Doubt
Group1
10/11/2021
About Transformation mark penalty
What we did
data <- read_excel("Proj1-Oct5-DOE -Tidy2.xlsx")
data <- as.data.frame(data)
data$Obs <- as.numeric(data$Obs)
data$`Ball Colour` <- as.factor(data$`Ball Colour`)first.model <- aov(data$Obs~data$`Ball Colour`,data = data)
summary(first.model)## Df Sum Sq Mean Sq F value Pr(>F)
## data$`Ball Colour` 2 84.51 42.26 14.05 3.08e-05 ***
## Residuals 36 108.23 3.01
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1plot(first.model,col="deepskyblue")
With Transformation
boxcox(data$Obs~data$`Ball Colour`)
lambda=0.5
data$transobs <- data$Obs ^ 0.5
data## Ball Colour Obs transobs
## 1 black 50.0 7.071068
## 2 black 51.0 7.141428
## 3 black 50.0 7.071068
## 4 black 48.5 6.964194
## 5 black 49.0 7.000000
## 6 black 53.0 7.280110
## 7 black 52.0 7.211103
## 8 black 51.0 7.141428
## 9 black 51.0 7.141428
## 10 black 51.0 7.141428
## 11 black 49.5 7.035624
## 12 black 50.0 7.071068
## 13 black 50.0 7.071068
## 14 Red 50.0 7.071068
## 15 Red 51.0 7.141428
## 16 Red 49.0 7.000000
## 17 Red 49.0 7.000000
## 18 Red 50.0 7.071068
## 19 Red 49.5 7.035624
## 20 Red 49.0 7.000000
## 21 Red 50.5 7.106335
## 22 Red 49.0 7.000000
## 23 Red 50.0 7.071068
## 24 Red 50.0 7.071068
## 25 Red 49.0 7.000000
## 26 Red 52.0 7.211103
## 27 Yellow 55.0 7.416198
## 28 Yellow 49.0 7.000000
## 29 Yellow 53.0 7.280110
## 30 Yellow 54.0 7.348469
## 31 Yellow 55.0 7.416198
## 32 Yellow 51.0 7.141428
## 33 Yellow 50.0 7.071068
## 34 Yellow 54.0 7.348469
## 35 Yellow 51.0 7.141428
## 36 Yellow 51.0 7.141428
## 37 Yellow 56.0 7.483315
## 38 Yellow 56.0 7.483315
## 39 Yellow 57.0 7.549834model2 <- aov(data$transobs~data$`Ball Colour`,data = data)
summary(model2)## Df Sum Sq Mean Sq F value Pr(>F)
## data$`Ball Colour` 2 0.4032 0.20160 14.03 3.12e-05 ***
## Residuals 36 0.5172 0.01437
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1plot(model2)
