Lab Report 3

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Seven different hardwood concentrations are being studied to determine their effect on the

strength of the paper produced. The experimenters thinks that when they run the experiment on

different day, it may affect the quality paper produced. So, they decided to use day as blocks.

However, the pilot plant can only produce three runs each day. Therefore, a balanced incomplete

block design must be used. The balanced incomplete block design for this experiment, along with

the observations recorded

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Question 1

i. TWO conditions of balanced incomplete block design

• P-Value < 0.05 is significant
• Any value that include 0 in the confidence level graph is significant

ii. Response Variable

• Strength

iii. Treatment Factor

• Concentration

iv. List all the treatment

• 2,4,6,8,10,12,14

Question 4

library(readr)
data <- read_csv("D:/UMP/Sem 5/EDA/Lab Report/Lab Report 3.csv")

## 
## -- Column specification --------------------------------------------------------
## cols(
##   Concentration = col_double(),
##   Days = col_double(),
##   strength = col_double()
## )

View(data)

Treatment = as.factor(data$Concentration)
block = as.factor(data$Days)

results = aov(strength~block+Treatment,data)
summary(results)

##             Df Sum Sq Mean Sq F value  Pr(>F)   
## block        6 1114.3  185.71   8.814 0.00358 **
## Treatment    6 1317.4  219.57  10.420 0.00205 **
## Residuals    8  168.6   21.07                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

a) State the hypothesis, the p-value

• H0: There is no treatments effect

• H1: there is treatment effect

b) Decision by comparing p-value and significance level

• p-value=0.0021

• Since p-value=0.0021<alpha=0.05, we reject H0.

c) Conclusion and decision

• At alpha=0.05, there is treatment effects

d) Further analysis interpretation

• 2)PostHocTest

library(DescTools)

## Warning: package 'DescTools' was built under R version 4.0.5

PostHocTest(results, method = "lsd")

## 
##   Posthoc multiple comparisons of means : Fisher LSD 
##     95% family-wise confidence level
## 
## $block
##              diff     lwr.ci      upr.ci    pval    
## 2-1  7.000000e+00  -1.642939  15.6429389 0.09876 .  
## 3-1 -5.000000e+00 -13.642939   3.6429389 0.21892    
## 4-1  1.800000e+01   9.357061  26.6429389 0.00135 ** 
## 5-1 -4.263256e-14  -8.642939   8.6429389 1.00000    
## 6-1 -3.000000e+00 -11.642939   5.6429389 0.44658    
## 7-1 -1.000000e+00  -9.642939   7.6429389 0.79637    
## 3-2 -1.200000e+01 -20.642939  -3.3570611 0.01258 *  
## 4-2  1.100000e+01   2.357061  19.6429389 0.01886 *  
## 5-2 -7.000000e+00 -15.642939   1.6429389 0.09876 .  
## 6-2 -1.000000e+01 -18.642939  -1.3570611 0.02845 *  
## 7-2 -8.000000e+00 -16.642939   0.6429389 0.06534 .  
## 4-3  2.300000e+01  14.357061  31.6429389 0.00028 ***
## 5-3  5.000000e+00  -3.642939  13.6429389 0.21892    
## 6-3  2.000000e+00  -6.642939  10.6429389 0.60811    
## 7-3  4.000000e+00  -4.642939  12.6429389 0.31701    
## 5-4 -1.800000e+01 -26.642939  -9.3570611 0.00135 ** 
## 6-4 -2.100000e+01 -29.642939 -12.3570611 0.00051 ***
## 7-4 -1.900000e+01 -27.642939 -10.3570611 0.00097 ***
## 6-5 -3.000000e+00 -11.642939   5.6429389 0.44658    
## 7-5 -1.000000e+00  -9.642939   7.6429389 0.79637    
## 7-6  2.000000e+00  -6.642939  10.6429389 0.60811    
## 
## $Treatment
##             diff       lwr.ci     upr.ci    pval    
## 4-2     3.000000  -5.64293889 11.6429389 0.44658    
## 6-2    11.666667   3.02372778 20.3096056 0.01439 *  
## 8-2    18.000000   9.35706111 26.6429389 0.00135 ** 
## 10-2   20.333333  11.69039444 28.9762722 0.00063 ***
## 12-2    5.666667  -2.97627222 14.3096056 0.16901    
## 14-2    9.000000   0.35706111 17.6429389 0.04309 *  
## 6-4     8.666667   0.02372778 17.3096056 0.04951 *  
## 8-4    15.000000   6.35706111 23.6429389 0.00394 ** 
## 10-4   17.333333   8.69039444 25.9762722 0.00170 ** 
## 12-4    2.666667  -5.97627222 11.3096056 0.49700    
## 14-4    6.000000  -2.64293889 14.6429389 0.14808    
## 8-6     6.333333  -2.30960556 14.9762722 0.12954    
## 10-6    8.666667   0.02372778 17.3096056 0.04951 *  
## 12-6   -6.000000 -14.64293889  2.6429389 0.14808    
## 14-6   -2.666667 -11.30960556  5.9762722 0.49700    
## 10-8    2.333333  -6.30960556 10.9762722 0.55091    
## 12-8  -12.333333 -20.97627222 -3.6903944 0.01101 *  
## 14-8   -9.000000 -17.64293889 -0.3570611 0.04309 *  
## 12-10 -14.666667 -23.30960556 -6.0237278 0.00446 ** 
## 14-10 -11.333333 -19.97627222 -2.6903944 0.01646 *  
## 14-12   3.333333  -5.30960556 11.9762722 0.39976    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

• Based on the output, the significants are 8-2, 10-2, 8-4, 10-4, 12-10 because it has p-value < alpha=0.05.

• The most significant comparison is 10-2 because it has the smallest p-value= 0.0006 and the largest difference.

knitr::include_graphics("D:/UMP/Sem 5/EDA/Lab Report/Marking Files.png")

knitr::include_graphics("D:/UMP/Sem 5/EDA/Lab Report/Rubrics.PNG")