Research Scenario 1

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?

PURPOSE

Used to test whether there is a statistically significant difference between the means of two independent groups

NULL HYPOTHESIS

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

ALTERNATE HYPOTHESIS

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

##install.packages(“readxl”)

chooseCRANmirror(graphics = FALSE, ind = 1) 
install.packages("readxl")

## Installing package into 'C:/Users/manit/AppData/Local/R/win-library/4.5'
## (as 'lib' is unspecified)

## package 'readxl' successfully unpacked and MD5 sums checked
## 
## The downloaded binary packages are in
##  C:\Users\manit\AppData\Local\Temp\RtmpIFFKei\downloaded_packages

LOAD THE PACKAGE

library(readxl)

IMPORT THE EXCEL FILE INTO R STUDIO

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

## # A tibble: 6 × 3
##   ParticipantID Medication HeadacheDays
##           <dbl> <chr>             <dbl>
## 1             1 A                     6
## 2             2 A                     7
## 3             3 A                    13
## 4             4 A                     8
## 5             5 A                     8
## 6             6 A                    13

DESCRIPTIVE STATISTICS

Calculate the mean, median, SD, and sample size for each variable. ## INSTALL THE 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 DATA`

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

HISTOGRAMS

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

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

hist(A6R1$HeadacheDays[A6R1$Medication == "B"],
     main = "Histogram of Medication B HeadacheDays ",
     xlab = "Headache Days",
     ylab = "Frequency",
     col = "lightgreen",
     border = "black",
     breaks = 20)

QUESTIONS

Answer the questions below as comments within the R script::
Q1)Check the SKEWNESS of the VARIABLE 1 histogram. In your opinion, does the histogram look symmetrical, positively skewed, or negatively skewed?
Ans)The histogram is slightly positively skewed, indicating a longer tail on the right.
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?
Ans)The histogram is moderately flat, showing no extreme peaks or outliers.
Q3) Check the SKEWNESS of the VARIABLE 2 histogram. In your opinion, does the histogram look symmetrical, positively skewed, or negatively skewed?
Ans)The histogram is slightly positively skewed, with a tail extending to the right.
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?
Ans)The histogram has a moderately flat distribution, with no sharp peaks.

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(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

Answer the questions below as a comment within the R script:
Was the data normally distributed for Variable 1?
Ans)Yes, the data for Medication A is normally distributed because the p-value (0.4913) is greater than 0.05.
Was the data normally distributed for Variable 2?
Ans)Yes, the data for Medication B is normally distributed because the p-value (0.8741) is greater than 0.05.

BOXPLOT

Purpose:

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

INSTALL REQUIRED PACKAGE

install.packages("ggplot2")

## Installing package into 'C:/Users/manit/AppData/Local/R/win-library/4.5'
## (as 'lib' is unspecified)

## package 'ggplot2' successfully unpacked and MD5 sums checked
## 
## The downloaded binary packages are in
##  C:\Users\manit\AppData\Local\Temp\RtmpIFFKei\downloaded_packages

install.packages("ggpubr")

## Installing package into 'C:/Users/manit/AppData/Local/R/win-library/4.5'
## (as 'lib' is unspecified)

## package 'ggpubr' successfully unpacked and MD5 sums checked
## 
## The downloaded binary packages are in
##  C:\Users\manit\AppData\Local\Temp\RtmpIFFKei\downloaded_packages

LOAD THE PACKAGE

Always reload the package you want to use.

library(ggplot2)
library(ggpubr)

CREATE THE BOXPLOT

ggboxplot(A6R1, x = "Medication", y = "HeadacheDays",
          color = "Medication",
          palette = "jco",
          add = "jitter")

QUESTION

Answer the questions below as a comment within the R script. Answer the questions for EACH boxplot:
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?
Ans)Yes,there are a few dots outside the boxplots for both Medication A and Medication B, but they are not very far from the whiskers. Since the outliers are few and close to the whiskers, it is reasonable to proceed with the independent t-test.

DETERMINE STATISTICAL SIGNIFICANCE

INDEPENDENT T-TEST

PURPOSE:

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

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

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 AND LOAD THE REQUIRED PACKAGE

install.packages("effectsize")

## Installing package into 'C:/Users/manit/AppData/Local/R/win-library/4.5'
## (as 'lib' is unspecified)

## package 'effectsize' successfully unpacked and MD5 sums checked
## 
## The downloaded binary packages are in
##  C:\Users\manit\AppData\Local\Temp\RtmpIFFKei\downloaded_packages

library(effectsize)

CALCULATE COHEN’S D

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

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

Q1) What is the size of the effect?
A) A Cohen’s D of -1.40 indicates the difference between the group averages was very large.
Q2) Which group had the higher average score?
Ans)Here Group B has the higher average score.

WRITTEN 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.

Team 6 Scene 1

2025-11-19

Research Scenario 1

PURPOSE

NULL HYPOTHESIS

ALTERNATE HYPOTHESIS

LOAD THE PACKAGE

IMPORT THE EXCEL FILE INTO R STUDIO

DESCRIPTIVE STATISTICS

LOAD THE PACKAGE

CALCULATE THE DESCRIPTIVE DATA`

HISTOGRAMS

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

QUESTIONS

SHAPIRO-WILK TEST

Purpose:

QUESTION

BOXPLOT

Purpose:

INSTALL REQUIRED PACKAGE

LOAD THE PACKAGE

Always reload the package you want to use.

CREATE THE BOXPLOT

QUESTION

DETERMINE STATISTICAL SIGNIFICANCE

INDEPENDENT T-TEST

PURPOSE:

DETERMINE STATISTICAL SIGNIFICANCE

EFFECT-SIZE

PURPOSE:

INSTALL AND LOAD THE REQUIRED PACKAGE

CALCULATE COHEN’S D

QUESTIONS

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

WRITTEN REPORT FOR INDEPENDENT T-TEST