One-Sample t-test & Paired-Samples t-test

Definition (#f7aeae)

Important (#edcae9)

Extra (#fffe9d)

Introduction to t-test: 3*

  • Involves comparison of 2 “groups” or “conditions” or “levels” (IV).

  • Whether differences between the groups/levels are significant or not.

  • DV must be a continuous variable.

  • 3 types:

    • One-sample t-test

    • Independent-samples t-test

    • Paired-samples t-test

One-sample t-test:

Overview: 3*

  • Used to compare the sample mean to a known or hypothesized population mean.

  • Tests whether the sample mean is significantly different from the population mean.

  • Only one group of participants is involved.

  • Ex: Is the average score of our class different from the national average?

When to use one-sample t-test: 3*

  • You have only 1 group of participants.

  • You want to compare their mean score to a fixed value.

  • The fixed value must be known and meaningful for comparison.

  • Used in descriptive and applied research.

  • Useful when evaluating if a group differs from a set standard or benchmark.

Assumptions: 3*

  • The DV is measured on an interval or ratio scale.

  • The data should be approximately normally distributed.

  • The observations are independent (each participant's score is not influenced by others).

  • The population mean used for comparison must be known.

Analyse:

  1. Analyze → Compare Means → One Sample T-test.

  2. Put variable of interest in “test variable”.

  3. Under “test value” → Put the fixed value → Click “OK”.

    Step 2-3
Output 1*3*

Paired-sample t-test:

Overview: 3*

  • Used to compare the means of two related measurements from the same group.

  • Tests whether there is a significant difference before and after an intervention.

  • Also known as dependent-samples t-test or repeated-measures t-test.

  • Each participant provides 2 scores (pre-test and post-test).

  • Ex: Comparing anxiety levels before and after therapy in the same participants.

When to use paired-sample t-test: 3*

  • You have 1 group measured at 2 different times or under 2 different conditions.

  • Used in within-subjects design.

  • Common in experiments measuring change (training effectiveness, mood changes).

  • Useful when comparing matched pairs (twins, partners, or case-control studies).

  • Minimum number of participants is recommended to be 20 or more for reliability.

Assumptions: 3*

  • The DV is measured on an interval or ratio scale.

  • The differences between the 2 scores should be approximately normally distributed.

  • The pairs of observations are dependent.

  • Each pair is independent of the other pairs.

Analysis:

  1. Analyze → Compare Means→ Paired-Samples T-Test.

  2. Put the first level/condition in “variable 1”

  3. Put the second condition / level in “variable 2” → Click “OK”.

    Step 2-3
Output 2* Interpretation

Template:

  • What test you ran and what variables were plugged in.

  • Is there a significant difference between group.

  • Report the “equation” above with the values.

  • Interpretation:

    • If significant: Which group scored higher and lower.

    • If not significant: Groups had similar scores.

2*3*