Question 1: Is there a mean difference in body weight (kg) before versus after all participants tried the low calorie diet?

#Import dataset
Q1 <- read_excel("C:/Users/Julia/OneDrive/Desktop/Assignment 6/Question 1/A6Q1.xlsx")

# Calculate descriptive statistics
#Groups: Before and After
Before <- Q1$Before
After <- Q1$After
Differences <- After - Before

#Descriptive Statistics
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
#Create histogram for Before and After
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 normally distributed. 
#The data is symmetrical.
#The data has a proper bell curve.

#Create Boxplot - Change from blue to light blue to help visibility

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

#Boxplot
#There is one dot outside the boxplot.
#The dot is not close to the whiskers.
#The dot is not very far away from the whiskers.
#Based on these findings, the boxplot is normal. 
#Shapiro-Wilk normality test
shapiro.test(Differences)
## 
##  Shapiro-Wilk normality test
## 
## data:  Differences
## W = 0.94757, p-value = 0.3318

Shapiro-Wilk Interpretation: The data is normally distributed, (p = .332).

#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

Dependent T-Test Interpretation: A Dependent T-Test was conducted to determine if there was a difference in body weight (kg) before the low calorie diet versus after the low calorie diet.Before scores (M = 76.13, SD = 7.78) were not significantly different from after scores (M = 71.59, SD = 6.64), t(19) = 1.90, p = .072.