Problema 1

df<-read.csv("https://raw.githubusercontent.com/PedroGonzalezBeermann2020/DExperimental2021/main/Problema1.csv")
df

##       Instructor          Town Sodium
## 1   BrendonSmall Squiggleville   1200
## 2   BrendonSmall Squiggleville   1400
## 3   BrendonSmall Squiggleville   1350
## 4   BrendonSmall Metalocalypse    950
## 5   BrendonSmall Squiggleville   1400
## 6   BrendonSmall Squiggleville   1150
## 7   BrendonSmall Squiggleville   1300
## 8   BrendonSmall Metalocalypse   1325
## 9   BrendonSmall Metalocalypse   1425
## 10  BrendonSmall Squiggleville   1500
## 11  BrendonSmall Squiggleville   1250
## 12  BrendonSmall Metalocalypse   1150
## 13  BrendonSmall Metalocalypse    950
## 14  BrendonSmall Squiggleville   1150
## 15  BrendonSmall Metalocalypse   1600
## 16  BrendonSmall Metalocalypse   1300
## 17  BrendonSmall Metalocalypse   1050
## 18  BrendonSmall Metalocalypse   1300
## 19  BrendonSmall Squiggleville   1700
## 20  BrendonSmall Squiggleville   1300
## 21  CoachMcGuirk Squiggleville   1100
## 22  CoachMcGuirk Squiggleville   1200
## 23  CoachMcGuirk Squiggleville   1250
## 24  CoachMcGuirk Metalocalypse   1050
## 25  CoachMcGuirk Metalocalypse   1200
## 26  CoachMcGuirk Metalocalypse   1250
## 27  CoachMcGuirk Squiggleville   1350
## 28  CoachMcGuirk Squiggleville   1350
## 29  CoachMcGuirk Squiggleville   1325
## 30  CoachMcGuirk Squiggleville   1525
## 31  CoachMcGuirk Squiggleville   1225
## 32  CoachMcGuirk Squiggleville   1125
## 33  CoachMcGuirk Metalocalypse   1000
## 34  CoachMcGuirk Metalocalypse   1125
## 35  CoachMcGuirk Squiggleville   1400
## 36  CoachMcGuirk Metalocalypse   1200
## 37  CoachMcGuirk Squiggleville   1150
## 38  CoachMcGuirk Squiggleville   1400
## 39  CoachMcGuirk Squiggleville   1500
## 40  CoachMcGuirk Squiggleville   1200
## 41 MelissaRobins Metalocalypse    900
## 42 MelissaRobins Metalocalypse   1100
## 43 MelissaRobins Metalocalypse   1150
## 44 MelissaRobins Metalocalypse    950
## 45 MelissaRobins Metalocalypse   1100
## 46 MelissaRobins Metalocalypse   1150
## 47 MelissaRobins Squiggleville   1250
## 48 MelissaRobins Squiggleville   1250
## 49 MelissaRobins Squiggleville   1225
## 50 MelissaRobins Squiggleville   1325
## 51 MelissaRobins Metalocalypse   1125
## 52 MelissaRobins Metalocalypse   1025
## 53 MelissaRobins Metalocalypse    950
## 54 MelissaRobins Metalocalypse    925
## 55 MelissaRobins Squiggleville   1200
## 56 MelissaRobins Metalocalypse   1100
## 57 MelissaRobins Metalocalypse    950
## 58 MelissaRobins Metalocalypse   1300
## 59 MelissaRobins Squiggleville   1400
## 60 MelissaRobins Metalocalypse   1100

df$Instructor=factor(df$Instructor)
df$Town=factor(df$Town)
df$Sodium=as.numeric(df$Sodium)
df

##       Instructor          Town Sodium
## 1   BrendonSmall Squiggleville   1200
## 2   BrendonSmall Squiggleville   1400
## 3   BrendonSmall Squiggleville   1350
## 4   BrendonSmall Metalocalypse    950
## 5   BrendonSmall Squiggleville   1400
## 6   BrendonSmall Squiggleville   1150
## 7   BrendonSmall Squiggleville   1300
## 8   BrendonSmall Metalocalypse   1325
## 9   BrendonSmall Metalocalypse   1425
## 10  BrendonSmall Squiggleville   1500
## 11  BrendonSmall Squiggleville   1250
## 12  BrendonSmall Metalocalypse   1150
## 13  BrendonSmall Metalocalypse    950
## 14  BrendonSmall Squiggleville   1150
## 15  BrendonSmall Metalocalypse   1600
## 16  BrendonSmall Metalocalypse   1300
## 17  BrendonSmall Metalocalypse   1050
## 18  BrendonSmall Metalocalypse   1300
## 19  BrendonSmall Squiggleville   1700
## 20  BrendonSmall Squiggleville   1300
## 21  CoachMcGuirk Squiggleville   1100
## 22  CoachMcGuirk Squiggleville   1200
## 23  CoachMcGuirk Squiggleville   1250
## 24  CoachMcGuirk Metalocalypse   1050
## 25  CoachMcGuirk Metalocalypse   1200
## 26  CoachMcGuirk Metalocalypse   1250
## 27  CoachMcGuirk Squiggleville   1350
## 28  CoachMcGuirk Squiggleville   1350
## 29  CoachMcGuirk Squiggleville   1325
## 30  CoachMcGuirk Squiggleville   1525
## 31  CoachMcGuirk Squiggleville   1225
## 32  CoachMcGuirk Squiggleville   1125
## 33  CoachMcGuirk Metalocalypse   1000
## 34  CoachMcGuirk Metalocalypse   1125
## 35  CoachMcGuirk Squiggleville   1400
## 36  CoachMcGuirk Metalocalypse   1200
## 37  CoachMcGuirk Squiggleville   1150
## 38  CoachMcGuirk Squiggleville   1400
## 39  CoachMcGuirk Squiggleville   1500
## 40  CoachMcGuirk Squiggleville   1200
## 41 MelissaRobins Metalocalypse    900
## 42 MelissaRobins Metalocalypse   1100
## 43 MelissaRobins Metalocalypse   1150
## 44 MelissaRobins Metalocalypse    950
## 45 MelissaRobins Metalocalypse   1100
## 46 MelissaRobins Metalocalypse   1150
## 47 MelissaRobins Squiggleville   1250
## 48 MelissaRobins Squiggleville   1250
## 49 MelissaRobins Squiggleville   1225
## 50 MelissaRobins Squiggleville   1325
## 51 MelissaRobins Metalocalypse   1125
## 52 MelissaRobins Metalocalypse   1025
## 53 MelissaRobins Metalocalypse    950
## 54 MelissaRobins Metalocalypse    925
## 55 MelissaRobins Squiggleville   1200
## 56 MelissaRobins Metalocalypse   1100
## 57 MelissaRobins Metalocalypse    950
## 58 MelissaRobins Metalocalypse   1300
## 59 MelissaRobins Squiggleville   1400
## 60 MelissaRobins Metalocalypse   1100

library(lme4)

## Loading required package: Matrix

modelo<-lmer(Sodium~(1|Instructor)+(1|Town), data=df)
#modelo<-lm(Sodium~Instructor*Town, data = df)
summary(modelo)

## Linear mixed model fit by REML ['lmerMod']
## Formula: Sodium ~ (1 | Instructor) + (1 | Town)
##    Data: df
## 
## REML criterion at convergence: 763.3
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.64670 -0.72097  0.03089  0.45329  2.87607 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  Instructor (Intercept)  2954     54.35  
##  Town       (Intercept) 12500    111.81  
##  Residual               20655    143.72  
## Number of obs: 60, groups:  Instructor, 3; Town, 2
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  1216.61      87.06   13.97

with(df, interaction.plot(x.factor = Instructor, trace.factor = Town, response = Sodium))

with(df, interaction.plot(x.factor = Town, trace.factor = Instructor, response = Sodium))

modelo1<-lm(Sodium~Instructor*Town, data=df)
anova<-aov(modelo1)
summary(anova)

##                 Df  Sum Sq Mean Sq F value   Pr(>F)    
## Instructor       2  290146  145073   6.920 0.002110 ** 
## Town             1  329551  329551  15.721 0.000218 ***
## Instructor:Town  2   26269   13135   0.627 0.538263    
## Residuals       54 1131992   20963                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Cálculo de F° con A fijo y B Aleatorio

A= Instructor B= Town AB= Interacción

F°A= CMA/CMAB F°A= 145073/13135 F°A= 11.04477

F°B= CMB/CMAB F°B= 329551/13135 F°B= 25.08953

F°AB= CMAB/CME F°AB= 13135/20963 F°AB= 0.6265802

Valores de P

1-pf(11.04477,2,2)Para Instructor 0.08302359

1-pf(> 1-pf(25.08953,1,2) Para Town 0.03762235

1-pf(0.665802,2,54) Para Interacción 0.5180283

Porcentajes de variabilidad

A= (2954/36109*100) A= 8.180786

B= (12500/36109*100) B= 34.61741

AB= (20655/36109*100) AB= 57.20181

Basándonos en los valores P>0.05 para las variables A, B e interacción, podemos que existe diferencia entre ellas, sin embargo los porcentajes de variabilidad nos podrían acercar a que el efecto mayoritario proviene de la interacción entre las variables A y B, lo que indica que el tratamiento junto con la ciudad va a inferir en la respuesta de dicho tratamiento. Con 95% de confianza. EN los graficos de interacción vemos que el efecto de la ciudad es más importante ya que las lines no son paralelas entre sí, lo que indica una interacción entre el tratamiento y la ciudad. En cambio en el gráfico de interacción de tratamientos las lineas son mas cercanas entre sí, por lo que no existe interacción o si existe es mínima. con 95% de confianza.