Research Scenario 1: Medication A vs Medication B

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

H0: There is no difference between the number of headaches of who took medication A and medication B

H1: There is a difference between the number of headaches of who took medication A and medication B

Load Required Library

library(readxl)

Read dataset

dataset <- read_excel("C:/Users/chkas/Downloads/A6R1.xlsx")

Descriptive Statistics

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

Calculate the Descriptive Statistics

dataset %>%
  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(dataset$HeadacheDays[dataset$Medication == "A"],
main = "Histogram of A Scores",
xlab = "Value",
ylab = "Frequency",
col = "lightblue",
border = "black",
breaks = 20)

hist(dataset$HeadacheDays[dataset$Medication == "B"],
main = "Histogram of B Scores",
xlab = "Value",
ylab = "Frequency",
col = "lightgreen",
border = "black",
breaks = 20)

QUESTIONS: Histogram Analysis

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

A) The histogram looks symmetrical

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?

A) The histogram too tall

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

A) The histogram looks somewhat 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?

A) The histogram too tall

Shapiro-wilk Test

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

Answer the questions below as a comment within the R script:

Q)Was the data normally distributed for Variable 1? A) The data is normal for variable 1 (p = 0.4913, which is > 0.05) Was the data normally distributed for Variable 2? A) The data is normal for variable 2 (p = 0.8741, which is > 0.05)

Load Required Library

library(ggplot2)
library(ggpubr)

Create the Boxplot

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

QUESTION

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

A) here are a few dots (two or less), and they are close to the whisker, So continue with Independent t-test.

Test if there was a difference between the means of the two groups.

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

DETERMINE STATISTICAL SIGNIFICANCE

The results are statistically significant continue to effect size install.packages(“effectsize”) Effect Size

library(effectsize)

Calculate the effect size

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

Q) What is the size of the effect?

A Cohen’s D of 1.40 indicates the difference between the group averages was very large.

Q) Which group had the higher average score?

Medication B had a higher average number of headache days than Medication A.

Final Report

An Independent t-test was conducted to compare headache days between patients who took Medication A (n = 50) and patients who took Medication B (n = 50). Patients who took Medication A had significantly fewer headache days (M = 8.10, SD = 2.81) than patients who took Medication B (M = 12.60, SD = 3.59), t(98) = -6.99, p < .001. The effect size was large (d = -1.40), indicating a very large difference between the two medications. Overall, Medication A resulted in significantly fewer headache days than Medication B.