What Are T-tests in R?

T-tests are widely used in statistics to compare the means of two groups. The assumption is that both groups come from normally distributed populations with equal variances.

Null Hypothesis (H₀): The group means are equal.

Alternative Hypothesis (H₁): The group means are different.

A t-statistic is calculated and compared with a t-distribution to test this hypothesis.

🔸 Welch's T-test

This is a variation of the T-test designed for situations where group variances are not equal.

🧪 Performing T-tests in R

In R, the t.test() function is used for all types of T-tests:

# Independent two-sample T-test t.test(y ~ x)         # y is numeric, x is binary factor t.test(y1, y2)        # both y1 and y2 are numeric # Paired T-test t.test(y1, y2, paired = TRUE) # One-sample T-test t.test(y, mu = 3)     # Tests if mean of y = 3 

Tip: Use alternative = "less" or "greater" for one-tailed tests.
Use var.equal = TRUE when you assume equal variances.

1️⃣ One-Sample T-test

Used to check if the mean of one group differs from a known value.

set.seed(0) ship_vol <- c(rnorm(75, mean = 37000, sd = 2500)) t.test(ship_vol, mu = 39000) 

Here, we're testing if the shipment volume is less than 39000 cubic feet.

2️⃣ Paired Sample T-test

Used when the same subjects are measured before and after a treatment.

Example: Measuring blood pressure before and after a drug trial.

set.seed(2820) pre_Treatment <- c(rnorm(2000, mean = 150, sd = 10)) post_Treatment <- c(rnorm(2000, mean = 144, sd = 9)) t.test(pre_Treatment, post_Treatment, paired = TRUE) 

The result shows a statistically significant drop in blood pressure.

3️⃣ Independent Samples T-test

Used to compare two independent groups.

Case 1: Numeric Vectors

set.seed(0) Spenders_Cleve <- rnorm(60, mean = 350, sd = 77) Spenders_NY <- rnorm(60, mean = 400, sd = 80) t.test(Spenders_Cleve, Spenders_NY, var.equal = TRUE) 

Case 2: Grouped by Factor

Amount_Spent <- c(Spenders_Cleve, Spenders_NY) city_name <- c(rep("Cleveland", 60), rep("New York", 60)) t.test(Amount_Spent ~ city_name, var.equal = TRUE) 

Case 3: Unequal Variances (Welch’s T-test)

t.test(Spenders_Cleve, Spenders_NY, var.equal = FALSE) 

To test if the variances are equal:

var.test(Spenders_Cleve, Spenders_NY) 

Why Use T-tests in R?

📊 To compare means between two groups.

🔍 Especially useful with small sample sizes.

✅ Welch’s T-test is preferred when variances or sample sizes differ.

🧪 One-sample T-test is used for single mean comparisons.

🎓 T-tests are a part of inferential statistics in research.

Summary

At DebugShala, we covered everything you need to know about T-tests in R:

Types: One-sample, paired, and independent T-tests

How to implement them using t.test()

When and why to use each type