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When I compared the techniques, the main difference between t-tests and ANOVAs is the number of means being compared. T-tests are limited to two means, while ANOVAs can handle three or more means, and factorial ANOVAs allow for more than one independent variable (Gravetter & Wallnau, 2013). Another difference is in the design: independent samples tests use separate groups of participants (between-subjects), while paired samples and repeated measures tests use the same participants measured multiple times (within-subjects) (Field, 2024). Factorial ANOVAs are more flexible and can combine both between- and within-subjects factors. Across all these techniques, the independent variable(s) are fixed (defined by the researcher), while the dependent variable is random (scores that vary across participants).

Reflection and Question

Seeing these techniques side by side helped me understand how they fit together as a system. For me, the biggest challenge is selecting the proper test for a specific research design. I consider how researchers consistently decide between a repeated measures ANOVA and a mixed factorial ANOVA when a design includes both repeated and independent elements. How do you reliably determine which test better answers the research question when the design could potentially be analyzed in more than one way?

References

Field, A. (2024). Discovering statistics using IBM SPSS statistics (6th ed.). Sage Publications Limited.

Gravetter, F. J., & Wallnau, L. B. (2013). Statistics for the behavioral sciences (10th ed.). Belmont, CA: Wadsworth, Cengage Learning.

Privitera, G. J. (2024). Research methods for the behavioral sciences (7th ed.). Sage Publications.

 please ask a question with feedback and a reply about table. Thank You.

Technique

Independent Variable

Dependent Variable

Definition

# of IVs

Fixed or Random

# of levels in IV (If Fixed)

Between or Within Subjects

# of DVs

Fixed or Random

One Sample t-test

 Compares a sample mean to a known or hypothesized population mean.

 1

 Fixed

 1

 N/A

 1

 Random

Independent Samples t-test

 Two groups of different people compared

 1 (only one manipulation)

 Fixed, people are in one group or the other

 2 (t-tests are always only 2 groups)

 Between (different people in each group)

 1 (just one outcome per t-test)

 Random (outcome can take on any value)

Paired Samples t-test (AKA repeated measures t-test or dependent measures t-test)

 Compares two measurements from the same participants or matched pairs.

 1

 Fixed

 2

 Within

 1

 Random

One-Way ANOVA

 Tests for mean differences among three or more independent groups

 1

 Fixed

 2+

 Between

 1

 Random

Two-Way ANOVA

Examines the effects of two independent variables on a single outcome, including interactions

 2

 Fixed

 2+

 Between

 1

 Random

Repeated Measures ANOVA

Tests for mean differences when the same participants are measured three or more times.

 1

 Fixed

 3+

 Within

 1

 Random

Factorial ANOVA (can also be called a Mixed Factors Factorial ANOVA)

Combines at least one between-subjects factor and one within-subjects factor to test for main effects and interactions.

 2+

 Fixed

 Depends on Design (At least 2 levels per factor e.g., 2×2, 2×3 designs)

 Mixed

 1

 Random