Effect of GA₃ and Imbibition Time on Germination (Raphanus sativus L.)
Santiago Gallego
2025-07-31
3^2 factorial design
library(agricolae)## Warning: package 'agricolae' was built under R version 4.4.3library(readxl)## Warning: package 'readxl' was built under R version 4.4.3datos <- read_xlsx("resultados1.xlsx", sheet = "Hoja3")datos$imb1 <- factor(datos$Imbibicion)
datos$gib1 <- factor(datos$GA3)anova <- aov(Porcentaje ~ imb1*gib1,data=datos)## Df Sum Sq Mean Sq F value Pr(>F)
## imb1 2 9495 4747 73.949 2.08e-09 ***
## gib1 2 991 495 7.718 0.00380 **
## imb1:gib1 4 1379 345 5.372 0.00501 **
## Residuals 18 1156 64
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1boxplot(datos$Porcentaje ~ datos$Imbibicion, xlab = 'Imbibition time', ylab = '% Germination', col ="pink")
boxplot(datos$Porcentaje ~ datos$GA3, xlab = 'GA3 ppm Concentration', ylab = '% Germination', col = "pink")
interaction.plot(datos$Imbibicion, datos$GA3, datos$Porcentaje, xlab = 'Imbibition time',
ylab = '% Germination', trace.label = 'GA3 ppm Concentration',
col = c("blue", "red", "green"),
lty = 1,
lwd = 2,
main = "Interaction between Imbibition and GA3 in Percentage")
residuales<-anova$residualsbartlett.test(anova$residuals, datos$Imbibicion) ##
## Bartlett test of homogeneity of variances
##
## data: anova$residuals and datos$Imbibicion
## Bartlett's K-squared = 0.56193, df = 2, p-value = 0.7551bartlett.test(anova$residuals, datos$GA3)##
## Bartlett test of homogeneity of variances
##
## data: anova$residuals and datos$GA3
## Bartlett's K-squared = 3.2811, df = 2, p-value = 0.1939shapiro.test(anova$residuals) ##
## Shapiro-Wilk normality test
##
## data: anova$residuals
## W = 0.97077, p-value = 0.6223Obtaining coefficients to characterize the type of curvature
TL <- rep(0,27)
TC <- rep(0,27)
for(i in 1:27)
{
if(datos$Imbibicion[i] == 0) #nivel bajo
{TL[i] <- -1 }
else {
if(datos$Imbibicion[i] == 12) #nivel alto
{TL[i] <- 1 }
}
if(datos$Imbibicion[i] == 0)
{TC[i] <- 1 }
else {
if(datos$Imbibicion[i] == 6) #nivel medio
{TC[i] <- -2 }
else {
if(datos$Imbibicion[i] == 12)
{TC[i] <- 1 }
}
}
}SL <- rep(0,27)
SC <- rep(0,27)
for(i in 1:27)
{
if(datos$GA3[i] == 0)
{SL[i] <- -1 }
else {
if(datos$GA3[i] == 6)
{SL[i] <- 1 }
}
if(datos$GA3[i] == 0)
{SC[i] <- 1 }
else {
if(datos$GA3[i] == 6)
{SC[i] <- 1 }
else {
if(datos$GA3[i] == 3)
{SC[i] <- -2 }
}}}TLSL <- TL*SL
TLSC <- TL*SC
TCSL <- TC*SL
TCSC <- TC*SCRegression analysis for the characterization of curvature
anova1 <- aov(datos$Porcentaje ~ TL+TC+SL+SC+TLSL+TLSC+TCSL+TCSC)summary(anova1)## Df Sum Sq Mean Sq F value Pr(>F)
## TL 1 9491 9491 147.846 4.08e-10 ***
## TC 1 3 3 0.051 0.823399
## SL 1 988 988 15.385 0.000998 ***
## SC 1 3 3 0.051 0.823399
## TLSL 1 300 300 4.673 0.044356 *
## TLSC 1 31 31 0.481 0.496925
## TCSL 1 357 357 5.558 0.029921 *
## TCSC 1 692 692 10.776 0.004137 **
## Residuals 18 1156 64
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1modelo.lm2 = lm (datos$Porcentaje ~ TL+TC+SL+SC+TLSL+TLSC+TCSL+TCSC)summary(modelo.lm2)##
## Call:
## lm(formula = datos$Porcentaje ~ TL + TC + SL + SC + TLSL + TLSC +
## TCSL + TCSC)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.333 -4.444 -2.222 4.444 13.333
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.7531 1.5420 25.781 1.16e-15 ***
## TL 22.9630 1.8885 12.159 4.08e-10 ***
## TC 0.2469 1.0903 0.226 0.823399
## SL 7.4074 1.8885 3.922 0.000998 ***
## SC 0.2469 1.0903 0.226 0.823399
## TLSL 5.0000 2.3130 2.162 0.044356 *
## TLSC 0.9259 1.3354 0.693 0.496925
## TCSL 3.1481 1.3354 2.357 0.029921 *
## TCSC 2.5309 0.7710 3.283 0.004137 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.012 on 18 degrees of freedom
## Multiple R-squared: 0.9113, Adjusted R-squared: 0.8718
## F-statistic: 23.1 on 8 and 18 DF, p-value: 5.855e-08modelo.lm3 = lm (datos$Porcentaje ~ TL+TC+SL+SC+TLSL+TCSL+TCSC) summary(modelo.lm3)##
## Call:
## lm(formula = datos$Porcentaje ~ TL + TC + SL + SC + TLSL + TCSL +
## TCSC)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.333 -4.444 -1.296 4.444 13.333
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.7531 1.5208 26.140 2.34e-16 ***
## TL 22.9630 1.8625 12.329 1.64e-10 ***
## TC 0.2469 1.0753 0.230 0.820845
## SL 7.4074 1.8625 3.977 0.000807 ***
## SC 0.2469 1.0753 0.230 0.820845
## TLSL 5.0000 2.2811 2.192 0.041047 *
## TCSL 3.1481 1.3170 2.390 0.027347 *
## TCSC 2.5309 0.7604 3.328 0.003532 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.902 on 19 degrees of freedom
## Multiple R-squared: 0.9089, Adjusted R-squared: 0.8753
## F-statistic: 27.07 on 7 and 19 DF, p-value: 1.341e-08Confidence interval for the regression betas
confint(modelo.lm2,level = 0.95)## 2.5 % 97.5 %
## (Intercept) 36.5135175 42.992655
## TL 18.9953176 26.930608
## TC -2.0438075 2.537635
## SL 3.4397620 11.375053
## SC -2.0438075 2.537635
## TLSL 0.1406467 9.859353
## TLSC -1.8796230 3.731475
## TCSL 0.3425992 5.953697
## TCSC 0.9110798 4.150649CONTOUR AND RESPONSE SURFACE GRAPH
imbp=seq(0,12,length.out=50)
giba=seq(0,6,length.out=50)We generate two equally spaced numeric sequences (imbp and giba) with 50 values each. These sequences define the resolution of the axes for the contour and response surface plots.
f1=function(imbp,giba){
modelo.lm3$coe[1]+
modelo.lm3$coe[2]*I((imbp-6)/6)+
modelo.lm3$coe[3]*I(-2+3*((imbp-6)/6)^2)+
modelo.lm3$coe[4]*I((giba-3)/3)+
modelo.lm3$coe[5]*I(-2+3*((giba-3)/3)^2)+
modelo.lm3$coe[6]*I((imbp-6)/6)*I((giba-3)/3)+
modelo.lm3$coe[7]*I(-2+3*((imbp-6)/6)^2)*I((giba-3)/3)+
modelo.lm3$coe[8]*I(-2+3*((imbp-6)/6)^2)*I(-2+3*((giba-3)/3)^2)
}z1= outer(imbp,giba,f1)
par(mfrow = c(1,2))
persp(imbp,giba,z1,col=rainbow(50),theta=30,phi=10,ticktype='detailed',zlab='Germination %', xlab = 'Imbibition h',ylab='GA ppm')
image(imbp,giba,z1,xlab='Imbibition h',ylab='GA ppm')
contour(imbp,giba,z1,xlab='Imbibition h',ylab='GA ppm',add=TRUE)
## Post-hoc analysis
tukey_result <- HSD.test(anova2, trt = "interaction", group = TRUE, console = TRUE)##
## Study: anova2 ~ "interaction"
##
## HSD Test for Porcentaje
##
## Mean Square Error: 64.19753
##
## interaction, means
##
## Porcentaje std r se Min Max Q25 Q50
## 0.0 13.33333 6.666667 3 4.625924 6.666667 20.00000 10.00000 13.33333
## 0.3 13.33333 6.666667 3 4.625924 6.666667 20.00000 10.00000 13.33333
## 0.6 24.44444 7.698004 3 4.625924 20.000000 33.33333 20.00000 20.00000
## 12.0 51.11111 7.698004 3 4.625924 46.666667 60.00000 46.66667 46.66667
## 12.3 55.55556 3.849002 3 4.625924 53.333333 60.00000 53.33333 53.33333
## 12.6 82.22222 10.183502 3 4.625924 73.333333 93.33333 76.66667 80.00000
## 6.0 33.33333 13.333333 3 4.625924 20.000000 46.66667 26.66667 33.33333
## 6.3 48.88889 3.849002 3 4.625924 46.666667 53.33333 46.66667 46.66667
## 6.6 35.55556 7.698004 3 4.625924 26.666667 40.00000 33.33333 40.00000
## Q75
## 0.0 16.66667
## 0.3 16.66667
## 0.6 26.66667
## 12.0 53.33333
## 12.3 56.66667
## 12.6 86.66667
## 6.0 40.00000
## 6.3 50.00000
## 6.6 40.00000
##
## Alpha: 0.05 ; DF Error: 18
## Critical Value of Studentized Range: 4.955209
##
## Minimun Significant Difference: 22.92242
##
## Treatments with the same letter are not significantly different.
##
## Porcentaje groups
## 12.6 82.22222 a
## 12.3 55.55556 b
## 12.0 51.11111 b
## 6.3 48.88889 b
## 6.6 35.55556 bc
## 6.0 33.33333 bc
## 0.6 24.44444 c
## 0.0 13.33333 c
## 0.3 13.33333 c