Is there a mean difference in body weight (kg) before versus after all participants tried the low calorie diet?

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)

A6Q1 <- read_excel("~/downloads/A6Q1.xlsx")

Before <- A6Q1$Before
After <- A6Q1$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] 71.58994
median(After, na.rm = TRUE)
## [1] 70.88045
sd(After, na.rm = TRUE)
## [1] 6.639509
hist(Differences,
     main = ("histogram of Difference Body Weight"),
     xlab = "Value",
     ylab = "Frequency",
     col = "blue",
     border = "black",
     breaks = 20)

Histogram of Difference Body Weight The difference in body weight look “normally” distributed.(corrected the distrubution from abnormal to normal) The data is “positively” skewed.(Corrected the skewness from negative to positive) The data “has” a proper bell curve.(corrected the data for the bell curve)

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

Boxplot There is one outside the boxplot. (updated data to show there is one dot outside of boxplot) The dots is close to the whiskers. (updated data to show dot is close to whiskers) The dots are 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 = 0.94757, p-value = 0.3318

Shapiro-Wilk Difference In Body Weight The data is normally distributed, (p = 0.3318).

wilcox.test(Before, After, paired = TRUE, na.action = na.omit)
## 
##  Wilcoxon signed rank exact test
## 
## data:  Before and After
## V = 148, p-value = 0.114
## alternative hypothesis: true location shift is not equal to 0

A Wilcoxon Signed-Rank Test was conducted to determine if there was a difference in OutcomeVariable before low calorie diet versus after low calorie diet. Before scores (Mdn = xx.xx) were [significantly / not significantly] different from after scores (Mdn = xx.xx), V = xx, p = [< .001 / = .xxx / > .05]. The effect size was [small / medium / large / very large], r = .xxx.

(Correction to run a Dependent T-Test)

t.test(Before, After, paired = TRUE, na.action = na.omit)
## 
##  Paired t-test
## 
## data:  Before and After
## t = 1.902, df = 19, p-value = 0.07245
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -0.4563808  9.5424763
## sample estimates:
## mean difference 
##        4.543048

A Dependent T-Test was conducted to determine if there was a difference in body weight before Independent Variable versus after Independent Variable. Before scores (M = 76.13, SD = 7.78) were no significant difference from after scores (M = 71.59 SD = 6.64), t(19) = 1.9, p <.005