R MARKDOWN PAUL A6Q2

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(effectsize)
library(effsize)
library(rstatix)

## 
## Attaching package: 'rstatix'

## The following objects are masked from 'package:effectsize':
## 
##     cohens_d, eta_squared

## The following object is masked from 'package:stats':
## 
##     filter

library(readxl)

A6Q2 <- read_excel("C:/Users/jrutebuka/Desktop/A6Q2.xlsx")

Before <- A6Q2$Before
After <- A6Q2$After
Differences <- After - Before

mean(Before, na.rm = TRUE)

## [1] 76.13299

median(Before, na.rm = TRUE)

## [1] 75.95988

sd(Before, na.rm = TRUE)

## [1] 7.781323

mean(After, na.rm = TRUE)

## [1] 57.17874

median(After, na.rm = TRUE)

## [1] 58.36459

sd(After, na.rm = TRUE)

## [1] 14.39364

hist(Differences,
     main = "Histogram of Difference Scores",
     xlab = "Value",
     ylab = "Frequency",
     col = "blue",
     border = "black",
     breaks = 20)

#Histogram of Difference Scores
#The difference scores look abnormally  distributed.
#The data is Asymmetrical and negatively skewed.
#The data  does not have a proper bell curve.

boxplot(Differences,
        main = "Distribution of Score Differences (After - Before)",
        ylab = "Difference in Scores",
        col = "blue",
        border = "darkblue")

#Boxplot
#There is one dot outside the boxplot.
#The dot is close to the whiskers.
#The dot is not very far away from the whiskers.
#Based on these findings, the boxplot is normal.

shapiro.test(Differences)

## 
##  Shapiro-Wilk normality test
## 
## data:  Differences
## W = 0.89142, p-value = 0.02856

#Shapiro-Wilk Difference Scores
#The data is abnormally distributed, (p =0.02).

wilcox.test(Before, After, paired = TRUE, na.action = na.omit)

## 
##  Wilcoxon signed rank exact test
## 
## data:  Before and After
## V = 210, p-value = 1.907e-06
## alternative hypothesis: true location shift is not equal to 0

# Cohen.d (Before, After, paired= TRUE)

effsize::cohen.d(Before, After, paired= TRUE)

## 
## Cohen's d
## 
## d estimate: 1.572335 (large)
## 95 percent confidence interval:
##     lower     upper 
## 0.7969027 2.3477670

df_long <- data.frame(
  id = rep(1:length(Before), 2),
  time = rep(c("Before", "After"), each = length(Before)),
  score = c(Before, After)
)

wilcox_effsize(df_long, score ~ time, paired = TRUE)

## # A tibble: 1 × 7
##   .y.   group1 group2 effsize    n1    n2 magnitude
## * <chr> <chr>  <chr>    <dbl> <int> <int> <ord>    
## 1 score After  Before   0.877    20    20 large

#A Dependent T-Test was conducted to determine if there was a difference in Outcome Variable before Independent Variable versus after Independent Variable.
#Before scores (M = 76.13, SD =  7.78) were  not significantly different from after scores (M = 57.17, SD = 14.39), t(df#) = 1.90, p =0.028.
#The effect size was  large, Cohen's d = 1.572 .

#A Wilcoxon Signed-Rank Test was conducted to determine if there was a difference in Outcome Variable before Independent Variable versus after Independent Variable.
#Before scores (Mdn = 75.95) were significantly different from after scores (Mdn = 58.36), V= 21, p = 1.907e-06.
#The effect size was small, r =1.57.