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?

H0:There is no difference between the scores of Group A and Group B.

H1:There is a difference between the scores of Group A and Group B.

#INSTSALL REQUIRED PACKAGE
#install.packages("readxl")
# LOAD THE PACKAGE
library(readxl)
# IMPORT EXCEL FILE INTO R STUDIO
dataset <- read_excel("C:\\Users\\DELL\\Downloads\\A6R1.xlsx")
DESCRIPTIVE STATISTICS

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

#INSTALL REQUIRED PACKAGE
#install.packages("dplyr")
# 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
HISTOGRAMS

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

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

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

# 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
QUESTION

Was the data normally distributed for Variable 1?

Yes, Normally distributed

Was the data normally distributed for Variable 2?

Yes, Normally distributed

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 REQUIRED PACKAGE
# install.packages("ggplot2")
# install.packages("ggpubr")

# LOAD THE PACKAGE
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?

For Both the box-plots, there are a few dots and are close to the whiskers. Hence we proceed 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")
# 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?

Very Large

Q2) Which group had the higher average score?

Group B has the higher average score

REPORT FOR INDEPENDENT T-TEST

An Independent t-test was conducted to compare the differences in the number of headaches between the Medication A (n = 50) and Medication B (n = 50). People who used medication B have higher average headache days (M = 12.6, SD = 3.59) than that of medication B (M = 8.1, SD = 2.81), t(100) = -6.9862, p < .001. The effect size was very large (d = -1.40), indicating a very large difference between headache days of medication A and medication B. Overall, medication B has significantly higher average days of headache among the participants.