🧩 What “Independent Samples” Means

Two samples are independent when the individuals in one group have no relationship to the individuals in the other group.

• No pairing
• No repeated measures
• No matching
• No overlap in membership

This is the setup for the independent‑samples t‑test, also called the two‑sample t‑test.

According to Statistics By Jim, this test is used when you want to compare the means of exactly two groups to determine whether their population means differ.

When You Use an Independent‑Samples Test

You use an independent‑samples hypothesis test when:

• You have two separate groups (e.g., men vs. women, treatment A vs. treatment B).
• You want to test whether their population means differ.
• The groups are unrelated and randomly sampled.

Hypotheses for Independent Samples

Most commonly:

Null hypothesis (H₀):

The two population means are equal.

Alternative hypothesis (Hₐ):

The two population means are not equal.

🧪 Example 1: Coffee vs. Tea and Reaction Time

A researcher wants to know whether coffee drinkers and tea drinkers differ in average reaction time.

• Group 1: 40 people who drink coffee every morning
• Group 2: 40 people who drink tea every morning

No one is in both groups, and they weren’t matched or paired → independent samples.

Hypotheses:

• 
• 

🧠 Example 2: Two Teaching Methods

A school tests whether a new teaching method improves math scores.

• Group 1: Students in Class A taught with the traditional method
• Group 2: Students in Class B taught with the new method

Different students, different classes → independent samples.

Hypotheses:

• 
• 

🏃 Example 3: Running Shoes and Speed

A sports scientist compares two brands of running shoes.

• Group 1: Runners randomly assigned to Shoe Brand X
• Group 2: Runners randomly assigned to Shoe Brand Y

Each runner uses only one shoe brand → independent samples.

Hypotheses:

• 
• 

🧬 Example 4: Medication vs. Placebo

A pharmaceutical company tests a new medication.

• Group 1: Patients receiving the medication
• Group 2: Patients receiving a placebo

Random assignment, no overlap → independent samples.

Hypotheses:

• 
• 

🎮 Example 5: Gaming and Stress Levels

A psychologist studies whether playing video games reduces stress.

• Group 1: People who play 1 hour of a calming game
• Group 2: People who sit quietly for 1 hour

Different participants in each condition → independent samples.

Hypotheses:

• 
• 

🛒 Example 6: Online vs. In‑Store Shoppers

A marketing team wants to know whether online shoppers spend more than in‑store shoppers.

• Group 1: 100 customers who shop online
• Group 2: 100 customers who shop in physical stores

Two unrelated groups → independent samples.

Hypotheses:

• 
• 

Why It Matters

Independent‑samples tests are foundational because most real‑world research compares two separate groups. As the social‑science text notes, comparing two means is one of the most common inferential tasks.