library(readxl)
library(ggpubr)
## Loading required package: ggplot2
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(effectsize)
library(effsize)
library(ggplot2)
library(rstatix)
## 
## Attaching package: 'rstatix'
## The following objects are masked from 'package:effectsize':
## 
##     cohens_d, eta_squared, omega_squared
## The following object is masked from 'package:stats':
## 
##     filter
A6Q2 <- read_excel("C:/Users/rmich/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 Weight - Before and After Keto",
     xlab = "Weight",
     ylab = "Frequency",
     col = "blue",
     border = "black",
     breaks = 20)

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

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

#Boxplot #There is a dot outside the boxplot. #The dot is not close to the whiskers. #The dot is very far away from the whiskers. #Based on these findings, the boxplot is not 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 = .029).
t.test(Before, After, paired = TRUE, na.action = na.omit)
## 
##  Paired t-test
## 
## data:  Before and After
## t = 6.1382, df = 19, p-value = 6.704e-06
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  12.49121 25.41730
## sample estimates:
## mean difference 
##        18.95425
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)
## 
## 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 Weight before Keto and after Keto. #Weight before (M = 76.13, SD = 7.78) were significantly different from weight after (M = 57.17, SD = 14.39), t(df19) = 6.14, p < .001 #The effect size was large, Cohen’s d = 1.57.

#A Wilcoxon Signed-Rank Test was conducted to determineif there was a difference in Weight before Keto and after Keto. #Weight before (Mdn = 75.96) were [significantly / not significantly] different from weight after (Mdn = 58.36), V = 210, p = < .001. #The effect size was large, r = .88