A6Q3

Open the Installed Packages

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)

Import and Name the Dataset

A6Q3 <- read_excel("C:/Users/krish/Downloads/A6Q3-2.xlsx")

Calculate the Descriptive Statistics

A6Q3 %>%
  group_by(Exercise) %>%
  summarise(
    Mean = mean(Weight, na.rm = TRUE),
    Median = median(Weight, na.rm = TRUE),
    SD = sd(Weight, na.rm = TRUE),
    N = n()
  )

## # A tibble: 2 × 5
##   Exercise  Mean Median    SD     N
##   <chr>    <dbl>  <dbl> <dbl> <int>
## 1 cardio    74.7   73.3  7.57    25
## 2 nocardio  70.8   69.5  7.35    25

Create Histograms (Normality Check #1)

hist(A6Q3$Weight[A6Q3$Exercise == "cardio"],
     main = "Histogram of Cardio",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightyellow",
     border = "black",
     breaks = 10)

hist(A6Q3$Weight[A6Q3$Exercise == "nocardio"],
     main = "Histogram of Nocardio",
     xlab = "Value",
     ylab = "Frequency",
     col = "brown",
     border = "black",
     breaks = 10)

Interpret the Histograms

Group 1: cardio

The first variable looks normally distributed.

The data is symmetrical.

The data has a proper bell curve.

Group 2: nocardio

The second variable looks normally distributed.

The data is symmetrical.

The data has a proper bell curve.

Create Boxplots for Outliers (Normality Check #2)

ggboxplot(A6Q3, x = "Exercise", y = "Weight",
          color = "Exercise",
          palette = "jco",
          add = "jitter")

Interpret the Boxplots

Boxplot 1: Nocardio

There are dots outside the boxplot.

The dots are close to the whiskers

The dots are not very far away from the whisker

Based on this findings,the boxplot is normal

Boxplot 2: Cardio

There are dots outside the boxplot.

The dots are close to the whiskers

The dots are not very far away from the whisker

Based on this findings,the boxplot is normal

Shapiro-Wilk Tests (Normality Check #3)

shapiro.test(A6Q3$Weight[A6Q3$Exercise == "cardio"])

## 
##  Shapiro-Wilk normality test
## 
## data:  A6Q3$Weight[A6Q3$Exercise == "cardio"]
## W = 0.96745, p-value = 0.5812

shapiro.test(A6Q3$Weight[A6Q3$Exercise == "nocardio"])

## 
##  Shapiro-Wilk normality test
## 
## data:  A6Q3$Weight[A6Q3$Exercise == "nocardio"]
## W = 0.97686, p-value = 0.8166

Interpret the Shapiro-Wilk Test Group 1: Exercise

The first group is normally distributed, p >.05.

Group 2: Weight

The second group is normally distributed, p >.05.

Conduct the Independent T-Test

t.test(Weight ~ Exercise, data = A6Q3, var.equal = TRUE)

## 
##  Two Sample t-test
## 
## data:  Weight by Exercise
## t = 1.8552, df = 48, p-value = 0.06971
## alternative hypothesis: true difference in means between group cardio and group nocardio is not equal to 0
## 95 percent confidence interval:
##  -0.3280454  8.1605622
## sample estimates:
##   mean in group cardio mean in group nocardio 
##               74.73336               70.81710

Report the Independent T-Test

An Independent T-Test was conducted to determine if there was a difference in Weight between cardio and nocardio.

Cardio scores (M = 74.7, SD = 7.57) were not significantly different from nocardio scores (M = 70.8, SD = 7.35), t(48) = 1.85, p >0.05.