333 -22.084520 -13.082147 0.0000000
## A3:C2-A2:C1 -18.7500000 -23.251186 -14.248814 0.0000000
## A1:C2-A3:C1 -19.8333333 -24.334520 -15.332147 0.0000000
## A2:C2-A3:C1 -19.3333333 -23.834520 -14.832147 0.0000000
## A3:C2-A3:C1 -20.5000000 -25.001186 -15.998814 0.0000000
## A2:C2-A1:C2 0.5000000 -4.001186 5.001186 0.9994780
## A3:C2-A1:C2 -0.6666667 -5.167853 3.834520 0.9979060
## A3:C2-A2:C2 -1.1666667 -5.667853 3.334520 0.9726219
##
## $`factor(B):factor(C)`
## diff lwr upr p adj
## B2:C1-B1:C1 3.388889 0.08981796 6.687960 0.0418949
## B1:C2-B1:C1 -20.166667 -23.46573760 -16.867596 0.0000000
## B2:C2-B1:C1 -13.222222 -16.52129315 -9.923151 0.0000000
## B1:C2-B2:C1 -23.555556 -26.85462649 -20.256485 0.0000000
## B2:C2-B2:C1 -16.611111 -19.91018204 -13.312040 0.0000000
## B2:C2-B1:C2 6.944444 3.64537351 10.243515 0.0000038
##
## $`factor(A):factor(B):factor(C)`
## diff lwr upr p adj
## A2:B1:C1-A1:B1:C1 -5.8333333 -13.1856861 1.5190194 0.2527629
## A3:B1:C1-A1:B1:C1 -0.5000000 -7.8523528 6.8523528 1.0000000
## A1:B2:C1-A1:B1:C1 -3.3333333 -10.6856861 4.0190194 0.9223912
## A2:B2:C1-A1:B1:C1 4.5000000 -2.8523528 11.8523528 0.6375599
## A3:B2:C1-A1:B1:C1 2.6666667 -4.6856861 10.0190194 0.9839113
## A1:B1:C2-A1:B1:C1 -18.3333333 -25.6856861 -10.9809806 0.0000000
## A2:B1:C2-A1:B1:C1 -27.0000000 -34.3523528 -19.6476472 0.0000000
## A3:B1:C2-A1:B1:C1 -21.5000000 -28.8523528 -14.1476472 0.0000000
## A1:B2:C2-A1:B1:C1 -19.1666667 -26.5190194 -11.8143139 0.0000000
## A2:B2:C2-A1:B1:C1 -9.5000000 -16.8523528 -2.1476472 0.0025052
## A3:B2:C2-A1:B1:C1 -17.3333333 -24.6856861 -9.9809806 0.0000000
## A3:B1:C1-A2:B1:C1 5.3333333 -2.0190194 12.6856861 0.3802875
## A1:B2:C1-A2:B1:C1 2.5000000 -4.8523528 9.8523528 0.9903398
## A2:B2:C1-A2:B1:C1 10.3333333 2.9809806 17.6856861 0.0006757
## A3:B2:C1-A2:B1:C1 8.5000000 1.1476472 15.8523528 0.0109430
## A1:B1:C2-A2:B1:C1 -12.5000000 -19.8523528 -5.1476472 0.0000176
## A2:B1:C2-A2:B1:C1 -21.1666667 -28.5190194 -13.8143139 0.0000000
## A3:B1:C2-A2:B1:C1 -15.6666667 -23.0190194 -8.3143139 0.0000001
## A1:B2:C2-A2:B1:C1 -13.3333333 -20.6856861 -5.9809806 0.0000041
## A2:B2:C2-A2:B1:C1 -3.6666667 -11.0190194 3.6856861 0.8630813
## A3:B2:C2-A2:B1:C1 -11.5000000 -18.8523528 -4.1476472 0.0000982
## A1:B2:C1-A3:B1:C1 -2.8333333 -10.1856861 4.5190194 0.9745590
## A2:B2:C1-A3:B1:C1 5.0000000 -2.3523528 12.3523528 0.4796825
## A3:B2:C1-A3:B1:C1 3.1666667 -4.1856861 10.5190194 0.9443710
## A1:B1:C2-A3:B1:C1 -17.8333333 -25.1856861 -10.4809806 0.0000000
## A2:B1:C2-A3:B1:C1 -26.5000000 -33.8523528 -19.1476472 0.0000000
## A3:B1:C2-A3:B1:C1 -21.0000000 -28.3523528 -13.6476472 0.0000000
## A1:B2:C2-A3:B1:C1 -18.6666667 -26.0190194 -11.3143139 0.0000000
## A2:B2:C2-A3:B1:C1 -9.0000000 -16.3523528 -1.6476472 0.0053152
## A3:B2:C2-A3:B1:C1 -16.8333333 -24.1856861 -9.4809806 0.0000000
## A2:B2:C1-A1:B2:C1 7.8333333 0.4809806 15.1856861 0.0271441
## A3:B2:C1-A1:B2:C1 6.0000000 -1.3523528 13.3523528 0.2172776
## A1:B1:C2-A1:B2:C1 -15.0000000 -22.3523528 -7.6476472 0.0000002
## A2:B1:C2-A1:B2:C1 -23.6666667 -31.0190194 -16.3143139 0.0000000
## A3:B1:C2-A1:B2:C1 -18.1666667 -25.5190194 -10.8143139 0.0000000
## A1:B2:C2-A1:B2:C1 -15.8333333 -23.1856861 -8.4809806 0.0000000
## A2:B2:C2-A1:B2:C1 -6.1666667 -13.5190194 1.1856861 0.1854455
## A3:B2:C2-A1:B2:C1 -14.0000000 -21.3523528 -6.6476472 0.0000012
## A3:B2:C1-A2:B2:C1 -1.8333333 -9.1856861 5.5190194 0.9993589
## A1:B1:C2-A2:B2:C1 -22.8333333 -30.1856861 -15.4809806 0.0000000
## A2:B1:C2-A2:B2:C1 -31.5000000 -38.8523528 -24.1476472 0.0000000
## A3:B1:C2-A2:B2:C1 -26.0000000 -33.3523528 -18.6476472 0.0000000
## A1:B2:C2-A2:B2:C1 -23.6666667 -31.0190194 -16.3143139 0.0000000
## A2:B2:C2-A2:B2:C1 -14.0000000 -21.3523528 -6.6476472 0.0000012
## A3:B2:C2-A2:B2:C1 -21.8333333 -29.1856861 -14.4809806 0.0000000
## A1:B1:C2-A3:B2:C1 -21.0000000 -28.3523528 -13.6476472 0.0000000
## A2:B1:C2-A3:B2:C1 -29.6666667 -37.0190194 -22.3143139 0.0000000
## A3:B1:C2-A3:B2:C1 -24.1666667 -31.5190194 -16.8143139 0.0000000
## A1:B2:C2-A3:B2:C1 -21.8333333 -29.1856861 -14.4809806 0.0000000
## A2:B2:C2-A3:B2:C1 -12.1666667 -19.5190194 -4.8143139 0.0000314
## A3:B2:C2-A3:B2:C1 -20.0000000 -27.3523528 -12.6476472 0.0000000
## A2:B1:C2-A1:B1:C2 -8.6666667 -16.0190194 -1.3143139 0.0086330
## A3:B1:C2-A1:B1:C2 -3.1666667 -10.5190194 4.1856861 0.9443710
## A1:B2:C2-A1:B1:C2 -0.8333333 -8.1856861 6.5190194 0.9999998
## A2:B2:C2-A1:B1:C2 8.8333333 1.4809806 16.1856861 0.0067858
## A3:B2:C2-A1:B1:C2 1.0000000 -6.3523528 8.3523528 0.9999985
## A3:B1:C2-A2:B1:C2 5.5000000 -1.8523528 12.8523528 0.3344782
## A1:B2:C2-A2:B1:C2 7.8333333 0.4809806 15.1856861 0.0271441
## A2:B2:C2-A2:B1:C2 17.5000000 10.1476472 24.8523528 0.0000000
## A3:B2:C2-A2:B1:C2 9.6666667 2.3143139 17.0190194 0.0019379
## A1:B2:C2-A3:B1:C2 2.3333333 -5.0190194 9.6856861 0.9945288
## A2:B2:C2-A3:B1:C2 12.0000000 4.6476472 19.3523528 0.0000418
## A3:B2:C2-A3:B1:C2 4.1666667 -3.1856861 11.5190194 0.7380170
## A2:B2:C2-A1:B2:C2 9.6666667 2.3143139 17.0190194 0.0019379
## A3:B2:C2-A1:B2:C2 1.8333333 -5.5190194 9.1856861 0.9993589
## A3:B2:C2-A2:B2:C2 -7.8333333 -15.1856861 -0.4809806 0.0271441%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(b) Prueba HSD de Tukey
TukeyHSD(mod1, "factor(A)")## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = f ~ factor(A) * factor(B) * factor(C), data = D3F1)
##
## $`factor(A)`
## diff lwr upr p adj
## A2-A1 0.7500000 -1.848344 3.348344 0.7680852
## A3-A1 1.0416667 -1.556678 3.640011 0.6026331
## A3-A2 0.2916667 -2.306678 2.890011 0.9607046plot(TukeyHSD(mod1, "factor(A)"))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
(c) Prueba HSD de Tukey
TukeyHSD(mod1, "factor(B)")## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = f ~ factor(A) * factor(B) * factor(C), data = D3F1)
##
## $`factor(B)`
## diff lwr upr p adj
## B2-B1 5.166667 3.400821 6.932513 2e-07plot(TukeyHSD(mod1, "factor(B)"))
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(d) Prueba HSD de Tukey
TukeyHSD(mod1, "factor(C)")## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = f ~ factor(A) * factor(B) * factor(C), data = D3F1)
##
## $`factor(C)`
## diff lwr upr p adj
## C2-C1 -18.38889 -20.15473 -16.62304 0plot(TukeyHSD(mod1, "factor(C)"))
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8.7 Diseños Factorial - Tres Factores con Python
8.8 Diseños Factorial Tres Factores - 2x2x3 con Python
8.9. Evaluación 6. Diseño Factorial I
https://forms.gle/vULzw9JY4Z4vGb2t6
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8.10. Evaluación 7. Diseño Factorial II
https://forms.gle/DYb3BmWNY75JHk2r8
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9.0 Tema 9: Diseños Factorial - Tres Factores: Ejemplo Cultivo comercial del Camarón
9.1. Video 9: Diseños Factorial - Tres Factores: Ejemplo Cultivo comercial del Camarón y Ejemplo en Statgraphics
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10.0 Tema 10: Diseños Completos Aleatorizados Usando RStudio
10.1. Video 10: Diseños Completos Aleatorizados Usando RStudio
embed_youtube("pFpH1eCkZ7w")%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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11.0 Tema 11: Diseños Factoriales \(2^k\) Usando RStudio: Generalidades
11.1. Video 11: Diseños Factoriales \(2^2\) Usando RStudio: Generalidades
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12.0 Tema 12: Diseños Factoriales \(2^k\) Usando Statgraphics: Generalidades
12.1. Video 12: Diseños Factoriales \(2^3\) Usando Statgraphics: Generalidades
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12.2. Evaluación 8. Diseño Factorial \(2^k\)
https://forms.gle/dSTpwtcYawFmtEPC9
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12.3. Evaluación 9. Diseño Factorial \(2^k\)
https://forms.gle/hhAQ7VUnkdfUMWQL9
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12.4 Diseño Factorial \(2^2\) No balancedo usando Python
13.0 Tema 13: Diseños Factoriales \(2^4\) Usando Statgraphics: Generalidades
13.1. Video 13: Diseños Factoriales \(2^4\) Usando Statgraphics: Generalidades
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14.0 Tema 14: Diseños Factoriales \(2^5\) Usando Statgraphics: Colasando un Diseño
14.1. Video 14: Diseños Factoriales \(2^5\) Usando Statgraphics: Colasando un Diseño
embed_youtube("Qtd9sKAKenE")14.2. Video 15: Diseños Factoriales \(2^5\) Usando Statgraphics: Colasando un Diseño
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14.3 Tema 14: Diseños Factoriales \(2^5\) Usando Python
https://github.com/JSEFERINO/JSEFERINO/blob/main/DOEJH10.ipynb
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14.4 Tema 14: Diseños Factoriales \(2^6\) Usando Python
https://github.com/JSEFERINO/JSEFERINO/blob/main/DOEJH12.ipynb
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15.0 Tema 15: Diseños Factoriales fraccionados \(2^(k-p)\) Usando Statgraphics: Generalidades
15.1. Video 15: Diseños Factoriales \(2^5\) Usando Statgraphics: Generalidades
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16.0 Tema 16: Diseños de Superficie de respuesta - Generalidaddes
16.1. Video 16: Diseños de Superficie de respuesta - Generalidaddes
embed_youtube("ql9DFse9bb8")16.1. Video 16: Diseños de Superficie de respuesta - Ejemplo ilustrativo
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16.2. Evaluación 10. Diseño en Superficie de Respuesta
https://forms.gle/t3Bymt5WwMzQvEVg8
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7.0 Tema 7: Experimento 2^5 no replicado
7.1 Ejemplo 7. (Texto Analisis y Diseno de Experimentos_Humberto-Roman_2da Ed_McGrawHill, pág. 63)
SEn una planta donde se fabrican semiconductores se quiere mejorar el rendimiento del proceso vía diseño de experimentos. De acuerdo con la experiencia del grupo de mejora, los factores que podrían tener mayor influencia sobre la variable de respuesta (rendimiento), así como los niveles de prueba utilizados son los siguientes:
A = Nivel de la abertura (pequeña, grande).
B = Tiempo de exposición (20% abajo, 20% arriba).
C = Tiempo de revelado (30 seg, 45 seg).
D = Dimensión de la máscara (pequeña, grande).
E = Tiempo de grabado (14.5 min, 15.5 min).
Se decide correr un experimento \(2^5\) con una sola corrida o réplica para estudiar estos cinco factores. Se hacen las 32 corridas a nivel proceso.*
| (1)=7 | d=8 | e=8 | de=6 |
| a=9 | ad=10 | ae=12 | ade=10 |
| b=34 | bd=32 | be=35 | bde=30 |
| ab=55 | abd=50 | abe=52 | abde=53 |
| c=16 | cd=18 | ce=15 | cde=15 |
| ac=20 | acd=21 | ace=22 | acde=20 |
| bc=41 | bcd=44 | bce=45 | bcde=41 |
| abc=60 | abcd=61 | abce=65 | abcde=63 |
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2.2 Ingresando los datos en RStudio
(a) Primero creamos los vectores teniendo en cuenta que los factores se deben crear como factor.
V.sanguíneo =c(4.1, 6.5,4.1, 4.9,
4.1, 5.3, 4.0, 6.2,
6.5, 6.9, 4.5, 4.8,
4.3, 6.8, 4.3,4.2,
6.0, 6.5,4.1, 6.9)
Tratamientos =factor( c(rep("A",1),
rep("B",1),
rep("C",1),
rep("D",1)))
Bloques = factor(c(rep("I",4),
rep("II",4),
rep("III",4),
rep("IV",4),
rep("V",4))) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(b) Se obtiene ahora la nueva tabla de datos del modelo
DBCA1 = data.frame(Bloques,Tratamientos, V.sanguíneo)
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2.3 Analizando los datos en RStudio
(a) Para el próximo paso debemos descargar los siguientes paquetes (gridExtra) y (ggplot2)
library(gridExtra)
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(b) Diagramas de caja: Los siguientes son gráficos descriptivos de los factores con la variable respuesta
Tratamientos2 <- ggplot(DBCA1, aes(x = Tratamientos, y = V.sanguíneo, fill=Tratamientos)) +
geom_boxplot() + theme(legend.position = "none")
Bloques2 <- ggplot(DBCA1, aes(x = Bloques, y = V.sanguíneo, fill=Bloques)) +
geom_boxplot() + theme(legend.position = "none")
grid.arrange(Tratamientos2,Bloques2, nrow=1, ncol=2)
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(c) El Modelo linal y tabla ANOVA
modeloDBCA1= lm(V.sanguíneo ~ Tratamientos + Bloques, DBCA1)
anovaDBCA1=aov(modeloDBCA1)
anovaDBCA1## Call:
## aov(formula = modeloDBCA1)
##
## Terms:
## Tratamientos Bloques Residuals
## Sum of Squares 12.550 3.755 8.345
## Deg. of Freedom 3 4 12
##
## Residual standard error: 0.8339165
## Estimated effects may be unbalancedsummary(anovaDBCA1)## Df Sum Sq Mean Sq F value Pr(>F)
## Tratamientos 3 12.550 4.183 6.016 0.00964 **
## Bloques 4 3.755 0.939 1.350 0.30797
## Residuals 12 8.345 0.695
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(d) Comparaciones múltiples: HSD de Tukey
TukeyHSD(anovaDBCA1)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = modeloDBCA1)
##
## $Tratamientos
## diff lwr upr p adj
## B-A 1.4 -0.1658432 2.9658432 0.0854565
## C-A -0.8 -2.3658432 0.7658432 0.4580868
## D-A 0.4 -1.1658432 1.9658432 0.8713824
## C-B -2.2 -3.7658432 -0.6341568 0.0061420
## D-B -1.0 -2.5658432 0.5658432 0.2800111
## D-C 1.2 -0.3658432 2.7658432 0.1586223
##
## $Bloques
## diff lwr upr p adj
## II-I 0.000000e+00 -1.8795268 1.879527 1.0000000
## III-I 7.750000e-01 -1.1045268 2.654527 0.6881671
## IV-I -8.881784e-16 -1.8795268 1.879527 1.0000000
## V-I 9.750000e-01 -0.9045268 2.854527 0.4944147
## III-II 7.750000e-01 -1.1045268 2.654527 0.6881671
## IV-II -8.881784e-16 -1.8795268 1.879527 1.0000000
## V-II 9.750000e-01 -0.9045268 2.854527 0.4944147
## IV-III -7.750000e-01 -2.6545268 1.104527 0.6881671
## V-III 2.000000e-01 -1.6795268 2.079527 0.9967411
## V-IV 9.750000e-01 -0.9045268 2.854527 0.4944147%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(e) Comparaciones múltiples: gráfico HSD de Tukey
plot(TukeyHSD(anovaDBCA1))
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2.4 Pruebas de Medias por comparaciones Múltiples
(a) (Prueba LSD). Instale el paquete “agricolae
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(b) Prueba LSD para Tratamientos
LSD.test(anovaDBCA1,"Tratamientos",console=TRUE)##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## LSD t Test for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means and individual ( 95 %) CI
##
## V.sanguíneo std r LCL UCL Min Max
## A 5.0 1.1575837 5 4.187436 5.812564 4.1 6.5
## B 6.4 0.6403124 5 5.587436 7.212564 5.3 6.9
## C 4.2 0.2000000 5 3.387436 5.012564 4.0 4.5
## D 5.4 1.1113055 5 4.587436 6.212564 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of t: 2.178813
##
## least Significant Difference: 1.149139
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 bc
## C 4.2 cplot(LSD.test(anovaDBCA1,"Tratamientos",console=TRUE))##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## LSD t Test for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means and individual ( 95 %) CI
##
## V.sanguíneo std r LCL UCL Min Max
## A 5.0 1.1575837 5 4.187436 5.812564 4.1 6.5
## B 6.4 0.6403124 5 5.587436 7.212564 5.3 6.9
## C 4.2 0.2000000 5 3.387436 5.012564 4.0 4.5
## D 5.4 1.1113055 5 4.587436 6.212564 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of t: 2.178813
##
## least Significant Difference: 1.149139
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 bc
## C 4.2 c
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(c) Prueba LSD para Bloques
LSD.test(anovaDBCA1,"Bloques",console=TRUE)##
## Study: anovaDBCA1 ~ "Bloques"
##
## LSD t Test for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Bloques, means and individual ( 95 %) CI
##
## V.sanguíneo std r LCL UCL Min Max
## I 4.900 1.131371 4 3.991526 5.808474 4.1 6.5
## II 4.900 1.048809 4 3.991526 5.808474 4.0 6.2
## III 5.675 1.201041 4 4.766526 6.583474 4.5 6.9
## IV 4.900 1.267544 4 3.991526 5.808474 4.2 6.8
## V 5.875 1.239287 4 4.966526 6.783474 4.1 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of t: 2.178813
##
## least Significant Difference: 1.284776
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## V 5.875 a
## III 5.675 a
## I 4.900 a
## II 4.900 a
## IV 4.900 aplot(LSD.test(anovaDBCA1,"Bloques",console=TRUE))##
## Study: anovaDBCA1 ~ "Bloques"
##
## LSD t Test for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Bloques, means and individual ( 95 %) CI
##
## V.sanguíneo std r LCL UCL Min Max
## I 4.900 1.131371 4 3.991526 5.808474 4.1 6.5
## II 4.900 1.048809 4 3.991526 5.808474 4.0 6.2
## III 5.675 1.201041 4 4.766526 6.583474 4.5 6.9
## IV 4.900 1.267544 4 3.991526 5.808474 4.2 6.8
## V 5.875 1.239287 4 4.966526 6.783474 4.1 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of t: 2.178813
##
## least Significant Difference: 1.284776
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## V 5.875 a
## III 5.675 a
## I 4.900 a
## II 4.900 a
## IV 4.900 a
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(f) Prueba de Tukey: Tratamientos
HSD.test(anovaDBCA1, "Tratamientos",console=TRUE)##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## HSD Test for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means
##
## V.sanguíneo std r Min Max
## A 5.0 1.1575837 5 4.1 6.5
## B 6.4 0.6403124 5 5.3 6.9
## C 4.2 0.2000000 5 4.0 4.5
## D 5.4 1.1113055 5 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of Studentized Range: 4.19866
##
## Minimun Significant Difference: 1.565843
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 ab
## C 4.2 bplot(HSD.test(anovaDBCA1, "Tratamientos",console=TRUE))##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## HSD Test for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means
##
## V.sanguíneo std r Min Max
## A 5.0 1.1575837 5 4.1 6.5
## B 6.4 0.6403124 5 5.3 6.9
## C 4.2 0.2000000 5 4.0 4.5
## D 5.4 1.1113055 5 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of Studentized Range: 4.19866
##
## Minimun Significant Difference: 1.565843
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 ab
## C 4.2 b
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(g) Prueba de Tukey: Bloques
HSD.test(anovaDBCA1, "Bloques",console=TRUE)##
## Study: anovaDBCA1 ~ "Bloques"
##
## HSD Test for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Bloques, means
##
## V.sanguíneo std r Min Max
## I 4.900 1.131371 4 4.1 6.5
## II 4.900 1.048809 4 4.0 6.2
## III 5.675 1.201041 4 4.5 6.9
## IV 4.900 1.267544 4 4.2 6.8
## V 5.875 1.239287 4 4.1 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of Studentized Range: 4.50771
##
## Minimun Significant Difference: 1.879527
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## V 5.875 a
## III 5.675 a
## I 4.900 a
## II 4.900 a
## IV 4.900 a%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(h) Prueba de Student-Newman-Keuls (SNK)
SNK.test(anovaDBCA1, "Tratamientos",console=TRUE)##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## Student Newman Keuls Test
## for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means
##
## V.sanguíneo std r Min Max
## A 5.0 1.1575837 5 4.1 6.5
## B 6.4 0.6403124 5 5.3 6.9
## C 4.2 0.2000000 5 4.0 4.5
## D 5.4 1.1113055 5 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
##
## Critical Range
## 2 3 4
## 1.149139 1.407072 1.565843
##
## Means with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 ab
## C 4.2 bplot(SNK.test(anovaDBCA1, "Tratamientos",console=TRUE))##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## Student Newman Keuls Test
## for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means
##
## V.sanguíneo std r Min Max
## A 5.0 1.1575837 5 4.1 6.5
## B 6.4 0.6403124 5 5.3 6.9
## C 4.2 0.2000000 5 4.0 4.5
## D 5.4 1.1113055 5 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
##
## Critical Range
## 2 3 4
## 1.149139 1.407072 1.565843
##
## Means with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 ab
## C 4.2 b
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(i) Prueba de Scheffé
scheffe.test(anovaDBCA1, "Bloques",console=TRUE)##
## Study: anovaDBCA1 ~ "Bloques"
##
## Scheffe Test for V.sanguíneo
##
## Mean Square Error : 0.6954167
##
## Bloques, means
##
## V.sanguíneo std r Min Max
## I 4.900 1.131371 4 4.1 6.5
## II 4.900 1.048809 4 4.0 6.2
## III 5.675 1.201041 4 4.5 6.9
## IV 4.900 1.267544 4 4.2 6.8
## V 5.875 1.239287 4 4.1 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of F: 3.259167
##
## Minimum Significant Difference: 2.129074
##
## Means with the same letter are not significantly different.
##
## V.sanguíneo groups
## V 5.875 a
## III 5.675 a
## I 4.900 a
## II 4.900 a
## IV 4.900 aplot(scheffe.test(anovaDBCA1, "Bloques",console=TRUE))##
## Study: anovaDBCA1 ~ "Bloques"
##
## Scheffe Test for V.sanguíneo
##
## Mean Square Error : 0.6954167
##
## Bloques, means
##
## V.sanguíneo std r Min Max
## I 4.900 1.131371 4 4.1 6.5
## II 4.900 1.048809 4 4.0 6.2
## III 5.675 1.201041 4 4.5 6.9
## IV 4.900 1.267544 4 4.2 6.8
## V 5.875 1.239287 4 4.1 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of F: 3.259167
##
## Minimum Significant Difference: 2.129074
##
## Means with the same letter are not significantly different.
##
## V.sanguíneo groups
## V 5.875 a
## III 5.675 a
## I 4.900 a
## II 4.900 a
## IV 4.900 a
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(j) Prueba de Duncan
duncan.test(anovaDBCA1, "Tratamientos",console=TRUE)##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## Duncan's new multiple range test
## for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means
##
## V.sanguíneo std r Min Max
## A 5.0 1.1575837 5 4.1 6.5
## B 6.4 0.6403124 5 5.3 6.9
## C 4.2 0.2000000 5 4.0 4.5
## D 5.4 1.1113055 5 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
##
## Critical Range
## 2 3 4
## 1.149139 1.202818 1.235342
##
## Means with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 b
## C 4.2 bplot(duncan.test(anovaDBCA1, "Tratamientos",console=TRUE))##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## Duncan's new multiple range test
## for V.sanguíneo
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means
##
## V.sanguíneo std r Min Max
## A 5.0 1.1575837 5 4.1 6.5
## B 6.4 0.6403124 5 5.3 6.9
## C 4.2 0.2000000 5 4.0 4.5
## D 5.4 1.1113055 5 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
##
## Critical Range
## 2 3 4
## 1.149139 1.202818 1.235342
##
## Means with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 b
## C 4.2 b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(k) Prueba de Bonferroni
LSD.test(anovaDBCA1, "Tratamientos", p.adj= "bon",console=TRUE)##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## LSD t Test for V.sanguíneo
## P value adjustment method: bonferroni
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means and individual ( 95 %) CI
##
## V.sanguíneo std r LCL UCL Min Max
## A 5.0 1.1575837 5 4.187436 5.812564 4.1 6.5
## B 6.4 0.6403124 5 5.587436 7.212564 5.3 6.9
## C 4.2 0.2000000 5 3.387436 5.012564 4.0 4.5
## D 5.4 1.1113055 5 4.587436 6.212564 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of t: 3.152681
##
## Minimum Significant Difference: 1.662772
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 ab
## C 4.2 bplot(LSD.test(anovaDBCA1, "Tratamientos", p.adj= "bon",console=TRUE))##
## Study: anovaDBCA1 ~ "Tratamientos"
##
## LSD t Test for V.sanguíneo
## P value adjustment method: bonferroni
##
## Mean Square Error: 0.6954167
##
## Tratamientos, means and individual ( 95 %) CI
##
## V.sanguíneo std r LCL UCL Min Max
## A 5.0 1.1575837 5 4.187436 5.812564 4.1 6.5
## B 6.4 0.6403124 5 5.587436 7.212564 5.3 6.9
## C 4.2 0.2000000 5 3.387436 5.012564 4.0 4.5
## D 5.4 1.1113055 5 4.587436 6.212564 4.2 6.9
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of t: 3.152681
##
## Minimum Significant Difference: 1.662772
##
## Treatments with the same letter are not significantly different.
##
## V.sanguíneo groups
## B 6.4 a
## D 5.4 ab
## A 5.0 ab
## C 4.2 b
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2.5 Supuestos del Modelo en RStudio: Normalidad
(a) Normalidad de los residuos
shapiro.test(anovaDBCA1$res)##
## Shapiro-Wilk normality test
##
## data: anovaDBCA1$res
## W = 0.95529, p-value = 0.4545%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(b) Supuesto del modelo:Normalidad de los residuos
summary(anovaDBCA1$residuals)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -1.025 -0.550 -0.025 0.000 0.450 1.150sd((anovaDBCA1$residuals))## [1] 0.6627296%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(c) Supuesto del modelo:Normalidad de los residuos
boxplot(anovaDBCA1$residuals,col="lightblue")
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(d) Supuesto del modelo:Normalidad de los residuos
hist(anovaDBCA1$residuals, col="lightgreen", main = "Histograma de los Residuos",
freq = F, xlab="Residuos",ylab="Densidad")
lines(density(anovaDBCA1$residuals), col="red", lwd=3)
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(e) ** Prueba de Normalidad con Q-Q Plot**
qqnorm(anovaDBCA1$residuals,col="blue", lwd=3)
qqline(anovaDBCA1$residuals,col="red", lwd=3)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ## 2.6 Supuestos del Modelo en RStudio: Supuesto de Independencia
(a) Supuesto de Independencia
plot(anovaDBCA1$residuals,main = "Residuos vs Observaciones",col="red", lwd=3)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ## 2.6 Supuestos del Modelo en RStudio: Supuesto de Homocedasticidad
(a) Homocedasticidad
boxplot(anovaDBCA1$residuals~Bloques, xlab="Bloques",ylab="Residuos",
col = c("yellow", "blue", "white","green", "red"))
names(anovaDBCA1)## [1] "coefficients" "residuals" "effects" "rank"
## [5] "fitted.values" "assign" "qr" "df.residual"
## [9] "contrasts" "xlevels" "call" "terms"
## [13] "model"%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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(d) Homocedasticidad: Gráfico de predichos contra residuos estandarizados
pred=fitted(anovaDBCA1)
resid=rstandard(anovaDBCA1)
plot(pred,resid,xlab="Valores predichos", ylab="Residuos estandarizados",abline(h=0),col="red", lwd=3)
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(e) Homocedasticidad: Prueba de Bartlett para Lisina
bartlett.test(anovaDBCA1$residuals ~ Bloques)##
## Bartlett test of homogeneity of variances
##
## data: anovaDBCA1$residuals by Bloques
## Bartlett's K-squared = 1.2802, df = 4, p-value = 0.8647%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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