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

Definition (#f7aeae)

Important (#edcae9)

Extra (#fffe9d)

Introduction:

• 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:

• 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?

• In SPSS:

  • Analyze > Compare Means > One Sample T-test

  • Put variable of interest in “test variable”.

  • Under “test value”, put the fixed value.

  • Click “OK”

When to use one-sample t-test:

• You have only one 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:

• The dependent variable 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.

Paired-sample t-test:

• 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 (e.g., pre-test and post-test).

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

When to use paired-sample t-test:

• 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.

• In SPSS:

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

  • Put the first level / condition in “variable 1”

  • Put the second condition / level in “variable 2”

  • Click “OK”

Assumptions:

• 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.

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 / what the values mean.

  • If significant: Which group scored higher and lower.

  • If not significant: Groups had similar scores.