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library(readxl)
library(ggpubr)
## Loading required package: ggplot2
#library(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(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
A6Q2<-read_excel("A6Q2.xlsx")
A6Q2
## # A tibble: 20 × 3
##       ID Before After
##    <dbl>  <dbl> <dbl>
##  1     1   70.5  47.6
##  2     2   73.2  52.9
##  3     3   87.5  47.2
##  4     4   75.6  58.0
##  5     5   76.0  51.9
##  6     6   88.7  66.3
##  7     7   78.7  55.1
##  8     8   64.9  64.4
##  9     9   69.5  60.5
## 10    10   71.4  13.9
## 11    11   84.8  77.2
## 12    12   77.9  74.0
## 13    13   78.2  39.3
## 14    14   75.9  57.5
## 15    15   70.6  58.7
## 16    16   89.3  79.9
## 17    17   79.0  60.2
## 18    18   59.3  50.4
## 19    19   80.6  63.7
## 20    20   71.2  64.9
Before <- A6Q2$Before
After <- A6Q2$After

Differences <- After - Before
Differences
##  [1] -22.9304181 -20.2699879 -40.2206673 -17.5279348 -24.0877851 -22.4511430
##  [7] -23.5597882  -0.4765162  -8.9677454 -57.5175962  -7.5992359  -3.8933673
## [13] -38.9533817 -18.4353860 -11.8602264  -9.4392012 -18.8196150  -8.8302696
## [19] -16.9393505  -6.3054720
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)

The difference scores look abnormally distributed. The data is positively 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")

#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 = .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
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
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 the diet versus after the diet. Before scores (M = 76.13, SD = 7.78) were significantly different from after scores (M = 57.19, SD = 14.39), t(19) = 6.1, p < .001. The effect size was large, Cohen’s d = 1.57.

Since the assumption of normality was violated, a Wilcoxon signed-rank test was conducted. The results showed a significant difference between weights before and after the diet, V = 210, p < .001. The effect size was large (r = 0.877), indicating that the diet led to a substantial reduction in weight.

#https://rpubs.com/jishimwe1/1426231