Assignment6 RQ1

Load Packages

library(readxl)
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(ggplot2)
library(ggpubr)
library(effectsize)

Import Dataset

dataset <- read_excel("/Users/patel777/Desktop/Week6/A6R1.xlsx")

score <- dataset$HeadacheDays
group <- dataset$Medication

Descriptive Statistics

dataset %>%
group_by(Medication) %>%
summarise(
Mean = mean(HeadacheDays),
Median = median(HeadacheDays),
SD = sd(HeadacheDays),
N = n()
)

## # A tibble: 2 × 5
##   Medication  Mean Median    SD     N
##   <chr>      <dbl>  <dbl> <dbl> <int>
## 1 A            8.1    8    2.81    50
## 2 B           12.6   12.5  3.59    50

Histograms

hist(dataset$HeadacheDays[dataset$Medication == "A"],
main = "Histogram: Medication A",
xlab = "Headache Days",
col = "lightblue", border = "black", breaks = 20)

hist(dataset$HeadacheDays[dataset$Medication == "B"],
main = "Histogram: Medication B",
xlab = "Headache Days",
col = "lightgreen", border = "black", breaks = 20)

Normality Tests (Shapiro-Wilk)

shapiro.test(dataset$HeadacheDays[dataset$Medication == "A"])

## 
##  Shapiro-Wilk normality test
## 
## data:  dataset$HeadacheDays[dataset$Medication == "A"]
## W = 0.97852, p-value = 0.4913

shapiro.test(dataset$HeadacheDays[dataset$Medication == "B"])

## 
##  Shapiro-Wilk normality test
## 
## data:  dataset$HeadacheDays[dataset$Medication == "B"]
## W = 0.98758, p-value = 0.8741

Boxplot

ggboxplot(dataset, x = "Medication", y = "HeadacheDays",
color = "Medication", palette = "jco", add = "jitter")

Independent t-test

t.test(HeadacheDays ~ Medication, data = dataset, var.equal = TRUE)

## 
##  Two Sample t-test
## 
## data:  HeadacheDays by Medication
## t = -6.9862, df = 98, p-value = 3.431e-10
## alternative hypothesis: true difference in means between group A and group B is not equal to 0
## 95 percent confidence interval:
##  -5.778247 -3.221753
## sample estimates:
## mean in group A mean in group B 
##             8.1            12.6

Effect Size (Cohen’s d)

cohens_d_result <- cohens_d(HeadacheDays ~ Medication,
data = dataset, pooled_sd = TRUE)
cohens_d_result

## Cohen's d |         95% CI
## --------------------------
## -1.40     | [-1.83, -0.96]
## 
## - Estimated using pooled SD.