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?

QUESTION

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

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

Alternative Hypotheses (H1):There is a difference in the number of headaches between participants taking Medication A and those taking Medication B.

options(repos = c(CRAN = "https://cloud.r-project.org"))
install.packages("readxl")
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## The downloaded binary packages are in
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library(readxl)
dataset <- read_excel("C:\\Users\\N Geetha Shivani\\Downloads\\A6R1.xlsx")

DESCRIPTIVE STATISTICS

PURPOSE: Calculate the mean, median, SD, and sample size for each group.

install.packages("dplyr")
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LOAD THE PACKAGE

Always reload the package you want to use.

 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

Purpose: Visually check the normality of the scores for each group.

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

hist(dataset$HeadacheDays[dataset$Medication == "B"],
     main = "Histogram of Group 2 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?

A)The histogram for Group A 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 has a proper bell shaped curve.

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 for Group A 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?

A)The histogram has a proper bell shaped curve.

SHAPIRO-WILK TEST

Purpose: Check the normality for each group’s score statistically. The Shapiro-Wilk Test is a test that checks skewness and kurtosis at the same time. The test is checking “Is this variable the SAME as normal data (null hypothesis) or DIFFERENT from normal data (alternate hypothesis)?” For this test, if p is GREATER than .05 (p > .05), the data is NORMAL. If p is LESS than .05 (p < .05), the data is NOT normal.

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

QUESTION

Q) Was the data normally distributed for Variable 1?

A)Yes, the data is Normally distributed for Group A

Q) Was the data normally distributed for Variable 2?

A)Yes, the data is Normally distributed for Group B

NOTE:

If p > 0.05 (P-value is GREATER than .05) this means the data is NORMAL. Continue to the box-plot test below. If p < 0.05 (P-value is LESS than .05) this means the data is NOT normal (switch to Mann-Whitney U).

BOXPLOT

Purpose: Check for any outliers impacting the mean for each group’s scores.

install.packages("ggplot2")
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install.packages("ggpubr")
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library(ggplot2)
library(ggpubr)

CREATE THE BOXPLOT

ggboxplot(dataset, 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?

A)For both the box-plots, there are a few dots and they are close to the whiskers. Hence we go with Independent T-test.

INDEPENDENT T-TEST

PURPOSE: 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

If results were statistically significant (p < .05), continue to effect size section below.

If results were NOT statistically significant (p > .05), skip to reporting section below.

NOTE:

Getting results that are not statistically significant does NOT mean you switch to Mann-Whitney U.

The Mann-Whitney U test is only for abnormally distributed data — not based on outcome significance.

EFFECT-SIZE

PURPOSE: Determine how big of a difference there was between the group means.

INSTALL REQUIRED PACKAGE

install.packages("effectsize")
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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.

QUESTIONS

Q1) What is the size of the effect?

  1. A Cohen’s D of –1.40 represents a very large effect size, indicating a substantial difference between the two group means.

Q2) Which group had the higher average score?

  1. Here Group B has the higher average score.

WRITTEN REPORT FOR INDEPENDENT T-TEST

An independent t-test was performed to compare the number of headache days between individuals using Medication A (n = 50) and Medication B (n = 50). Results indicated that Medication B users reported more headache days (M = 12.6, SD = 3.59) than Medication A users (M = 8.1, SD = 2.81), t(100) = –6.99, p < .001. The effect size was large (d = –1.40), reflecting a substantial difference between the groups. These findings demonstrate that Medication B is associated with a significantly higher number of headache days.