# INDEPENDENT T-TEST & MANN-WHITNEY U TEST
# HYPOTHESIS TESTED:
# Used to test if there is a difference between the means of two groups.
# QUESTION
# What are the null and alternate hypotheses for YOUR research scenario?
# H0:There is no difference in the number of headacheDays between participants who take Medication A and those who take Medication B.
# H1: There is a difference in the number of headacheDays between participants who take Medication A and those who take Medication B.
# IMPORT EXCEL FILE
# Purpose: Import your Excel dataset into R to conduct analyses.
# INSTALL REQUIRED PACKAGE
# install.packages("readxl")
# LOAD THE PACKAGE
library(readxl)
A6R1 <- read_excel("C:\\Users\\deept\\Documents\\Zoom\\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
A6R1 %>%
group_by(Medication) %>%
summarise(
Mean = mean(Medication, na.rm = TRUE),
Median = median(HeadacheDays, na.rm = TRUE),
SD = sd(HeadacheDays, na.rm = TRUE),
N = n()
)
## Warning: There were 2 warnings in `summarise()`.
## The first warning was:
## ℹ In argument: `Mean = mean(Medication, na.rm = TRUE)`.
## ℹ In group 1: `Medication = "A"`.
## Caused by warning in `mean.default()`:
## ! argument is not numeric or logical: returning NA
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 1 remaining warning.
## # A tibble: 2 × 5
## Medication Mean Median SD N
## <chr> <dbl> <dbl> <dbl> <int>
## 1 A NA 8 2.81 50
## 2 B NA 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 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
# 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?
# The Histogram is 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?
# The histogram is bell curve
# Q3) Check the SKEWNESS of the VARIABLE 2 histogram. In your opinion, does the histogram look symmetrical, positively skewed, or negatively skewed?
# The histogram is negatively 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?
# The histogram is too tall
# SHAPIRO-WILK TEST
# Purpose: Check the normality for each group's score statistically.
# CONDUCT THE SHAPIRO-WILK TEST
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?
# The data is normally distributed
# Was the data normally distributed for Variable 2?
# The data is 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
# If previously installed, put a hashtag in front of the code.
# install.packages("ggplot2")
# install.packages("ggpubr")
# LOAD THE PACKAGE
# Always reload the package you want to use.
library(ggplot2)
library(ggpubr)
# CREATE THE BOXPLOT
# Replace "dataset" with your dataset name (without .xlsx)
# Replace "score" with your dependent variable R code name (example: USD)
# Replace "group" with your independent variable R code name (example: Country)
ggboxplot(A6R1, x = "Medication", y = "HeadacheDays",
color = "Medication",
palette = "jco",
add = "jitter")
# QUESTION
# Answer the questions below as a comment within the R script:
# Q1) Were there any dots outside of the boxplots? These dots represent participants with extreme scores.
# There are dots outside the boxplots
# Q2) If there are outliers, in your opinion are the scores of those dots changing the mean so much that the mean no longer accurately represents the average score?
# No
# 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
# The results were statistically significant (p < .05), continue to effect size section below.
# EFFECT-SIZE
# PURPOSE: Determine how big of a difference there was between the group means.
# INSTALL REQUIRED PACKAGE
# install.packages("effectsize")
# LOAD THE PACKAGE
# Always load the package you want to use.
library(effectsize)
# CALCULATE COHEN’S D
cohen_d_result <- cohens_d(HeadacheDays ~ Medication, data = A6R1, pooled_sd = TRUE)
print(cohen_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 Cohen's D of -1.40 indicates the difference between the group averages was very large.
# Q2) Which group had the higher average score?
# Group B has higher average score.
# WRITTEN REPORT FOR INDEPENDENT T-TEST
# Write a paragraph summarizing your findings.
# 2) REPORT YOUR DATA AS A PARAGRAPH
# An Independent t-test was conducted to compare
# number of headacheDays between participants who take Medication A (n = 50) and without Medication (n = 50).
# number of headacheDays between participants who take Medication A are significantly higher (M = 12.5, SD = 3.59) than
# participnats without medication (M =8 SD =2.81 ), t(50) = -6.9862, p = 0.00.
# The effect size was very large (d =98)
# Overall, number of headacheDays between participants without Medication have higher scores.