Independent Samples t-test

In many real-world problems, we need to compare the average values between two separate and unrelated groups.

The Independent Samples t-test is used to determine whether the means of two independent groups are statistically different from each other.

When to Use an Independent Samples t-test

This test is appropriate when:

• You have one categorical variable with two independent groups
• You have one numerical (scale) dependent variable
• Observations in one group are not related to the other

Common examples include:

• Comparing exam scores of two different classes
• Comparing salaries between two departments
• Comparing customer satisfaction between two regions

Example Dataset

Consider the following dataset comparing exam scores between two teaching methods:

The goal is to determine whether the teaching method leads to a significant difference in scores.

Assumptions of the Test

Before running the t-test, these assumptions should be checked:

• Independence of observations
• Normality of the dependent variable
• Homogeneity of variances

SPSS helps evaluate these assumptions automatically.

Running Independent Samples t-test (Menu)

To perform the test using the SPSS menu:

• Go to Analyze → Compare Means → Independent-Samples T Test
• Move the numerical variable to Test Variable(s)
• Move the grouping variable to Grouping Variable
• Define the two groups
• Click OK

SPSS produces group statistics and t-test results.

Using SPSS Syntax

T-TEST GROUPS=Method('Online' 'Offline')
  /VARIABLES=Score
  /CRITERIA=CI(.95).

This syntax compares mean scores between Online and Offline groups.

Interpreting the Output

Focus on two main sections:

• Group Statistics – shows mean and standard deviation
• Independent Samples Test – shows t-value and p-value

Interpretation rule:

• p < 0.05 → significant difference between group means
• p ≥ 0.05 → no significant difference

Also check Levene’s Test to assess equality of variances.

Common Mistakes

Frequent errors include:

• Using the test for paired data
• Ignoring assumption violations
• Misinterpreting non-significant results

Correct test selection is essential for valid conclusions.

Quiz 1

What does an independent samples t-test compare?

Quiz 2

What type of variable is required as the grouping variable?

Quiz 3

What does p < 0.05 indicate?

Quiz 4

Which test checks equality of variances?

Quiz 5

Can this test be used for paired data?

Mini Practice

Create a dataset comparing two marketing strategies based on monthly sales.

Perform an independent samples t-test to determine whether sales differ between the two strategies.

What’s Next

In the next lesson, you will learn about the Paired Samples t-test, used when measurements are related or repeated.