Independent T-Test & Mann-Whitney U Test

What Are These Tests?

An Independent T-Test compares the means of two independent groups. For example, you might compare exam scores for females and males.

A Mann-Whitney U Test is the nonparametric alternative used when the outcome variable does not meet the normality assumption required for the independent t-test.

Below is an example of what your code will look like. Your code will be different because the dataset name, variable name, expected proportions, results, and interpretations will depend on your assigned dataset.

library(readxl)
library(ggpubr)
library(dplyr)
library(effectsize)
library(effsize)

DatasetName %>%
  group_by(GroupVariable) %>%
  summarise(
    Mean = mean(OutcomeVariable, na.rm = TRUE),
    Median = median(OutcomeVariable, na.rm = TRUE),
    SD = sd(OutcomeVariable, na.rm = TRUE),
    N = n()
  )

hist(DatasetName$OutcomeVariable[DatasetName$GroupVariable == "Group1Name"],
     breaks = 15,
     col = "skyblue",
     border = "white")

hist(DatasetName$OutcomeVariable[DatasetName$GroupVariable == "Group2Name"],
     breaks = 15,
     col = "firebrick",
     border = "white")


ggboxplot(DatasetName,
          x = "GroupVariable",
          y = "OutcomeVariable",
          color = "GroupVariable",
          palette = "jco",
          add = "jitter")


shapiro.test(
  DatasetName$OutcomeVariable[
    DatasetName$GroupVariable == "Group1Name"
  ]
)

shapiro.test(
  DatasetName$OutcomeVariable[
    DatasetName$GroupVariable == "Group2Name"
  ]
)


# Independent t-test


t.test(
  OutcomeVariable ~ GroupVariable,
  data = DatasetName,
  var.equal = TRUE
)

cohens_d_result <- cohens_d(
  OutcomeVariable ~ GroupVariable,
  data = DatasetName,
  pooled_sd = TRUE
)

print(cohens_d_result)


# Mann-Whitney U Test

wilcox.test(
  ExamScores ~ Gender,
  data = DatasetZ
)


# Cliff's Delta

mw_effect <- cliff.delta(
  OutcomeVariable ~ GroupVariable,
  data = DatasetName
)

print(mw_effect)

Install and Load the Packages

You will use several R packages for this analysis.

# Install packages only if you have never installed them before

install.packages("readxl")
install.packages("ggpubr")
install.packages("dplyr")
install.packages("effectsize")
install.packages("effsize")

After the packages are installed, load them with:

library(readxl)
library(ggpubr)
library(dplyr)
library(effectsize)
library(effsize)

Although datasets can be imported entirely through code, many students experience difficulty locating file paths. Therefore, this course uses the point-and-click import method to generate the necessary code automatically.

Import the Excel File

1. Select File → Import Dataset → From Excel.
2. Select Browse.
3. Locate where you saved the downloaded dataset.
4. Select the dataset and choose Open.
5. Return to the import window and select Import.

What Happens When You Click Import?

Once imported, the dataset will appear in the Environment pane.

RStudio also automatically generates the code used to import the dataset. Copy this line of code into your R Script. This allows the dataset to be automatically imported whenever you reopen your R Script.

General Example

DatasetName <- read_excel("filepath")

Example with a Sample File Path

DatasetZ <- read_excel(
"C:/Users/John/OneDrive/Documents/AA5221/Datasets/DatasetZ.xlsx"
)

Describe the Two Groups

Start by calculating the mean, median, standard deviation, and sample size for each group.

DatasetZ %>%
  group_by(Gender) %>%
  summarise(
    Mean = mean(ExamScores, na.rm = TRUE),
    Median = median(ExamScores, na.rm = TRUE),
    SD = sd(ExamScores, na.rm = TRUE),
    N = n()
  )

Example Output

# A tibble: 2 × 5
  Gender   Mean Median    SD     N
  <chr>   <dbl>  <dbl> <dbl> <int>
1 Females  83.0   79.3  7.50    50
2 Males    76.7   79.5  6.00    50

Look at the Distribution

Create a histogram for each group. Look for a distribution that is approximately bell-shaped rather than strongly skewed or irregular.

hist(DatasetZ$ExamScores[DatasetZ$Gender == "Females"],
     breaks = 15,
     col = "skyblue",
     border = "white")

hist(DatasetZ$ExamScores[DatasetZ$Gender == "Males"],
     breaks = 15,
     col = "firebrick",
     border = "white")

Use the histograms as a visual check. Do not make your final normality decision from the histogram alone.

#Data for Group #1 appears normally / abnormally distributed.
#Data for Group #2 appears normally / abnormally distributed.

Check for Potential Outliers

A boxplot helps you identify the center, spread, and potential outliers in each group.

ggboxplot(
  DatasetZ,
  x = "Gender",
  y = "ExamScores",
  color = "Gender",
  palette = "jco",
  add = "jitter"
)

Look for potential outliers in each group. An extreme value can influence the distribution and may contribute to skewness.

For example, if a dataset contains mostly typical incomes but includes one extremely high income, that value could create positive (right) skew.

Conduct the Shapiro-Wilk Test

The Shapiro-Wilk test provides the formal normality check used for this course.

shapiro.test(
  DatasetZ$ExamScores[
    DatasetZ$Gender == "Females"
  ]
)

shapiro.test(
  DatasetZ$ExamScores[
    DatasetZ$Gender == "Males"
  ]
)

Example Output

Females

W = 0.91523, p-value = 0.0778


Males

W = 0.89172, p-value = 0.0611

#The first group is normally / abnormally distributed (p > or < .05).
#The second group is normally / abnormally distributed (p > or < .05).

Choose Your Statistical Test

Use the Shapiro-Wilk results to select the test.

After completing your R Script, the next step is to convert it into an R Markdown document.

An R Markdown document combines your code, output, and written explanation into a single HTML report. This allows others to reproduce your analysis and view both the code and results in one document.

Before proceeding, review the R Markdown lesson.

R Markdown Files

Create a New R Markdown File

1. Open RStudio.
2. Select: File → New File → R Markdown
3. Ensure that HTML is selected as the output format.
4. Select OK.

You do not need to complete any of the optional fields. The default settings are sufficient for this assignment.

Save the R Markdown File

1. Select File → Save As.
2. Save the file to your desktop.
3. Delete all of the prewritten sample text generated by RStudio.
4. Open your completed R Script.
5. Copy all of your code.
6. Paste the code into the empty R Markdown document.

Create a Code Chunk

R code inside an R Markdown file must be placed inside a code chunk.

Add the following line at the very beginning of your document:

```{r}

Then add the following line at the very end of your document:

```

All of your code should now be located between the two lines.

Example Structure

```{r}

paste all your code here

```

When the code chunk has been created correctly, the code region will typically appear shaded or highlighted within RStudio.

Step 5: Knit the Document

Once the code chunk has been created, generate the HTML report.

1. Select the Knit button at the top of the R Markdown document.
2. The Knit button resembles a ball of yarn with a knitting needle.
3. Wait for the document to compile.
4. A new HTML report should open automatically.

The report will display your code, output, tables, charts, and statistical results in a web-friendly format.

After creating and knitting your R Markdown document, the final step is to publish your report to RPubs.

RPubs allows you to share your analysis as a web page that can be viewed in any browser without requiring RStudio.

Before beginning, review the RPubs lesson.

RPubs

Open Your R Markdown File

1. Open your completed R Markdown file.
2. Verify that the document knits successfully and displays all output correctly.
3. Select the Knit button if you have not already generated the HTML report.

After knitting, the completed HTML report should appear in the Viewer pane or open in a web browser.

Publish to RPubs

1. Locate the Publish button in the Viewer pane.
2. Select Publish to RPubs.
3. Log in to your RPubs account.
4. If you do not already have an account, create a free RPubs account.
5. Enter a title for your report.
6. Optionally enter a description.
7. Select Publish.

Save the RPubs HTML File

In addition to publishing the report online, save a copy of the HTML file for your records.

1. Open your published RPubs report in a web browser.
2. Press Ctrl + S (Windows) or Command + S (Mac).
3. Choose a location on your computer.
4. If available, select Webpage, HTML Only.
5. Save the file.