Understanding and Applying Welch’s T-Test for Comparing Customer Types with R

Introduction to R Beginner: Loops on a Welch t-test

Overview of the Problem

In this blog post, we will explore how to compare means for different customer types using a Welch’s t-test in R. The problem revolves around avoiding manual testing for each pair of factor levels and exploring ways to use the t.test() function across a vector of unique factor levels.

Understanding the Basics of Welch’s t-test

Before diving into the solution, it’s essential to understand what a Welch’s t-test is. A Welch’s t-test is a statistical test used to compare the means of two groups (in this case, different customer types) when the variances of the two groups are unknown or unequal. The test is also known as a paired t-test, although it can be used with independent samples.

Setting Up the Data

To work on our problem, we need a dataset that includes the measurements for each customer type. We will create a sample dataset using R’s built-in functions and then use this data to perform the Welch’s t-test.

# Load necessary libraries
library(stats)
library(dplyr)

# Create a sample dataset
data <- data.frame(
  purchases = rnorm(100, 50, 20), 
  MemberType = factor(sample(c("a", "b", "c"), 100, replace= TRUE)),
  ItemType = factor(sample(c("d","e","f"), 100, replace=TRUE))
)

# Create a subset of the data for item type 'a'
df2 <- data[data$ItemType == "a", ]

Using `pairwise.t.test()`

The most straightforward way to compare means for different customer types is to use R’s built-in function pairwise.t.test() from the stats package. This function allows us to specify the type of multiple-test adjustment we want to use (in this case, Bonferroni corrections) and whether we are using pooled or unpooled standard deviations.

# Perform pairwise Welch's t-tests with Bonferroni corrections and unpooled standard deviations
pairwise.t.test(df2$purchases, df2$MemberType, p.adj = "bonf", pool.sd = FALSE)

Understanding the `apply()` Family of Functions

The apply() family of functions in R is used to apply a function across an entire dataset or vector. However, we need to be aware that these functions require two inputs: the data and the function to apply.

# Example usage of the apply() family of functions
function(i) {
  t.test(df2$purchases[MemberType == i], df2$MemberType)
}

# Apply the function using lapply()
lapply(levels(df2$MemberType), function(i) {
  t.test(df2$purchases[MemberType == i], df2$MemberType)
})

# Apply the function using sapply()
sapply(levels(df2$MemberType), function(i) {
  t.test(df2$purchases[MemberType == i], df2$MemberType)
})

Using Nested Loops

Now, let’s explore how to use nested loops in R to compare means for different customer types. We can use a for() loop and an additional layer of nesting to apply the t.test() function across each level of the factor.

# Create an empty vector to store the results of t-tests
results <- c()

# Iterate over each level of the MemberType factor
for (i in levels(df2$MemberType)) {
  # Apply the t-test and append the result to the vector
  results[i] <- t.test(df2$purchases[MemberType == i], df2$MemberType)
}

Handling Multiple-Test Adjustments

When performing multiple statistical tests, we need to account for the family-wise error rate (FWER) to avoid Type I errors. The FWER is the probability of making at least one Type I error.

There are several methods to adjust for the FWER, including:

Bonferroni corrections
Holm-Bonferroni method
Tamhane’s method

# Perform pairwise Welch's t-tests with Bonferroni corrections and unpooled standard deviations
pairwise.t.test(df2$purchases, df2$MemberType, p.adj = "bonf", pool.sd = FALSE)

# Perform pairwise Welch's t-tests with Holm-Bonferroni method and pooled standard deviation
pairwise.t.test(df2$purchases, df2$MemberType, p.adj = "holm", pool.sd = TRUE)

Handling Pooled vs Unpooled Standard Deviations

When performing the Welch’s t-test, we need to decide whether to use pooled or unpooled standard deviations. The choice depends on the assumption about the variances of the two groups.

# Perform pairwise Welch's t-tests with Bonferroni corrections and unpooled standard deviations
pairwise.t.test(df2$purchases, df2$MemberType, p.adj = "bonf", pool.sd = FALSE)

# Perform pairwise Welch's t-tests with Holm-Bonferroni method and pooled standard deviation
pairwise.t.test(df2$purchases, df2$MemberType, p.adj = "holm", pool.sd = TRUE)

Conclusion

In this blog post, we explored how to compare means for different customer types using a Welch’s t-test in R. We discussed the basics of the test, set up a sample dataset, and used various functions and methods to perform the test.

We also examined the apply() family of functions and nested loops to apply the test across each level of the factor. Additionally, we discussed how to handle multiple-test adjustments and whether to use pooled or unpooled standard deviations.

By following these steps and understanding the nuances of the Welch’s t-test, you can perform accurate statistical comparisons in R.

Last modified on 2025-02-12