Research Question

A medical research team created a new medication to reduce headaches (Medication A). They want to determine if Medication A is more effective at reducing headaches than the current medication on the market (Medication B). A group of participants were randomly assigned to either take Medication A or Medication B. Data was collected for 30 days through an app and participants reported each day if they did or did not have a headache. Was there a difference in the number of headaches between the groups?

Hypothesis

Null Hypothesis (H0): There is no difference in the number of headacheDays between participants taking Medication A and those taking Medication B.

Alternate Hypothesis (H1): There is a difference in the number of headacheDays between participants taking Medication A and those taking Medication B.

# Install .packages("readxl")
# Load required 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
#Import the excel file
A6R1 <- read_excel("C:/Users/sravz/Downloads/A6R1.xlsx")

DESCRIPTIVE STATISTICS

# calculate descriptive statistics
A6R1 %>%
  group_by(Medication) %>%
  summarise(
    Mean = mean(HeadacheDays, na.rm = TRUE),
    Median = median(HeadacheDays, na.rm = TRUE),
    SD = sd(HeadacheDays, na.rm = TRUE),
    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(A6R1$HeadacheDays[A6R1$Medication == "A"],
main = "Histogram for Medication A",
xlab = "Value",
ylab = "Frequency",
col = "lightpink",
border = "black",
breaks = 20)

hist(A6R1$HeadacheDays[A6R1$Medication == "B"],
main = "Histogram for Medication B",
xlab = "Value",
ylab = "Frequency",
col = "orange",
border = "black",
breaks = 20)

QUESTIONS

Q1) Check the SKEWNESS of the VARIABLE 1 histogram. In your opinion, does the histogram look symmetrical, positively skewed, or negatively skewed?

The histogram for Medication A appears to be slightly positively skewed.

Q2) Check the KURTOSIS of the VARIABLE 1 histogram. In your opinion, does the histogram look too flat, too tall, or does it have a proper bell curve?

The histogram for Medication A appears to have a proper bell curve shape, or perhaps is slightly too tall.

Q3) Check the SKEWNESS of the VARIABLE 2 histogram. In your opinion, does the histogram look symmetrical, positively skewed, or negatively skewed?

The histogram for Medication B is slightly positively skewed.

Q4) Check the KUROTSIS of the VARIABLE 2 histogram. In your opinion, does the histogram look too flat, too tall, or does it have a proper bell curve?

It looks slightly tall, meaning mildly leptokurtic, but still close to normal.

SHAPIRO-WILK TEST

shapiro.test(A6R1$HeadacheDays[A6R1$Medication == "A"])
## 
##  Shapiro-Wilk normality test
## 
## data:  A6R1$HeadacheDays[A6R1$Medication == "A"]
## W = 0.97852, p-value = 0.4913
shapiro.test(A6R1$HeadacheDays[A6R1$Medication == "B"])
## 
##  Shapiro-Wilk normality test
## 
## data:  A6R1$HeadacheDays[A6R1$Medication == "B"]
## W = 0.98758, p-value = 0.8741

QUESTIONs

Was the data normally distributed for Variable 1?

Data is normally distributed.

Was the data normally distributed for Variable 2?

Data is normally distributed.

library(ggplot2)
library(ggpubr)

BOXPLOT

ggboxplot(A6R1, x = "Medication", y = "HeadacheDays",
          color = "Medication",
          palette = "jco",
          add = "jitter")

QUESTION

Q1) Were there any dots outside of the boxplot? Are these dots close to the whiskers of the boxplot or are they very far away?

Medication A: maybe 1 small outlier, near whisker

Medication B: maybe 1–2 small outliers, but close to whiskers

INDEPENDENT T-TEST

t.test(HeadacheDays ~ Medication, data = A6R1, 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
library(effectsize)

Cohen’s D

cohens_d_result <- cohens_d(HeadacheDays ~ Medication, data = A6R1, pooled_sd = TRUE)
print(cohens_d_result)
## Cohen's d |         95% CI
## --------------------------
## -1.40     | [-1.83, -0.96]
## 
## - Estimated using pooled SD.

QUESTIONS

Q1) What is the size of the effect?

Cohen’s d = - 1.40, which is a VERY LARGE effect size.

Q2) Which group had the higher average rank?

Medication B had the higher average score (Mean = 12.6).

Final Report

An independent samples t-test was conducted to compare the number of headache days between participants taking Medication A and participants taking Medication B. Participants taking Medication A (M = 8.10, SD = 2.81, n = 50) reported significantly fewer headache days over the 30-day period than participants taking Medication B (M = 12.60, SD = 3.59, n = 50), t = –6.99, p < .001. The effect size was very large (Cohen’s d = -1.40), indicating that Medication A substantially reduced headache frequency compared to Medication B.