Importing Data

library(readxl)
ING <- read_excel("D:/COLLEGE 4TH YEAR/1st SEMESTER/STAT 55 EXPERIMENTAL DESIGN/FINAL/FINAL EXAM - DATA FOR FIVE DIFFERENT INGREDIENTS (DUHAYLUNGSOD_BS MATH-STAT 4).xlsx")
ING

Viewing Data

head(ING)

Verify the Variables Structure

str(ING)
tibble [25 × 4] (S3: tbl_df/tbl/data.frame)
 $ Batch      : num [1:25] 1 1 1 1 1 2 2 2 2 2 ...
 $ Day        : num [1:25] 1 2 3 4 5 1 2 3 4 5 ...
 $ Ingredients: chr [1:25] "A" "B" "D" "C" ...
 $ Hours      : num [1:25] 8 7 1 7 3 11 2 7 3 8 ...

Changing Variables Structure into Factors

ING$Batch <- as.factor(ING$Batch)
ING$Day <- as.factor(ING$Day)
ING$Ingredients <- as.factor(ING$Ingredients)
str(ING)
tibble [25 × 4] (S3: tbl_df/tbl/data.frame)
 $ Batch      : Factor w/ 5 levels "1","2","3","4",..: 1 1 1 1 1 2 2 2 2 2 ...
 $ Day        : Factor w/ 5 levels "1","2","3","4",..: 1 2 3 4 5 1 2 3 4 5 ...
 $ Ingredients: Factor w/ 5 levels "A","B","C","D",..: 1 2 4 3 5 3 5 1 4 2 ...
 $ Hours      : num [1:25] 8 7 1 7 3 11 2 7 3 8 ...
attach(ING)

Applying Analysis of Variance Model

model <- lm(Hours ~ Batch+Day+Ingredients)
anova(model)
Analysis of Variance Table

Response: Hours
            Df Sum Sq Mean Sq F value    Pr(>F)    
Batch        4  15.44   3.860  1.2345 0.3476182    
Day          4  12.24   3.060  0.9787 0.4550143    
Ingredients  4 141.44  35.360 11.3092 0.0004877 ***
Residuals   12  37.52   3.127                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Mean Comparison Test

library(agricolae)
# LSD test
LSD.test(y = model,
         trt = "Ingredients",
         DFerror = model$df.residual,
         MSerror = deviance(model)/model$df.residual,
         alpha = 0.05,
         group = TRUE,
         console = TRUE)

Study: model ~ "Ingredients"

LSD t Test for Hours 

Mean Square Error:  3.126667 

Ingredients,  means and individual ( 95 %) CI

  Hours      std r      LCL       UCL Min Max
A   8.4 1.140175 5 6.677038 10.122962   7  10
B   5.6 2.073644 5 3.877038  7.322962   3   8
C   8.8 1.643168 5 7.077038 10.522962   7  11
D   3.4 2.073644 5 1.677038  5.122962   1   6
E   3.2 1.923538 5 1.477038  4.922962   1   6

Alpha: 0.05 ; DF Error: 12
Critical Value of t: 2.178813 

least Significant Difference: 2.436636 

Treatments with the same letter are not significantly different.

  Hours groups
C   8.8      a
A   8.4      a
B   5.6      b
D   3.4      b
E   3.2      b
# SNK test
SNK.test(y = Hours,
         trt = Ingredients,
         DFerror = model$df.residual,
         MSerror = deviance(model)/model$df.residual,
         alpha = 0.05,
         group = TRUE,
         console = TRUE)

Study: Hours ~ Ingredients

Student Newman Keuls Test
for Hours 

Mean Square Error:  3.126667 

Ingredients,  means

  Hours      std r Min Max
A   8.4 1.140175 5   7  10
B   5.6 2.073644 5   3   8
C   8.8 1.643168 5   7  11
D   3.4 2.073644 5   1   6
E   3.2 1.923538 5   1   6

Alpha: 0.05 ; DF Error: 12 

Critical Range
       2        3        4        5 
2.436636 2.983558 3.320217 3.564608 

Means with the same letter are not significantly different.

  Hours groups
C   8.8      a
A   8.4      a
B   5.6      b
D   3.4      b
E   3.2      b