A6R1

HYPOTHESIS TESTED:

QUESTION

What are the null and alternate hypotheses for YOUR research scenario?

H0:There is no difference in the number of headaches between participants taking Medication A and participants taking Medication B.

H1:There is a difference in the number of headaches between participants taking Medication A and participants taking Medication B.

library(readxl)

A6R1 <- read_excel("C:\\Users\\kuppi\\OneDrive\\Desktop\\A6R1.xlsx")

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

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

hist(A6R1$HeadacheDays[A6R1$Medication == "A"],
main = "Histogram of A Scores",
xlab = "Value",
ylab = "Frequency",
col = "lightblue",
border = "black",
breaks = 20)

hist(A6R1$HeadacheDays[A6R1$Medication == "B"],
main = "Histogram of B Scores",
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?

1. The histogram of variable 1 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?

1. The kurtosis of variable 1 has a proper bell curve

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

1. The histogram of variable 2 looks symmetrical

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?

1. The kurtosis of variable 2 has a proper bell curve

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

QUESTION

Was the data normally distributed for Variable 1?

yes

Was the data normally distributed for Variable 2?

yes

library(ggplot2)
library(ggpubr)

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?

1. there are very few dots and close to the whiskers

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)

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?

1. The effect size is very large

Q2) Which group had the higher average score?

1. Group B has the higher average score

Summary

An independent t-test was conducted to compare headache days between patients who took Medication A (n = 50) and Medication B (n = 50). Patients who took Medication B had significantly more headache days (M = 12.6, SD = 3.59) than patients who took Medication A (M = 8.1, SD = 2.81), t(98) = –6.99, p = 3.431e–10. The effect size was very large (d = –1.40, 95% CI [–1.83, –0.96]), indicating a substantial difference between the two medication groups. Overall, Medication A was associated with fewer headache days compared to Medication B.