Open the data set

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

Check the first and last 6 rows, structure of the data and generate a summary

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

Create subsets by test administration and groups

#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

Test for Normality with Anderson-Darling

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

Generate Probability Density Function Plots

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

## NULL

Generate Descriptive Statistics

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

Test for Sig. Diff. in Pretest Scores of Control and Treatment

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

Test for Sig. Diff. in Pretest and Posttest Scores of Control Group

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

Test for Sig. Diff. in Pretest and Posttest Scores of Treatment Group

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

Test for Sig. Diff. in PostTest Scores of Control and Treatment Group

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

As such it can be noted that the introduction of the treatment does not necessarily lead to improvement in scores given that there is no significant difference in the post test scores of the Control and Treatment group; any difference observed in the median is attributed to chance. Although a significant increase in scores can be noted between the Pre and Post Test of the Treatment Group, it may be inaccurate to attribute this to the treatment knowing that such significant increase is also observed in the Pre and Post Test scores of the Control Group.