Análisis de homogeneidad de varianzas

setwd("C:/Users/alex/Documents/R")
getwd()
## [1] "C:/Users/alex/Documents/R"
DTangelica<-read.csv("DTangelica.csv", sep = ";", header = T)#
summary(DTangelica)
##       trat           epoc         rept          DVIVOS     
##  citrico:8   trimestre3:12   Min.   :1.00   Min.   : 5.00  
##  H2O    :8   Trimestre4:12   1st Qu.:1.75   1st Qu.: 6.60  
##  MS3K   :8                   Median :2.50   Median :11.77  
##                              Mean   :2.50   Mean   :10.69  
##                              3rd Qu.:3.25   3rd Qu.:13.96  
##                              Max.   :4.00   Max.   :14.93  
##      DOXID           PCONT             BACT             HONG       
##  Min.   :0.200   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:1.195   1st Qu.:0.0675   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :1.815   Median :0.1700   Median :0.1300   Median :0.0000  
##  Mean   :1.778   Mean   :0.2521   Mean   :0.1442   Mean   :0.1079  
##  3rd Qu.:2.493   3rd Qu.:0.4000   3rd Qu.:0.2000   3rd Qu.:0.2000  
##  Max.   :3.000   Max.   :0.6000   Max.   :0.6000   Max.   :0.4000  
##      DMUERT         ResDVIVOS         ResDOXIDA         RESPCONT    
##  Min.   :0.0700   Min.   :0.03000   Min.   :0.0500   Min.   :0.100  
##  1st Qu.:0.7525   1st Qu.:0.05750   1st Qu.:0.2800   1st Qu.:0.580  
##  Median :2.2600   Median :0.07000   Median :0.3550   Median :1.610  
##  Mean   :3.8896   Mean   :0.07083   Mean   :0.3371   Mean   :1.194  
##  3rd Qu.:7.2000   3rd Qu.:0.09000   3rd Qu.:0.4275   3rd Qu.:1.810  
##  Max.   :9.6000   Max.   :0.11000   Max.   :0.5800   Max.   :1.810  
##     RESBACT         RESHONGO       RESDMUERT      
##  Min.   :0.030   Min.   :0.420   Min.   :0.03000  
##  1st Qu.:1.670   1st Qu.:2.040   1st Qu.:0.06000  
##  Median :2.285   Median :2.040   Median :0.07000  
##  Mean   :1.965   Mean   :1.853   Mean   :0.07208  
##  3rd Qu.:2.450   3rd Qu.:2.180   3rd Qu.:0.09000  
##  Max.   :2.620   Max.   :2.530   Max.   :0.11000

Test de Bartlett

Permite contrastar la igualdad de varianzas en 2 o más poblaciones sin ser necesario que el tamaño de todas las muestras sea el mismo. Es más sensible que el test de Levene a la falta de normalidad. Pero si se está seguro de que los datos provienen de una distribución normal, es la mejor opción.

library(ggplot2)
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
bartlett.test(DTangelica$ResDVIVOS ~ DTangelica$trat)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  DTangelica$ResDVIVOS by DTangelica$trat
## Bartlett's K-squared = 1.5467, df = 2, p-value = 0.4615
bartlett.test(DTangelica$ResDOXIDA ~ DTangelica$trat)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  DTangelica$ResDOXIDA by DTangelica$trat
## Bartlett's K-squared = 5.3805, df = 2, p-value = 0.06787
bartlett.test(DTangelica$RESPCONT ~ DTangelica$trat)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  DTangelica$RESPCONT by DTangelica$trat
## Bartlett's K-squared = 22.274, df = 2, p-value = 1.456e-05
bartlett.test(DTangelica$RESBACT ~ DTangelica$trat)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  DTangelica$RESBACT by DTangelica$trat
## Bartlett's K-squared = 26.102, df = 2, p-value = 2.148e-06
bartlett.test(DTangelica$RESHONGO ~ DTangelica$trat)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  DTangelica$RESHONGO by DTangelica$trat
## Bartlett's K-squared = Inf, df = 2, p-value < 2.2e-16
bartlett.test(DTangelica$RESDMUERT ~ DTangelica$trat)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  DTangelica$RESDMUERT by DTangelica$trat
## Bartlett's K-squared = 3.288, df = 2, p-value = 0.1932
bartlett.test(DTangelica$ResDVIVOS ~ DTangelica$epoc)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  DTangelica$ResDVIVOS by DTangelica$epoc
## Bartlett's K-squared = 2.3609, df = 1, p-value = 0.1244
bartlett.test(DTangelica$ResDOXIDA ~ DTangelica$epoc)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  DTangelica$ResDOXIDA by DTangelica$epoc
## Bartlett's K-squared = 2.7014, df = 1, p-value = 0.1003
bartlett.test(DTangelica$RESPCONT ~ DTangelica$epoc)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  DTangelica$RESPCONT by DTangelica$epoc
## Bartlett's K-squared = 0.35951, df = 1, p-value = 0.5488
bartlett.test(DTangelica$RESBACT ~ DTangelica$epoc)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  DTangelica$RESBACT by DTangelica$epoc
## Bartlett's K-squared = 6.9643, df = 1, p-value = 0.008315
bartlett.test(DTangelica$RESHONGO ~ DTangelica$epoc)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  DTangelica$RESHONGO by DTangelica$epoc
## Bartlett's K-squared = 39.771, df = 1, p-value = 2.856e-10
bartlett.test(DTangelica$RESDMUERT ~ DTangelica$epoc)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  DTangelica$RESDMUERT by DTangelica$epoc
## Bartlett's K-squared = 4.6243, df = 1, p-value = 0.03152

Análisis gráfico

ggplot(data = DTangelica, aes(x = trat, y = ResDVIVOS, colour = trat)) + 
  geom_boxplot() + theme_bw()

ggplot(data = DTangelica, aes(x = trat, y = ResDOXIDA, colour = trat)) + 
  geom_boxplot() + theme_bw()

ggplot(data = DTangelica, aes(x = trat, y = RESPCONT, colour = trat)) + 
  geom_boxplot() + theme_bw()

ggplot(data = DTangelica, aes(x = trat, y = RESBACT, colour = trat)) + 
  geom_boxplot() + theme_bw()

ggplot(data = DTangelica, aes(x = trat, y = RESHONGO, colour = trat)) + 
  geom_boxplot() + theme_bw()

ggplot(data = DTangelica, aes(x = trat, y = RESDMUERT, colour = trat)) + 
  geom_boxplot() + theme_bw()

Conclusión

Si se tiene seguridad de que existe homogeneidad entre las varianzas de las muestras (ResDVIVOS, ResDOXIDA y RESDMUERT) con un nivel de confianza del p<0.05