A6Q3

Question 3

Is there a difference in mean body weight (kg) between participants who do cardio versus participants who do not do cardio?

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 dataset

A6Q3_2 <- read_excel("A6Q3-2.xlsx")

Descriptive statistics

A6Q3_2 %>%
  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 the Histograms

hist(A6Q3_2$Weight[A6Q3_2$Exercise == "nocardio"],
     main = "Histogram of Nocardio Weight",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightgreen",
     border = "black",
     breaks = 10)

hist(A6Q3_2$Weight[A6Q3_2$Exercise == "cardio"],
     main = "Histogram of cardio Weight",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightblue",
     border = "black",
     breaks = 10)

Correction to colors they were reversed in first try

Group1: NoCardio The first variable looks normally distributed. The data is symmetrical. The data has a proper bell curve.

Group 2: Cardio The second variable looks normally distributed. The data is symmetrical. The data has a proper bell curve.

ggboxplot(A6Q3_2, x = "Exercise", y = "Weight",
          color = "Exercise",
          palette = "jco",
          add = "jitter")

Create boxplots

Boxplot 1: NoCardio There are dots outside the boxplot. The dots are close to the whiskers. Based on these findings, the boxplot is normal. Update to the finding analysis.

Boxplot 2: Cardio There are dots outside the boxplot. The dots are close to the whiskers. Based on these findings, the boxplot is normal.

Statistical normality test

shapiro.test(A6Q3_2$Weight[A6Q3_2$Exercise == "nocardio"])

## 
##  Shapiro-Wilk normality test
## 
## data:  A6Q3_2$Weight[A6Q3_2$Exercise == "nocardio"]
## W = 0.97686, p-value = 0.8166

shapiro.test(A6Q3_2$Weight[A6Q3_2$Exercise == "cardio"])

## 
##  Shapiro-Wilk normality test
## 
## data:  A6Q3_2$Weight[A6Q3_2$Exercise == "cardio"]
## W = 0.96745, p-value = 0.5812

Group 1: Name of noncardio The first group is normally distributed, (p = .8166). Group 2: Name of cardio The second group is normally distributed, (p = .5812).

Independent T-Test.

t.test(Weight ~ Exercise, data = A6Q3_2, 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

cohens_d_result <- cohens_d(Weight ~ Exercise, data = A6Q3_2, pooled_sd = TRUE)
print(cohens_d_result)

## Cohen's d |        95% CI
## -------------------------
## 0.52      | [-0.04, 1.09]
## 
## - Estimated using pooled SD.

An Independent T-Test was conducted to determine if there was a difference in Weight between nocardio and cardio exercise. The weight of the group that did cardio (M = 74.70, SD = 7.57) was not significantly different from the group that did not do cardio (M = 70.80, SD = 7.35), t(48) = 1.86, p > .05.An update to the significance analysis has been made and corrected.