Diseño factorial 3 factores
Ejercicio
El departamento de control de calidad de una planta de acabados textiles estudia el efecto de varios factores sobre el teñido de una tela de algodón y fibras sintéticas utilizada para fabricar camisas para caballero. Se seleccionaron tres operadores,tres duraciones del ciclo y dos temperaturas, y se tiñeron tres ejemplares pequeños de la tela bajo cada conjunto de condiciones. La tela terminada se comparó con un patrón , y se le asignó una evaluación numérica. Los datos se presentan enseguida. Analizar los datos y sacar conclusiones.
Duracion=as.factor((rep(c(40,50,60),each=18)))
Temperatura=rep(rep(c("300°","350°"),each=3),time=9)
Operador=as.factor(rep(c(1,2,3),time=18))
Resultado=c(23,27,31,24,38,34,24,28,32,23,36,36,25,26,29,28,35,39,
36,34,33,37,34,34,35,38,34,39,38,36,36,39,35,35,36,31,28,
35,26,26,36,28,24,35,27,29,37,26,27,34,25,25,34,24)
Datos=data.frame(Duracion,Temperatura,Operador,Resultado)head(Datos)summary(Datos)## Duracion Temperatura Operador Resultado
## 40:18 Length:54 1:18 Min. :23.00
## 50:18 Class :character 2:18 1st Qu.:27.00
## 60:18 Mode :character 3:18 Median :34.00
## Mean :31.56
## 3rd Qu.:36.00
## Max. :39.00Datos_lm=lm(Resultado~Duracion*Temperatura*Operador)
anova=aov(Datos_lm)
summary(anova)## Df Sum Sq Mean Sq F value Pr(>F)
## Duracion 2 436.0 218.00 66.508 8.14e-13 ***
## Temperatura 1 50.1 50.07 15.277 0.000393 ***
## Operador 2 261.3 130.67 39.864 7.44e-10 ***
## Duracion:Temperatura 2 78.8 39.41 12.023 0.000100 ***
## Duracion:Operador 4 355.7 88.92 27.127 1.98e-10 ***
## Temperatura:Operador 2 11.3 5.63 1.718 0.193895
## Duracion:Temperatura:Operador 4 46.2 11.55 3.523 0.015870 *
## Residuals 36 118.0 3.28
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1qf(0.05,2,36,lower.tail =F )## [1] 3.259446qf(0.05,1,36,lower.tail =F )## [1] 4.113165qf(0.05,4,36,lower.tail =F )## [1] 2.633532Con un nivel de confiabilidad del 95% tenemos que los efectos de los tratamientos de Duracion y Operador son significativo, sin embargo los efectos de los tratamiento para la Temperatura no es significativo. Para los efectos de las iteraciones de Duracion con Temperatura y Duracion con Operador observamos que son significativo, los efectos de la iteracion de Temperatura con Operador no es significativa y finalmente la iteracion de Duracion,Temperatura y Operador es significativa.
Graficos de iteraciones
library(ggplot2)
ggplot(Datos, aes(x = Duracion, y = Resultado,color = Operador,linetype=Operador)) +
stat_summary(fun = mean, geom ="line" ,aes(group = Operador), size = 1, ) +
stat_summary(fun = mean, geom = "point", aes(group = Operador), size = 2 )+
labs(title="Interacción Duracion:Operador")+theme_gray()
ggplot(Datos, aes(x = Temperatura, y = Resultado,color = Operador,linetype=Operador)) +
stat_summary(fun = mean, geom = "line", aes(group = Operador), size = 1, ) +
stat_summary(fun = mean, geom = "point", aes(group = Operador), size = 2 )+
labs(title="Interacción Temperatura:Operador")+theme_gray()
Supuestos
##
## Shapiro-Wilk normality test
##
## data: Resultado
## W = 0.90769, p-value = 0.0005275
Banda de confianza del 95%
ggplot(data=Datos,mapping = aes(x=Duracion,y=Resultado))+geom_boxplot()
ggplot(data=Datos,mapping = aes(x=Temperatura,y=Resultado))+geom_boxplot()
ggplot(data=Datos,mapping = aes(x=Operador,y=Resultado))+geom_boxplot()
ggplot(Datos, aes(x = Resultado)) +
stat_ecdf(
geom = "step", size = 1.5) +
scale_color_manual(values ="#00AFBB")+
labs(y = "f(weight)")
ECDF (o función de distribución acumulativa empírica)proporciona una visualización alternativa de la distribución. Informa para cualquier número dado el porcentaje de individuos que están por debajo de ese umbral.
residuo=residuals(Datos_lm)
fit=fitted(Datos_lm)
plot(x=fit,y=residuo,title("Grafica de los residuos"))
abline(h=0)
library("dplyr")
MSE=3.28
residuos=residuals(Datos_lm)
dij=data.frame(residuos/sqrt(MSE))
colnames(dij)="residuos_est"
dij=arrange(dij,residuos_est)
head(dij)print(c(dij[1,],dij[54,]))## [1] -1.656473 1.656473Se considera que no hay datos atipicos
TukeyHSD(aov(Datos_lm))## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Datos_lm)
##
## $Duracion
## diff lwr upr p adj
## 50-40 5.6666667 4.191563 7.1417702 0.0000000
## 60-40 -0.6666667 -2.141770 0.8084368 0.5174386
## 60-50 -6.3333333 -7.808437 -4.8582298 0.0000000
##
## $Temperatura
## diff lwr upr p adj
## 350°-300° 1.925926 0.9265913 2.925261 0.0003934
##
## $Operador
## diff lwr upr p adj
## 2-1 5.333333 3.8582298 6.808437 0.0000000
## 3-1 2.000000 0.5248965 3.475103 0.0058235
## 3-2 -3.333333 -4.8084368 -1.858230 0.0000089
##
## $`Duracion:Temperatura`
## diff lwr upr p adj
## 50:300°-40:300° 8.3333333 5.7656332 10.9010334 0.0000000
## 60:300°-40:300° 1.7777778 -0.7899223 4.3454779 0.3186030
## 40:350°-40:300° 5.3333333 2.7656332 7.9010334 0.0000046
## 50:350°-40:300° 8.3333333 5.7656332 10.9010334 0.0000000
## 60:350°-40:300° 2.2222222 -0.3454779 4.7899223 0.1224477
## 60:300°-50:300° -6.5555556 -9.1232556 -3.9878555 0.0000001
## 40:350°-50:300° -3.0000000 -5.5677001 -0.4322999 0.0141486
## 50:350°-50:300° 0.0000000 -2.5677001 2.5677001 1.0000000
## 60:350°-50:300° -6.1111111 -8.6788112 -3.5434110 0.0000003
## 40:350°-60:300° 3.5555556 0.9878555 6.1232556 0.0023718
## 50:350°-60:300° 6.5555556 3.9878555 9.1232556 0.0000001
## 60:350°-60:300° 0.4444444 -2.1232556 3.0121445 0.9949924
## 50:350°-40:350° 3.0000000 0.4322999 5.5677001 0.0141486
## 60:350°-40:350° -3.1111111 -5.6788112 -0.5434110 0.0100236
## 60:350°-50:350° -6.1111111 -8.6788112 -3.5434110 0.0000003
##
## $`Duracion:Operador`
## diff lwr upr p adj
## 50:1-40:1 11.8333333 8.38697904 15.2796876 0.0000000
## 60:1-40:1 2.0000000 -1.44635429 5.4463543 0.6094198
## 40:2-40:1 7.1666667 3.72031238 10.6130210 0.0000017
## 50:2-40:1 12.0000000 8.55364571 15.4463543 0.0000000
## 60:2-40:1 10.6666667 7.22031238 14.1130210 0.0000000
## 40:3-40:1 9.0000000 5.55364571 12.4463543 0.0000000
## 50:3-40:1 9.3333333 5.88697904 12.7796876 0.0000000
## 60:3-40:1 1.5000000 -1.94635429 4.9463543 0.8765649
## 60:1-50:1 -9.8333333 -13.27968762 -6.3869790 0.0000000
## 40:2-50:1 -4.6666667 -8.11302096 -1.2203124 0.0022191
## 50:2-50:1 0.1666667 -3.27968762 3.6130210 1.0000000
## 60:2-50:1 -1.1666667 -4.61302096 2.2796876 0.9678544
## 40:3-50:1 -2.8333333 -6.27968762 0.6130210 0.1799642
## 50:3-50:1 -2.5000000 -5.94635429 0.9463543 0.3188565
## 60:3-50:1 -10.3333333 -13.77968762 -6.8869790 0.0000000
## 40:2-60:1 5.1666667 1.72031238 8.6130210 0.0005489
## 50:2-60:1 10.0000000 6.55364571 13.4463543 0.0000000
## 60:2-60:1 8.6666667 5.22031238 12.1130210 0.0000000
## 40:3-60:1 7.0000000 3.55364571 10.4463543 0.0000028
## 50:3-60:1 7.3333333 3.88697904 10.7796876 0.0000011
## 60:3-60:1 -0.5000000 -3.94635429 2.9463543 0.9999077
## 50:2-40:2 4.8333333 1.38697904 8.2796876 0.0013999
## 60:2-40:2 3.5000000 0.05364571 6.9463543 0.0441881
## 40:3-40:2 1.8333333 -1.61302096 5.2796876 0.7102602
## 50:3-40:2 2.1666667 -1.27968762 5.6130210 0.5063157
## 60:3-40:2 -5.6666667 -9.11302096 -2.2203124 0.0001313
## 60:2-50:2 -1.3333333 -4.77968762 2.1130210 0.9320230
## 40:3-50:2 -3.0000000 -6.44635429 0.4463543 0.1304605
## 50:3-50:2 -2.6666667 -6.11302096 0.7796876 0.2425915
## 60:3-50:2 -10.5000000 -13.94635429 -7.0536457 0.0000000
## 40:3-60:2 -1.6666667 -5.11302096 1.7796876 0.8014293
## 50:3-60:2 -1.3333333 -4.77968762 2.1130210 0.9320230
## 60:3-60:2 -9.1666667 -12.61302096 -5.7203124 0.0000000
## 50:3-40:3 0.3333333 -3.11302096 3.7796876 0.9999959
## 60:3-40:3 -7.5000000 -10.94635429 -4.0536457 0.0000007
## 60:3-50:3 -7.8333333 -11.27968762 -4.3869790 0.0000003
##
## $`Temperatura:Operador`
## diff lwr upr p adj
## 350°:1-300°:1 0.8888889 -1.6788112 3.45658898 0.9005660
## 300°:2-300°:1 4.2222222 1.6545221 6.78992231 0.0002401
## 350°:2-300°:1 7.3333333 4.7656332 9.90103342 0.0000000
## 300°:3-300°:1 1.5555556 -1.0121445 4.12325565 0.4646556
## 350°:3-300°:1 3.3333333 0.7656332 5.90103342 0.0049313
## 300°:2-350°:1 3.3333333 0.7656332 5.90103342 0.0049313
## 350°:2-350°:1 6.4444444 3.8767444 9.01214454 0.0000001
## 300°:3-350°:1 0.6666667 -1.9010334 3.23436676 0.9689935
## 350°:3-350°:1 2.4444444 -0.1232556 5.01214454 0.0697355
## 350°:2-300°:2 3.1111111 0.5434110 5.67881120 0.0100236
## 300°:3-300°:2 -2.6666667 -5.2343668 -0.09896658 0.0379175
## 350°:3-300°:2 -0.8888889 -3.4565890 1.67881120 0.9005660
## 300°:3-350°:2 -5.7777778 -8.3454779 -3.21007769 0.0000009
## 350°:3-350°:2 -4.0000000 -6.5677001 -1.43229991 0.0005215
## 350°:3-300°:3 1.7777778 -0.7899223 4.34547787 0.3186030
##
## $`Duracion:Temperatura:Operador`
## diff lwr upr p adj
## 50:300°:1-40:300°:1 1.166667e+01 6.1227575 17.2105758 0.0000003
## 60:300°:1-40:300°:1 2.333333e+00 -3.2105758 7.8772425 0.9759357
## 40:350°:1-40:300°:1 1.000000e+00 -4.5439092 6.5439092 0.9999994
## 50:350°:1-40:300°:1 1.300000e+01 7.4560908 18.5439092 0.0000000
## 60:350°:1-40:300°:1 2.666667e+00 -2.8772425 8.2105758 0.9268932
## 40:300°:2-40:300°:1 3.000000e+00 -2.5439092 8.5439092 0.8360873
## 50:300°:2-40:300°:1 1.300000e+01 7.4560908 18.5439092 0.0000000
## 60:300°:2-40:300°:1 1.066667e+01 5.1227575 16.2105758 0.0000023
## 40:350°:2-40:300°:1 1.233333e+01 6.7894242 17.8772425 0.0000001
## 50:350°:2-40:300°:1 1.200000e+01 6.4560908 17.5439092 0.0000002
## 60:350°:2-40:300°:1 1.166667e+01 6.1227575 17.2105758 0.0000003
## 40:300°:3-40:300°:1 6.666667e+00 1.1227575 12.2105758 0.0068317
## 50:300°:3-40:300°:1 1.000000e+01 4.4560908 15.5439092 0.0000089
## 60:300°:3-40:300°:1 2.000000e+00 -3.5439092 7.5439092 0.9947478
## 40:350°:3-40:300°:1 1.233333e+01 6.7894242 17.8772425 0.0000001
## 50:350°:3-40:300°:1 9.666667e+00 4.1227575 15.2105758 0.0000176
## 60:350°:3-40:300°:1 2.000000e+00 -3.5439092 7.5439092 0.9947478
## 60:300°:1-50:300°:1 -9.333333e+00 -14.8772425 -3.7894242 0.0000345
## 40:350°:1-50:300°:1 -1.066667e+01 -16.2105758 -5.1227575 0.0000023
## 50:350°:1-50:300°:1 1.333333e+00 -4.2105758 6.8772425 0.9999643
## 60:350°:1-50:300°:1 -9.000000e+00 -14.5439092 -3.4560908 0.0000678
## 40:300°:2-50:300°:1 -8.666667e+00 -14.2105758 -3.1227575 0.0001332
## 50:300°:2-50:300°:1 1.333333e+00 -4.2105758 6.8772425 0.9999643
## 60:300°:2-50:300°:1 -1.000000e+00 -6.5439092 4.5439092 0.9999994
## 40:350°:2-50:300°:1 6.666667e-01 -4.8772425 6.2105758 1.0000000
## 50:350°:2-50:300°:1 3.333333e-01 -5.2105758 5.8772425 1.0000000
## 60:350°:2-50:300°:1 7.105427e-15 -5.5439092 5.5439092 1.0000000
## 40:300°:3-50:300°:1 -5.000000e+00 -10.5439092 0.5439092 0.1169913
## 50:300°:3-50:300°:1 -1.666667e+00 -7.2105758 3.8772425 0.9993500
## 60:300°:3-50:300°:1 -9.666667e+00 -15.2105758 -4.1227575 0.0000176
## 40:350°:3-50:300°:1 6.666667e-01 -4.8772425 6.2105758 1.0000000
## 50:350°:3-50:300°:1 -2.000000e+00 -7.5439092 3.5439092 0.9947478
## 60:350°:3-50:300°:1 -9.666667e+00 -15.2105758 -4.1227575 0.0000176
## 40:350°:1-60:300°:1 -1.333333e+00 -6.8772425 4.2105758 0.9999643
## 50:350°:1-60:300°:1 1.066667e+01 5.1227575 16.2105758 0.0000023
## 60:350°:1-60:300°:1 3.333333e-01 -5.2105758 5.8772425 1.0000000
## 40:300°:2-60:300°:1 6.666667e-01 -4.8772425 6.2105758 1.0000000
## 50:300°:2-60:300°:1 1.066667e+01 5.1227575 16.2105758 0.0000023
## 60:300°:2-60:300°:1 8.333333e+00 2.7894242 13.8772425 0.0002609
## 40:350°:2-60:300°:1 1.000000e+01 4.4560908 15.5439092 0.0000089
## 50:350°:2-60:300°:1 9.666667e+00 4.1227575 15.2105758 0.0000176
## 60:350°:2-60:300°:1 9.333333e+00 3.7894242 14.8772425 0.0000345
## 40:300°:3-60:300°:1 4.333333e+00 -1.2105758 9.8772425 0.2851252
## 50:300°:3-60:300°:1 7.666667e+00 2.1227575 13.2105758 0.0009884
## 60:300°:3-60:300°:1 -3.333333e-01 -5.8772425 5.2105758 1.0000000
## 40:350°:3-60:300°:1 1.000000e+01 4.4560908 15.5439092 0.0000089
## 50:350°:3-60:300°:1 7.333333e+00 1.7894242 12.8772425 0.0019036
## 60:350°:3-60:300°:1 -3.333333e-01 -5.8772425 5.2105758 1.0000000
## 50:350°:1-40:350°:1 1.200000e+01 6.4560908 17.5439092 0.0000002
## 60:350°:1-40:350°:1 1.666667e+00 -3.8772425 7.2105758 0.9993500
## 40:300°:2-40:350°:1 2.000000e+00 -3.5439092 7.5439092 0.9947478
## 50:300°:2-40:350°:1 1.200000e+01 6.4560908 17.5439092 0.0000002
## 60:300°:2-40:350°:1 9.666667e+00 4.1227575 15.2105758 0.0000176
## 40:350°:2-40:350°:1 1.133333e+01 5.7894242 16.8772425 0.0000006
## 50:350°:2-40:350°:1 1.100000e+01 5.4560908 16.5439092 0.0000012
## 60:350°:2-40:350°:1 1.066667e+01 5.1227575 16.2105758 0.0000023
## 40:300°:3-40:350°:1 5.666667e+00 0.1227575 11.2105758 0.0407710
## 50:300°:3-40:350°:1 9.000000e+00 3.4560908 14.5439092 0.0000678
## 60:300°:3-40:350°:1 1.000000e+00 -4.5439092 6.5439092 0.9999994
## 40:350°:3-40:350°:1 1.133333e+01 5.7894242 16.8772425 0.0000006
## 50:350°:3-40:350°:1 8.666667e+00 3.1227575 14.2105758 0.0001332
## 60:350°:3-40:350°:1 1.000000e+00 -4.5439092 6.5439092 0.9999994
## 60:350°:1-50:350°:1 -1.033333e+01 -15.8772425 -4.7894242 0.0000046
## 40:300°:2-50:350°:1 -1.000000e+01 -15.5439092 -4.4560908 0.0000089
## 50:300°:2-50:350°:1 -7.105427e-15 -5.5439092 5.5439092 1.0000000
## 60:300°:2-50:350°:1 -2.333333e+00 -7.8772425 3.2105758 0.9759357
## 40:350°:2-50:350°:1 -6.666667e-01 -6.2105758 4.8772425 1.0000000
## 50:350°:2-50:350°:1 -1.000000e+00 -6.5439092 4.5439092 0.9999994
## 60:350°:2-50:350°:1 -1.333333e+00 -6.8772425 4.2105758 0.9999643
## 40:300°:3-50:350°:1 -6.333333e+00 -11.8772425 -0.7894242 0.0126556
## 50:300°:3-50:350°:1 -3.000000e+00 -8.5439092 2.5439092 0.8360873
## 60:300°:3-50:350°:1 -1.100000e+01 -16.5439092 -5.4560908 0.0000012
## 40:350°:3-50:350°:1 -6.666667e-01 -6.2105758 4.8772425 1.0000000
## 50:350°:3-50:350°:1 -3.333333e+00 -8.8772425 2.2105758 0.7070210
## 60:350°:3-50:350°:1 -1.100000e+01 -16.5439092 -5.4560908 0.0000012
## 40:300°:2-60:350°:1 3.333333e-01 -5.2105758 5.8772425 1.0000000
## 50:300°:2-60:350°:1 1.033333e+01 4.7894242 15.8772425 0.0000046
## 60:300°:2-60:350°:1 8.000000e+00 2.4560908 13.5439092 0.0005093
## 40:350°:2-60:350°:1 9.666667e+00 4.1227575 15.2105758 0.0000176
## 50:350°:2-60:350°:1 9.333333e+00 3.7894242 14.8772425 0.0000345
## 60:350°:2-60:350°:1 9.000000e+00 3.4560908 14.5439092 0.0000678
## 40:300°:3-60:350°:1 4.000000e+00 -1.5439092 9.5439092 0.4113870
## 50:300°:3-60:350°:1 7.333333e+00 1.7894242 12.8772425 0.0019036
## 60:300°:3-60:350°:1 -6.666667e-01 -6.2105758 4.8772425 1.0000000
## 40:350°:3-60:350°:1 9.666667e+00 4.1227575 15.2105758 0.0000176
## 50:350°:3-60:350°:1 7.000000e+00 1.4560908 12.5439092 0.0036294
## 60:350°:3-60:350°:1 -6.666667e-01 -6.2105758 4.8772425 1.0000000
## 50:300°:2-40:300°:2 1.000000e+01 4.4560908 15.5439092 0.0000089
## 60:300°:2-40:300°:2 7.666667e+00 2.1227575 13.2105758 0.0009884
## 40:350°:2-40:300°:2 9.333333e+00 3.7894242 14.8772425 0.0000345
## 50:350°:2-40:300°:2 9.000000e+00 3.4560908 14.5439092 0.0000678
## 60:350°:2-40:300°:2 8.666667e+00 3.1227575 14.2105758 0.0001332
## 40:300°:3-40:300°:2 3.666667e+00 -1.8772425 9.2105758 0.5578421
## 50:300°:3-40:300°:2 7.000000e+00 1.4560908 12.5439092 0.0036294
## 60:300°:3-40:300°:2 -1.000000e+00 -6.5439092 4.5439092 0.9999994
## 40:350°:3-40:300°:2 9.333333e+00 3.7894242 14.8772425 0.0000345
## 50:350°:3-40:300°:2 6.666667e+00 1.1227575 12.2105758 0.0068317
## 60:350°:3-40:300°:2 -1.000000e+00 -6.5439092 4.5439092 0.9999994
## 60:300°:2-50:300°:2 -2.333333e+00 -7.8772425 3.2105758 0.9759357
## 40:350°:2-50:300°:2 -6.666667e-01 -6.2105758 4.8772425 1.0000000
## 50:350°:2-50:300°:2 -1.000000e+00 -6.5439092 4.5439092 0.9999994
## 60:350°:2-50:300°:2 -1.333333e+00 -6.8772425 4.2105758 0.9999643
## 40:300°:3-50:300°:2 -6.333333e+00 -11.8772425 -0.7894242 0.0126556
## 50:300°:3-50:300°:2 -3.000000e+00 -8.5439092 2.5439092 0.8360873
## 60:300°:3-50:300°:2 -1.100000e+01 -16.5439092 -5.4560908 0.0000012
## 40:350°:3-50:300°:2 -6.666667e-01 -6.2105758 4.8772425 1.0000000
## 50:350°:3-50:300°:2 -3.333333e+00 -8.8772425 2.2105758 0.7070210
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