practica Diseños
Javier
2022-10-13
Diseño factorial simple en bloques al azar
Respuesta: rendimiento en gramos de 4 variedades de lechuga
Factor = N1: Morada romana, N2: Morada crespa, N3: Verde romana, N4: Verde crespa
Bloque 1: en descubierto. Bloque 2: en invernadero
set.seed(11)
rto = sort(c(rnorm(40,500,150), rnorm(40,1000,50)))
var = gl(4,10,80,c("Mromana","Mcrespa","Vromana","Vcrespa"))
cultivo = gl(2,40,80, c("Lote 1","Lote 2"))
dt=data.frame(cultivo,var,rto)
library(collapsibleTree)
collapsibleTree(dt,hierarchy = c("cultivo","var","rto"))Diseño factorial completo en arreglo completamente al azar
Respuesta: rendimiento en gramos de 4 variedades de lechuga
Factor 1 = N1: Morada romana, N2: Morada crespa, N3: Verde romana, N4: Verde crespa
Factor 2 = N1: riego a 50 - 70% de Capacidad de camp, N2: riego a 80 - 100% de Capacidad de campo.
set.seed(11)
rto = sort(c(rnorm(20,600,100), rnorm(20,1000,50)))
var = gl(4,5,40,c("Mromana","Mcrespa","Vromana","Vcrespa"))
riego = gl(2,20,40, c("50-70% CC","80-100% CC"))
dt=data.frame(riego,var,rto)
collapsibleTree(dt,hierarchy = c("riego","var","rto"))boxplot(dt$rto~dt$var)
boxplot(dt$rto~dt$riego)
Analisis de varianza
Modelo
\[y_{ijk} = \mu+\tau_i+\theta_j+\tau\theta_{ij}+\epsilon_{ijk} \\ i: 1\cdots4~ \text{variedades de lechuga} \\ j: 1,2 ~ \text{niveles de riego}\\k:\text{Repeticiones} \]
Hipotesis
\[H_o:\tau\theta = 0\\H_{o2}:\mu_{\tau1}=\mu_{\tau2}=\mu_{\tau3}=\mu_{\tau4}\\H_{o3}:\mu_{\theta1}=\mu_{\theta2}=\mu_{\theta3}=\mu_{\theta4}\\\]
mod1= aov(rto~var*riego,data = dt)
summary(mod1)## Df Sum Sq Mean Sq F value Pr(>F)
## var 3 120274 40091 67.92 5.73e-14 ***
## riego 1 1768027 1768027 2995.09 < 2e-16 ***
## var:riego 3 21682 7227 12.24 1.69e-05 ***
## Residuals 32 18890 590
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1tb = summary(mod1)
ifelse(unlist(tb)[19]<0.05,"Rechazo Ho", "No rechazo Ho")## Pr(>F)3
## "Rechazo Ho"ifelse(unlist(tb)[17]<0.05,"Rechazo Ho2", "No rechazo Ho2")## Pr(>F)1
## "Rechazo Ho2"ifelse(unlist(tb)[18]<0.05,"Rechazo Ho3", "No rechazo Ho3")## Pr(>F)2
## "Rechazo Ho3"TukeyHSD(x=mod1)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = rto ~ var * riego, data = dt)
##
## $var
## diff lwr upr p adj
## Mcrespa-Mromana 42.81826 13.379348 72.25718 0.0022285
## Vromana-Mromana 81.46308 52.024166 110.90199 0.0000001
## Vcrespa-Mromana 149.16966 119.730743 178.60857 0.0000000
## Vromana-Mcrespa 38.64482 9.205905 68.08373 0.0062413
## Vcrespa-Mcrespa 106.35140 76.912481 135.79031 0.0000000
## Vcrespa-Vromana 67.70658 38.267663 97.14549 0.0000032
##
## $riego
## diff lwr upr p adj
## 80-100% CC-50-70% CC 420.4792 404.8291 436.1293 0
##
## $`var:riego`
## diff lwr upr p adj
## Mcrespa:50-70% CC-Mromana:50-70% CC 59.40153 9.625441 109.17762 0.0106209
## Vromana:50-70% CC-Mromana:50-70% CC 114.22566 64.449572 164.00175 0.0000005
## Vcrespa:50-70% CC-Mromana:50-70% CC 212.25888 162.482794 262.03497 0.0000000
## Mromana:80-100% CC-Mromana:50-70% CC 476.69672 426.920630 526.47280 0.0000000
## Mcrespa:80-100% CC-Mromana:50-70% CC 502.93171 453.155626 552.70780 0.0000000
## Vromana:80-100% CC-Mromana:50-70% CC 525.39722 475.621131 575.17331 0.0000000
## Vcrespa:80-100% CC-Mromana:50-70% CC 562.77715 513.001062 612.55324 0.0000000
## Vromana:50-70% CC-Mcrespa:50-70% CC 54.82413 5.048044 104.60022 0.0226712
## Vcrespa:50-70% CC-Mcrespa:50-70% CC 152.85735 103.081266 202.63344 0.0000000
## Mromana:80-100% CC-Mcrespa:50-70% CC 417.29519 367.519102 467.07128 0.0000000
## Mcrespa:80-100% CC-Mcrespa:50-70% CC 443.53019 393.754098 493.30627 0.0000000
## Vromana:80-100% CC-Mcrespa:50-70% CC 465.99569 416.219604 515.77178 0.0000000
## Vcrespa:80-100% CC-Mcrespa:50-70% CC 503.37562 453.599535 553.15171 0.0000000
## Vcrespa:50-70% CC-Vromana:50-70% CC 98.03322 48.257135 147.80931 0.0000093
## Mromana:80-100% CC-Vromana:50-70% CC 362.47106 312.694971 412.24715 0.0000000
## Mcrespa:80-100% CC-Vromana:50-70% CC 388.70605 338.929967 438.48214 0.0000000
## Vromana:80-100% CC-Vromana:50-70% CC 411.17156 361.395472 460.94765 0.0000000
## Vcrespa:80-100% CC-Vromana:50-70% CC 448.55149 398.775403 498.32758 0.0000000
## Mromana:80-100% CC-Vcrespa:50-70% CC 264.43784 214.661749 314.21392 0.0000000
## Mcrespa:80-100% CC-Vcrespa:50-70% CC 290.67283 240.896744 340.44892 0.0000000
## Vromana:80-100% CC-Vcrespa:50-70% CC 313.13834 263.362250 362.91442 0.0000000
## Vcrespa:80-100% CC-Vcrespa:50-70% CC 350.51827 300.742181 400.29436 0.0000000
## Mcrespa:80-100% CC-Mromana:80-100% CC 26.23500 -23.541092 76.01108 0.6826761
## Vromana:80-100% CC-Mromana:80-100% CC 48.70050 -1.075586 98.47659 0.0587445
## Vcrespa:80-100% CC-Mromana:80-100% CC 86.08043 36.304345 135.85652 0.0000858
## Vromana:80-100% CC-Mcrespa:80-100% CC 22.46551 -27.310581 72.24159 0.8211062
## Vcrespa:80-100% CC-Mcrespa:80-100% CC 59.84544 10.069349 109.62152 0.0098509
## Vcrespa:80-100% CC-Vromana:80-100% CC 37.37993 -12.396156 87.15602 0.2606271Revisión de supuestos
\[H_{o4}: los~residuales~tienen~distribución~normal\]
shapiro.test(mod1$residuals)##
## Shapiro-Wilk normality test
##
## data: mod1$residuals
## W = 0.92401, p-value = 0.01032shap = shapiro.test(mod1$residuals)
ifelse(unlist(shap)[2]<0.05,"Rechazo Ho4", "No rechazo Ho4")## p.value
## "Rechazo Ho4"Homocedasticidad
\[H_{o5}: var_{\tau1}=var_{\tau2}=var_{\tau3}=var_{\tau4}\\H_{o6}: var_{\theta1}=var_{\theta2}=var_{\theta3}=var_{\theta4}\]
bartlett.test(rto~var,data = dt)##
## Bartlett test of homogeneity of variances
##
## data: rto by var
## Bartlett's K-squared = 0.758, df = 3, p-value = 0.8595bar=bartlett.test(rto~var,data = dt)
ifelse(unlist(bar)[3]<0.05,"Rechazo Ho5", "No rechazo Ho5")## p.value
## "No rechazo Ho5"bartlett.test(rto~riego,data = dt)##
## Bartlett test of homogeneity of variances
##
## data: rto by riego
## Bartlett's K-squared = 12.372, df = 1, p-value = 0.0004359bar2=bartlett.test(rto~riego,data = dt)
ifelse(unlist(bar2)[3]<0.05,"Rechazo Ho6", "No rechazo Ho6")## p.value
## "Rechazo Ho6"# las varianzas entre el rendimiento de las variedades son similares
# las varianzas entre el rendimiento de los riegos son estadisticamente diferenteskruskal.test(rto~var,data = dt)##
## Kruskal-Wallis rank sum test
##
## data: rto by var
## Kruskal-Wallis chi-squared = 9.1463, df = 3, p-value = 0.02741