```
library(xlsx)
data <- read.xlsx("Experiment1.xlsx", sheetIndex = "Sheet1")
```

`head(data)`

```
## Pre Post Group
## 1 2.03 17.23 Cntrl
## 2 4.02 16.04 Cntrl
## 3 14.34 19.22 Cntrl
## 4 15.55 19.45 Cntrl
## 5 2.05 18.53 Cntrl
## 6 11.07 21.00 Cntrl
```

`tail(data)`

```
## Pre Post Group
## 69 17.32 19.67 Tx
## 70 8.95 6.86 Tx
## 71 8.34 17.63 Tx
## 72 17.52 18.84 Tx
## 73 5.21 15.11 Tx
## 74 3.73 19.07 Tx
```

`str(data)`

```
## 'data.frame': 74 obs. of 3 variables:
## $ Pre : num 2.03 4.02 14.34 15.55 2.05 ...
## $ Post : num 17.2 16 19.2 19.4 18.5 ...
## $ Group: Factor w/ 2 levels "Cntrl","Tx": 1 1 1 1 1 1 1 1 1 1 ...
```

`summary(data)`

```
## Pre Post Group
## Min. : 0.37 Min. : 5.28 Cntrl:37
## 1st Qu.: 5.48 1st Qu.:16.05 Tx :37
## Median :11.67 Median :18.20
## Mean :10.93 Mean :16.92
## 3rd Qu.:15.74 3rd Qu.:19.16
## Max. :19.77 Max. :21.04
```

```
#Retrieve Pretest scores from Control Group
CntrlPre <- data[data$Group =="Cntrl",]$Pre
#Retrieve Pretest scores from Treatment Group
TxPre <- data[data$Group == "Tx",]$Pre
#Retrieve PostTest scores from Control Group
CntrlPost <- data[data$Group == "Cntrl",]$Post
#Retrive PostTest scores from Treatment Group
TxPost <- data[data$Group == "Tx",]$Post
```

```
library(nortest)
nordata <- cbind(CntrlPre, CntrlPost, TxPre, TxPost)
apply(nordata, 2, function(x) ad.test(x))
```

```
## $CntrlPre
##
## Anderson-Darling normality test
##
## data: x
## A = 0.75109, p-value = 0.04608
##
##
## $CntrlPost
##
## Anderson-Darling normality test
##
## data: x
## A = 2.4165, p-value = 3.078e-06
##
##
## $TxPre
##
## Anderson-Darling normality test
##
## data: x
## A = 0.83981, p-value = 0.02754
##
##
## $TxPost
##
## Anderson-Darling normality test
##
## data: x
## A = 1.9828, p-value = 3.726e-05
```

```
par(mfrow=c(2,2))
apply(nordata, 2, function(x) plot(density(x), col = "firebrick"))
```

`## NULL`

```
library(psych)
describeBy(data$Pre, data$Group) #Median is the measure for central tendency given the result of normality test
```

```
##
## Descriptive statistics by group
## group: Cntrl
## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 37 11.48 5.92 11.65 11.68 8.35 1.37 19.7 18.33 -0.25 -1.33
## se
## X1 0.97
## --------------------------------------------------------
## group: Tx
## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 37 10.37 5.79 11.69 10.35 7.99 0.37 19.77 19.4 -0.05 -1.43
## se
## X1 0.95
```

`describeBy(data$Post, data$Group) #Median is the measure for central tendency given the result of normality test`

```
##
## Descriptive statistics by group
## group: Cntrl
## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 37 17.23 3.52 19.05 17.67 1.44 5.28 21.04 15.76 -1.47 1.77
## se
## X1 0.58
## --------------------------------------------------------
## group: Tx
## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 37 16.62 3.17 17.63 17.03 1.96 6.86 20.83 13.97 -1.32 1.1
## se
## X1 0.52
```

`wilcox.test(CntrlPre, jitter(TxPre), alternative = "two.sided", paired = FALSE) # There is no significant difference in the pretest scores between Control and Treatment. This is consistent with the expectations of an experimental design. `

```
##
## Wilcoxon rank sum test
##
## data: CntrlPre and jitter(TxPre)
## W = 758, p-value = 0.4323
## alternative hypothesis: true location shift is not equal to 0
```

`wilcox.test(CntrlPre, jitter(CntrlPost), alternative = "two.sided", paired = TRUE) # Presence of significant difference in pretest and post test scores of the Control Group indicate that an increase in scores in the Post Test may be attributed by other factors beside chance. This makes the findings rather intriguing considering the change in scores despite the fact that it occured in the Control Group; one that was not introduced with Treatment.`

```
##
## Wilcoxon signed rank test
##
## data: CntrlPre and jitter(CntrlPost)
## V = 31, p-value = 3.456e-08
## alternative hypothesis: true location shift is not equal to 0
```

`wilcox.test(TxPre, jitter(TxPost), alternative = "two.sided", paired = TRUE) # There exists a significant difference in the pretest and post test scores for the Treatment group which somehow indicates that the change may be related to the introduction of the treatment rather than chance. However, this is questionable considering the observation in the Control group wherein there is an increase in scores despite the fact that there was no treatment introduced. `

```
##
## Wilcoxon signed rank test
##
## data: TxPre and jitter(TxPost)
## V = 25, p-value = 1.315e-08
## alternative hypothesis: true location shift is not equal to 0
```

`wilcox.test(CntrlPost, jitter(TxPost), alternative = "two.sided", paired = FALSE) # When comparing the Post Test Scores of Control and Treatment Group, no significant difference is observed. This further explains the observations made earlier. `

```
##
## Wilcoxon rank sum test
##
## data: CntrlPost and jitter(TxPost)
## W = 841, p-value = 0.09181
## alternative hypothesis: true location shift is not equal to 0
```