Módulo 3
Alberto Montezuma
2026-03-12
Módulo 3
Distribución Normal
x<-rnorm(5000,0.0,1)
x2<-seq(-4,4,length=200)
hist(x,breaks=30,freq = FALSE)
lines(x2,dnorm(x2,0,1),type="l")
print(mean(x))## [1] 0.01725774abline(v=-1.96)
abline(v=1.96)
x2<-seq(-4,4,length=200)
plot(x2,dnorm(x2,0,1),type = "l")
pnorm(1.96,0,1) #Probabilidad acumulativa## [1] 0.9750021qnorm(0.97,0,1) #quantile## [1] 1.880794Ho: media grupo_A <> media grupo_B Ha: media grupo_A = media grupo_B
grupo_A <- rnorm(30, mean = 75, sd = 10)
grupo_B <- rnorm(30, mean = 80, sd = 12)
resultado <- t.test(grupo_A, grupo_B,
alternative = "two.sided",
var.equal = FALSE)
print(resultado)##
## Welch Two Sample t-test
##
## data: grupo_A and grupo_B
## t = -3.0321, df = 57.462, p-value = 0.00364
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -15.283842 -3.127017
## sample estimates:
## mean of x mean of y
## 71.80845 81.01388x<-seq(50,120,length=200)
plot(x,dnorm(x,75,5),type="l")
lines(x,dnorm(x,90,5),type="l")
qqnorm(grupo_B)
qqline(grupo_B)
Ho: no es normAl Ha: es normal pvalue>0.05 se acepta Ha
shapiro.test(grupo_A)##
## Shapiro-Wilk normality test
##
## data: grupo_A
## W = 0.97858, p-value = 0.7866##Prueba de ANOVA
parcela<-c("A","A","A","A","B","B","B","B","C","C","C","C")
datos<-c(rnorm(4,12,2),rnorm(4,25,2.3),rnorm(4,11,1.9))
df<-data.frame(parcela=parcela,datos=datos)
df$parcela<-factor(df$parcela)
df## parcela datos
## 1 A 9.458031
## 2 A 8.184695
## 3 A 11.737808
## 4 A 10.692292
## 5 B 23.270964
## 6 B 26.194433
## 7 B 23.287987
## 8 B 25.170899
## 9 C 13.451401
## 10 C 9.415386
## 11 C 11.181436
## 12 C 9.436402Ho: media 1 = media2 = media 3 Ha: por lo menos uno de los tratamientos es diferente pvalue>0.05
modelo<-aov(datos~parcela,data=df)
summary(modelo)## Df Sum Sq Mean Sq F value Pr(>F)
## parcela 2 526.8 263.4 97.49 7.96e-07 ***
## Residuals 9 24.3 2.7
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1boxplot(datos~parcela,data=df)
url<-"https://sigpri.com/seminarioR/DatosModulo3.csv"
df2<-read.csv(url)
df2$Especie<-factor(df2$Especie)
df2$Tratamiento<-factor(df2$Tratamiento)
df2## Especie Tratamiento Valor
## 1 A trat1 6.7415120
## 2 A trat1 1.5898228
## 3 A trat1 7.3666530
## 4 A trat1 5.3171126
## 5 A trat1 1.3756336
## 6 A trat1 4.7247241
## 7 A trat2 3.6096438
## 8 A trat2 1.0660475
## 9 A trat2 9.9657925
## 10 A trat2 9.5981954
## 11 A trat2 0.4573696
## 12 A trat2 4.8660935
## 13 A trat3 3.4173670
## 14 A trat3 2.3257174
## 15 A trat3 0.2024711
## 16 A trat3 7.8728936
## 17 A trat3 1.3620005
## 18 A trat3 8.9337429
## 19 B trat1 3.2295988
## 20 B trat1 5.8473325
## 21 B trat1 8.2547306
## 22 B trat1 6.3732184
## 23 B trat1 7.0241692
## 24 B trat1 5.2308266
## 25 B trat2 4.0866511
## 26 B trat2 4.3561235
## 27 B trat2 8.7170661
## 28 B trat2 6.5464608
## 29 B trat2 0.3247144
## 30 B trat2 0.5892915
## 31 B trat3 9.6694802
## 32 B trat3 5.5677655
## 33 B trat3 2.7433846
## 34 B trat3 7.3186340
## 35 B trat3 3.4272121
## 36 B trat3 0.9509871modelo2<-aov(Valor~Especie*Tratamiento,data=df2)
summary(modelo2)## Df Sum Sq Mean Sq F value Pr(>F)
## Especie 1 2.49 2.488 0.249 0.621
## Tratamiento 2 4.59 2.297 0.230 0.796
## Especie:Tratamiento 2 8.65 4.323 0.433 0.653
## Residuals 30 299.84 9.995qqnorm(modelo2$residuals)
qqline(modelo2$residuals)
shapiro.test(modelo2$residuals)##
## Shapiro-Wilk normality test
##
## data: modelo2$residuals
## W = 0.94173, p-value = 0.05752TukeyHSD(modelo2)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Valor ~ Especie * Tratamiento, data = df2)
##
## $Especie
## diff lwr upr p adj
## B-A 0.5258252 -1.626335 2.677986 0.621435
##
## $Tratamiento
## diff lwr upr p adj
## trat2-trat1 -0.74099040 -3.922779 2.440798 0.8348484
## trat3-trat1 -0.77363988 -3.955429 2.408149 0.8214834
## trat3-trat2 -0.03264948 -3.214438 3.149139 0.9996472
##
## $`Especie:Tratamiento`
## diff lwr upr p adj
## B:trat1-A:trat1 1.47406966 -4.077591 7.025730 0.9638858
## A:trat2-A:trat1 0.40794732 -5.143713 5.959608 0.9999148
## B:trat2-A:trat1 -0.41585846 -5.967519 5.135802 0.9999063
## A:trat3-A:trat1 -0.50021096 -6.051871 5.051450 0.9997675
## B:trat3-A:trat1 0.42700086 -5.124660 5.978661 0.9998932
## A:trat2-B:trat1 -1.06612235 -6.617783 4.485538 0.9913587
## B:trat2-B:trat1 -1.88992812 -7.441589 3.661732 0.9021165
## A:trat3-B:trat1 -1.97428062 -7.525941 3.577380 0.8848057
## B:trat3-B:trat1 -1.04706881 -6.598729 4.504592 0.9920442
## B:trat2-A:trat2 -0.82380578 -6.375466 4.727855 0.9974052
## A:trat3-A:trat2 -0.90815827 -6.459819 4.643502 0.9958906
## B:trat3-A:trat2 0.01905354 -5.532607 5.570714 1.0000000
## A:trat3-B:trat2 -0.08435250 -5.636013 5.467308 1.0000000
## B:trat3-B:trat2 0.84285932 -4.708801 6.394520 0.9971084
## B:trat3-A:trat3 0.92721181 -4.624449 6.478872 0.9954711boxplot(Valor~Especie+Tratamiento,data=df2)
Especie<-rep(c("A","B"),each=18)
Tratamiento<-rep(rep(c("Trat1","Trat2","Trat3"),each=6),2)
Tratamiento## [1] "Trat1" "Trat1" "Trat1" "Trat1" "Trat1" "Trat1" "Trat2" "Trat2" "Trat2"
## [10] "Trat2" "Trat2" "Trat2" "Trat3" "Trat3" "Trat3" "Trat3" "Trat3" "Trat3"
## [19] "Trat1" "Trat1" "Trat1" "Trat1" "Trat1" "Trat1" "Trat2" "Trat2" "Trat2"
## [28] "Trat2" "Trat2" "Trat2" "Trat3" "Trat3" "Trat3" "Trat3" "Trat3" "Trat3"Valor<-c(rnorm(6,5,0.9),rnorm(6,8,0.9),rnorm(6,4,0.9),rnorm(6,7,0.9),rnorm(6,5,0.9),rnorm(6,5.8,0.9))
df3<-data.frame(Especie=Especie,Tratamiento=Tratamiento,Valor=Valor)
boxplot(Valor~Especie+Tratamiento,data=df3)
modelo3<-aov(Valor~Especie*Tratamiento,data=df3)
summary(modelo3)## Df Sum Sq Mean Sq F value Pr(>F)
## Especie 1 1.39 1.386 1.498 0.23053
## Tratamiento 2 12.43 6.214 6.713 0.00389 **
## Especie:Tratamiento 2 53.37 26.684 28.828 1.04e-07 ***
## Residuals 30 27.77 0.926
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1qqnorm(modelo3$residuals)
qqline(modelo3$residuals)
shapiro.test(modelo3$residuals)##
## Shapiro-Wilk normality test
##
## data: modelo3$residuals
## W = 0.9818, p-value = 0.8044TukeyHSD(modelo3)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Valor ~ Especie * Tratamiento, data = df3)
##
## $Especie
## diff lwr upr p adj
## B-A 0.3924927 -0.2624621 1.047447 0.2305281
##
## $Tratamiento
## diff lwr upr p adj
## Trat2-Trat1 -0.2852273 -1.253523 0.6830684 0.7500398
## Trat3-Trat1 -1.3642941 -2.332590 -0.3959985 0.0043890
## Trat3-Trat2 -1.0790668 -2.047362 -0.1107712 0.0264439
##
## $`Especie:Tratamiento`
## diff lwr upr p adj
## B:Trat1-A:Trat1 1.9385458 0.2490406 3.6280510 0.0172279
## A:Trat2-A:Trat1 2.2067878 0.5172826 3.8962931 0.0050216
## B:Trat2-A:Trat1 -0.8386966 -2.5282018 0.8508086 0.6607972
## A:Trat3-A:Trat1 -1.5372296 -3.2267348 0.1522756 0.0911353
## B:Trat3-A:Trat1 0.7471872 -0.9423181 2.4366924 0.7579726
## A:Trat2-B:Trat1 0.2682420 -1.4212632 1.9577473 0.9964286
## B:Trat2-B:Trat1 -2.7772424 -4.4667476 -1.0877372 0.0003104
## A:Trat3-B:Trat1 -3.4757754 -5.1652806 -1.7862702 0.0000095
## B:Trat3-B:Trat1 -1.1913586 -2.8808639 0.4981466 0.2927104
## B:Trat2-A:Trat2 -3.0454844 -4.7349896 -1.3559792 0.0000813
## A:Trat3-A:Trat2 -3.7440174 -5.4335227 -2.0545122 0.0000025
## B:Trat3-A:Trat2 -1.4596007 -3.1491059 0.2299045 0.1215241
## A:Trat3-B:Trat2 -0.6985330 -2.3880382 0.9909722 0.8049168
## B:Trat3-B:Trat2 1.5858838 -0.1036215 3.2753890 0.0755981
## B:Trat3-A:Trat3 2.2844168 0.5949116 3.9739220 0.0034730boxplot(Valor~Especie+Tratamiento,data=df3)