Quantitative Research Methods

Statistical T-Tests

Understanding the critical difference between independent and paired samples.

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What Is a t-test?

A t-test compares the means of two groups to determine whether the difference is statistically significant. The key to choosing the right test lies in how those groups are related.

Independent Samples

Comparing separate groups.

Paired Samples

Comparing the same group twice.

Independent Samples

Separate Groups

Also called a two-sample t-test. Used when comparing means of two completely separate groups.

Use when:

  • Participant is in only one group.
  • Groups are not related or matched.

Example

Comparing English test scores between:

  • A Students using AI tools
  • B Students NOT using AI tools

Null Hypothesis ($H_0$)

μ1 = μ2

Paired Samples

Dependent / Matched

Also called a dependent t-test. Used when comparing two sets of scores from the same group.

Use when:

  • Measuring the same group twice (Pre/Post).
  • Participants are matched (e.g., twins).

Example

Testing grammar scores:

  • 1 Before using chatbot
  • 2 After 4 weeks of use

Null Hypothesis ($H_0$)

μd = 0

Summary Comparison

Feature Independent t-test Paired t-test
Groups Two separate groups Same group (or matched)
Data Unrelated observations Repeated/Related observations
Example Group A vs. Group B Pre-test vs. Post-test

The Golden Rule

Ask yourself: "Are the scores coming from the same people at two different times, or from different people?"