Answer scheme Lab Report 2

QUESTION 1 I. Type of the experiment and reason : Randomized Complete Block Design because it has one nuisance factor as blocking factor. II. Blocking factor : experimental field III. Treatment factor : fertelizer IV. List all the treatments : Control, Absent, High

#import data
library(readr)
data <- read_csv("/Volumes/GoogleDrive/My Drive/NORATIKAH/EDA/Assessments/Lab Report/Lab Report 2/Lab Report 2 data.csv")

── Column specification ───────────────────────────────────────────────────────────────────────────────
cols(
  Field = col_double(),
  Fertilizer = col_character(),
  Yields = col_double()
)

data

Treatment = as.factor(data$Fertilizer)
Block = as.factor(data$Field)
results = aov(Yields~Treatment+Block,data)
summary(results)

            Df Sum Sq Mean Sq F value   Pr(>F)    
Treatment    2 11.606   5.803  29.145 1.02e-05 ***
Block        7 12.166   1.738   8.729 0.000339 ***
Residuals   14  2.787   0.199                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

\(H_{0}\): All population means are equal @ no treatments effect
\(H_{1}\): At least one of the population means is different @ there is treatment effects
\(p-value=0.0000\)
Since (\(p-value=0.0000\))\(<\)(\(\alpha=0.05\)), reject \(H_{0}\).
At \(\alpha=0.05\), At least one of the population means is different @ there is treatment effects

TukeyHSD(results)

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

Fit: aov(formula = Yields ~ Treatment + Block, data = data)

$Treatment
                 diff        lwr       upr     p adj
Control-Absent 1.2250  0.6410661 1.8089339 0.0002202
High-Absent    1.6375  1.0535661 2.2214339 0.0000104
High-Control   0.4125 -0.1714339 0.9964339 0.1902056

$Block
           diff        lwr         upr     p adj
2-1 -1.03333333 -2.3189419  0.25227522 0.1617626
3-1 -0.03333333 -1.3189419  1.25227522 1.0000000
4-1  0.13333333 -1.1522752  1.41894189 0.9999321
5-1  0.60000000 -0.6856086  1.88560855 0.7177024
6-1 -0.70000000 -1.9856086  0.58560855 0.5592509
7-1 -1.53333333 -2.8189419 -0.24772478 0.0147814
8-1 -1.26666667 -2.5522752  0.01894189 0.0547957
3-2  1.00000000 -0.2856086  2.28560855 0.1869296
4-2  1.16666667 -0.1189419  2.45227522 0.0882072
5-2  1.63333333  0.3477248  2.91894189 0.0090123
6-2  0.33333333 -0.9522752  1.61894189 0.9793776
7-2 -0.50000000 -1.7856086  0.78560855 0.8552781
8-2 -0.23333333 -1.5189419  1.05227522 0.9974342
4-3  0.16666667 -1.1189419  1.45227522 0.9997009
5-3  0.63333333 -0.6522752  1.91894189 0.6657032
6-3 -0.66666667 -1.9522752  0.61894189 0.6125196
7-3 -1.50000000 -2.7856086 -0.21439145 0.0174345
8-3 -1.23333333 -2.5189419  0.05227522 0.0643162
5-4  0.46666667 -0.8189419  1.75227522 0.8917015
6-4 -0.83333333 -2.1189419  0.45227522 0.3627445
7-4 -1.66666667 -2.9522752 -0.38105811 0.0076457
8-4 -1.40000000 -2.6856086 -0.11439145 0.0285772
6-5 -1.30000000 -2.5856086 -0.01439145 0.0466279
7-5 -2.13333333 -3.4189419 -0.84772478 0.0008154
8-5 -1.86666667 -3.1522752 -0.58105811 0.0028793
7-6 -0.83333333 -2.1189419  0.45227522 0.3627445
8-6 -0.56666667 -1.8522752  0.71894189 0.7673652
8-7  0.26666667 -1.0189419  1.55227522 0.9942330

plot(TukeyHSD(results))

The significant pair of treatments are Fertlizer Contro-Absent and High-Absent. The most significant treatment pairs is High-Absent.