Research question 1

INDEPENDENT T-TEST & MANN-WHITNEY U TEST

QUESTION
What are the null and alternate hypotheses for YOUR research scenario?
H0:There is no difference between the Medications A and B.
H1: Medication A has lower headaches than Medication B.

LOAD THE PACKAGE

library(readxl)

IMPORT EXCEL FILE INTO R STUDIO

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

LOAD THE PACKAGE

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

CREATE THE HISTOGRAMS

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

hist(dataset$HeadacheDays[dataset$Medication == "B"],
main = "Histogram of Medication B",
xlab = "Value",
ylab = "Frequency",
col = "lightgreen",
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?
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?
. Too flat
Q3) Check the SKEWNESS of the VARIABLE 2 histogram. In your opinion, does the histogram look symmetrical, positively skewed, or negatively skewed?
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?
Too flat.

CONDUCT THE 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:
Was the data normally distributed for Variable 1?
NO
Was the data normally distributed for Variable 2?
NO

LOAD THE PACKAGE.

library(ggplot2)
library(ggpubr)

CREATE THE BOXPLOT

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

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?
yes, there are two dots and they are close to whiskers.

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

LOAD THE PACKAGE

library(effectsize)

CALCULATE COHEN’S D

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.

Q1) What is the size of the effect?
Cohen’s D of 1.40 indicates the difference between the group averages was very large.

Q2) Which group had the lower headache?
Participants taking Medication A has lowe headache than participants taking medication B.

REPORT
An Independent t-test was conducted to compare headache by taking Medication A (n=50) or Medication B(n=50). Participants taking Medication A has lower headaches (Mean= 8.1 and Median= 8) than participants taking Medication B(Mean = 12.6 and Median= 12.5) The effect size was large (d = 1.40)indicatesvery large difference in participants taking medication A and B. Overall, Participants taking medication A has lower headaches than participants taking medication B.