Diseño Completamente al azar

Problema a analizar: Se desea probar el efecto de probar el efecto de diferentes fuentes de azúcar sobre la actividad enzimática de las xilanasas,. Variable Respuesta: actividad enzimática xilanasa en UI obtenidos al final del cultivo para cada tratamiento ensayado con diferentes fuentes de azúcar

##     Marca                PH                  AE       
##  Length:16          Length:16          Min.   :0.470  
##  Class :character   Class :character   1st Qu.:0.650  
##  Mode  :character   Mode  :character   Median :0.695  
##                                        Mean   :0.685  
##                                        3rd Qu.:0.760  
##                                        Max.   :0.840

Cálculo de ANOVA y el Modelo Lineal

## 
## Call:
## lm(formula = AE ~ (PH + Marca))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.04250 -0.01812 -0.00875  0.01937  0.04500 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.80000    0.02385  33.545 9.16e-11 ***
## PHPH6       -0.14500    0.02550  -5.687 0.000299 ***
## PHPH7        0.03250    0.02550   1.275 0.234321    
## PHPH8        0.05250    0.02550   2.059 0.069568 .  
## MarcaB      -0.16750    0.02550  -6.570 0.000103 ***
## MarcaC      -0.13500    0.02550  -5.295 0.000497 ***
## MarcaD      -0.09750    0.02550  -3.824 0.004063 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03606 on 9 degrees of freedom
## Multiple R-squared:  0.9314, Adjusted R-squared:  0.8857 
## F-statistic: 20.37 on 6 and 9 DF,  p-value: 9.227e-05
##             Df  Sum Sq Mean Sq F value   Pr(>F)    
## PH           3 0.09575 0.03192   24.55 0.000115 ***
## Marca        3 0.06315 0.02105   16.19 0.000570 ***
## Residuals    9 0.01170 0.00130                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Supuestos del Diseño Experimental

1.Normalidad

## 
##  Shapiro-Wilk normality test
## 
## data:  resid(modelo)
## W = 0.9316, p-value = 0.2584

De manera gráfica, se puede evidenciar la normalidad

## Warning: package 'car' was built under R version 4.4.2
## Cargando paquete requerido: carData
## Warning: package 'carData' was built under R version 4.4.2

## [1]  2 16

2.Homocedasticidad

## 
##  Bartlett test of homogeneity of variances
## 
## data:  resid(modelo) by PH
## Bartlett's K-squared = 2.4076, df = 3, p-value = 0.4922
## 
##  Bartlett test of homogeneity of variances
## 
## data:  resid(modelo) by PH
## Bartlett's K-squared = 2.4076, df = 3, p-value = 0.4922

3.Independencia

Pruebas Aposteriori

library(agricolae)
## Warning: package 'agricolae' was built under R version 4.4.2
outHSD<-HSD.test(anova, "PH",console=TRUE)
## 
## Study: anova ~ "PH"
## 
## HSD Test for AE 
## 
## Mean Square Error:  0.0013 
## 
## PH,  means
## 
##         AE        std r         se  Min  Max    Q25   Q50    Q75
## PH5 0.7000 0.06218253 4 0.01802776 0.65 0.79 0.6650 0.680 0.7150
## PH6 0.5550 0.10214369 4 0.01802776 0.47 0.70 0.4925 0.525 0.5875
## PH7 0.7325 0.07274384 4 0.01802776 0.68 0.84 0.6950 0.705 0.7425
## PH8 0.7525 0.07320064 4 0.01802776 0.65 0.81 0.7250 0.775 0.8025
## 
## Alpha: 0.05 ; DF Error: 9 
## Critical Value of Studentized Range: 4.41489 
## 
## Minimun Significant Difference: 0.07959056 
## 
## Treatments with the same letter are not significantly different.
## 
##         AE groups
## PH8 0.7525      a
## PH7 0.7325      a
## PH5 0.7000      a
## PH6 0.5550      b

Otra opcion cuando cambiamos el argumento “group” a F(false)

## 
## Study: anova ~ "PH"
## 
## LSD t Test for AE 
## 
## Mean Square Error:  0.0013 
## 
## PH,  means and individual ( 95 %) CI
## 
##         AE        std r         se       LCL       UCL  Min  Max    Q25   Q50
## PH5 0.7000 0.06218253 4 0.01802776 0.6592184 0.7407816 0.65 0.79 0.6650 0.680
## PH6 0.5550 0.10214369 4 0.01802776 0.5142184 0.5957816 0.47 0.70 0.4925 0.525
## PH7 0.7325 0.07274384 4 0.01802776 0.6917184 0.7732816 0.68 0.84 0.6950 0.705
## PH8 0.7525 0.07320064 4 0.01802776 0.7117184 0.7932816 0.65 0.81 0.7250 0.775
##        Q75
## PH5 0.7150
## PH6 0.5875
## PH7 0.7425
## PH8 0.8025
## 
## Alpha: 0.05 ; DF Error: 9
## Critical Value of t: 2.262157 
## 
## least Significant Difference: 0.05767392 
## 
## Treatments with the same letter are not significantly different.
## 
##         AE groups
## PH8 0.7525      a
## PH7 0.7325      a
## PH5 0.7000      a
## PH6 0.5550      b

Pruebas aposterio para detrrminar el efecto del factor sobre la actividad enzimatica 

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = modelo)
## 
## $PH
##            diff         lwr         upr     p adj
## PH6-PH5 -0.1450 -0.22459056 -0.06540944 0.0013870
## PH7-PH5  0.0325 -0.04709056  0.11209056 0.5994840
## PH8-PH5  0.0525 -0.02709056  0.13209056 0.2368653
## PH7-PH6  0.1775  0.09790944  0.25709056 0.0003124
## PH8-PH6  0.1975  0.11790944  0.27709056 0.0001366
## PH8-PH7  0.0200 -0.05959056  0.09959056 0.8596851
## 
## $Marca
##        diff          lwr         upr     p adj
## B-A -0.1675 -0.247090564 -0.08790944 0.0004843
## C-A -0.1350 -0.214590564 -0.05540944 0.0022833
## D-A -0.0975 -0.177090564 -0.01790944 0.0175388
## C-B  0.0325 -0.047090564  0.11209056 0.5994840
## D-B  0.0700 -0.009590564  0.14959056 0.0879632
## D-C  0.0375 -0.042090564  0.11709056 0.4912626