Exercise 3.5

The yield of a chemical process was measured using five batches of raw material, five acid concentrations, five catalyst concentrations (A, B, C, D, E), and five standing times (𝛼, 𝛽, 𝛾, 𝛿, 𝜖). The Graeco-Latin square that as in table below. Analyze the data from this experiment (use 𝛼 = 0.05) and draw conclusions.

#import data
library(readr)
data <- read_csv("/Volumes/GoogleDrive/My Drive/NORATIKAH/EDA/coding/Exercise 3.5.csv")

── Column specification ────────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  Batch = col_double(),
  Acid = col_double(),
  Times = col_character(),
  Catalyst = col_character(),
  Time = col_double()
)

data

Treatment1 = as.factor(data$Catalyst)
Row = as.factor(data$Batch)
Column = as.factor(data$Acid)
Treatment2 = as.factor(data$Times)
results = aov(Time~Row+Column+Treatment1+Treatment2,data)
summary(results)

            Df Sum Sq Mean Sq F value   Pr(>F)    
Row          4   10.0    2.50   0.427 0.785447    
Column       4   24.4    6.10   1.043 0.442543    
Treatment1   4  342.8   85.70  14.650 0.000941 ***
Treatment2   4   12.0    3.00   0.513 0.728900    
Residuals    8   46.8    5.85                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

TukeyHSD(results)

  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = Time ~ Row + Column + Treatment1 + Treatment2, data = data)

$Row
    diff       lwr      upr     p adj
2-1 -0.2 -5.484751 5.084751 0.9999182
3-1 -0.8 -6.084751 4.484751 0.9823986
4-1 -1.4 -6.684751 3.884751 0.8834072
5-1 -1.6 -6.884751 3.684751 0.8279246
3-2 -0.6 -5.884751 4.684751 0.9939694
4-2 -1.2 -6.484751 4.084751 0.9281909
5-2 -1.4 -6.684751 3.884751 0.8834072
4-3 -0.6 -5.884751 4.684751 0.9939694
5-3 -0.8 -6.084751 4.484751 0.9823986
5-4 -0.2 -5.484751 5.084751 0.9999182

$Column
    diff       lwr      upr     p adj
2-1 -0.2 -5.484751 5.084751 0.9999182
3-1  0.6 -4.684751 5.884751 0.9939694
4-1 -1.2 -6.484751 4.084751 0.9281909
5-1 -2.2 -7.484751 3.084751 0.6232282
3-2  0.8 -4.484751 6.084751 0.9823986
4-2 -1.0 -6.284751 4.284751 0.9610846
5-2 -2.0 -7.284751 3.284751 0.6948188
4-3 -1.8 -7.084751 3.484751 0.7640759
5-3 -2.8 -8.084751 2.484751 0.4197369
5-4 -1.0 -6.284751 4.284751 0.9610846

$Treatment1
     diff        lwr        upr     p adj
B-A  -8.0 -13.284751 -2.7152488 0.0051639
C-A  -4.8 -10.084751  0.4847512 0.0770797
D-A  -8.6 -13.884751 -3.3152488 0.0032815
E-A -10.6 -15.884751 -5.3152488 0.0008219
C-B   3.2  -2.084751  8.4847512 0.3087034
D-B  -0.6  -5.884751  4.6847512 0.9939694
E-B  -2.6  -7.884751  2.6847512 0.4837165
D-C  -3.8  -9.084751  1.4847512 0.1869031
E-C  -5.8 -11.084751 -0.5152488 0.0317351
E-D  -2.0  -7.284751  3.2847512 0.6948188

$Treatment2
            diff       lwr      upr     p adj
Beta-Alpha   0.4 -4.884751 5.684751 0.9987373
Delta-Alpha -0.2 -5.484751 5.084751 0.9999182
Eta-Alpha    1.2 -4.084751 6.484751 0.9281909
Gamma-Alpha  1.6 -3.684751 6.884751 0.8279246
Delta-Beta  -0.6 -5.884751 4.684751 0.9939694
Eta-Beta     0.8 -4.484751 6.084751 0.9823986
Gamma-Beta   1.2 -4.084751 6.484751 0.9281909
Eta-Delta    1.4 -3.884751 6.684751 0.8834072
Gamma-Delta  1.8 -3.484751 7.084751 0.7640759
Gamma-Eta    0.4 -4.884751 5.684751 0.9987373

plot(TukeyHSD(results))

Treatment = as.factor(data$Catalyst)
results = aov(Time~Treatment,data)
summary(results)

            Df Sum Sq Mean Sq F value   Pr(>F)    
Treatment    4  342.8   85.70   18.39 1.77e-06 ***
Residuals   20   93.2    4.66                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Treatment1 = as.factor(data$Catalyst)
Row = as.factor(data$Batch)
Column = as.factor(data$Acid)
results = aov(Time~Row+Column+Treatment1,data)
summary(results)

            Df Sum Sq Mean Sq F value   Pr(>F)    
Row          4   10.0     2.5   0.510    0.730    
Column       4   24.4     6.1   1.245    0.344    
Treatment1   4  342.8    85.7  17.490 6.03e-05 ***
Residuals   12   58.8     4.9                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1