Question
Which statistical test should I use for comparing two or more groups in my experiment?
Answer
Choosing the correct statistical test for comparing two or more groups in an experiment is crucial for accurate data interpretation. The choice depends on several factors, including the type of data, the distribution of the data, and the specific hypotheses being tested.
Key Considerations for Choosing a Statistical Test
Data Type and Distribution:
Parametric Tests: Use these when data is normally distributed. Common tests include the t-test for comparing two groups and ANOVA for more than two groups (Ledolter, Gramlich and Kardon, 2020; Chapman and Feit, 2020).
Non-Parametric Tests: Use these when data is not normally distributed or when dealing with small sample sizes. Examples include the Mann-Whitney-Wilcoxon U test for two groups and the Kruskal-Wallis test for more than two groups (Midway et al., 2020; Ledolter, Gramlich and Kardon, 2020).
Number of Groups:
Two Groups: For normally distributed data, use a t-test. For non-normally distributed data, consider the Mann-Whitney-Wilcoxon U test (Midway et al., 2020; Ledolter, Gramlich and Kardon, 2020).
More Than Two Groups: Use ANOVA for normally distributed data and the Kruskal-Wallis test for non-normally distributed data (Ledolter, Gramlich and Kardon, 2020; Chapman and Feit, 2020).
Comparison Type:
Independent Samples: Use independent t-tests or ANOVA for parametric data, and Mann-Whitney or Kruskal-Wallis for non-parametric data (Ledolter, Gramlich and Kardon, 2020; Wilcox, 2022).
Dependent Samples: Use paired t-tests for parametric data and the Wilcoxon signed-rank test for non-parametric data (Ledolter, Gramlich and Kardon, 2020; Wilcox, 2022).
Specific Data Characteristics:
Circular Data: Use Watson’s U2 test or MANOVA for circular data comparisons (Landler, Ruxton and Malkemper, 2021).
High-Dimensional Data: Consider specialized tests like the approximate randomization test for high-dimensional data (Wang and Xu, 2021).
Conclusion
Selecting the appropriate statistical test involves understanding the data type, distribution, and the specific research question. For normally distributed data, parametric tests like t-tests and ANOVA are suitable, while non-parametric tests are better for non-normally distributed data. Consider the number of groups and whether samples are independent or dependent to further refine your choice.
References
Midway, S., Robertson, M., Flinn, S., & Kaller, M., 2020. Comparing multiple comparisons: practical guidance for choosing the best multiple comparisons test. PeerJ, 8. https://doi.org/10.7717/peerj.10387
Ledolter, J., Gramlich, O., & Kardon, R., 2020. Parametric Statistical Inference for Comparing Means and Variances. Investigative Ophthalmology & Visual Science, 61. https://doi.org/10.1167/iovs.61.8.25
Landler, L., Ruxton, G., & Malkemper, E., 2021. Advice on comparing two independent samples of circular data in biology. Scientific Reports, 11. https://doi.org/10.1038/s41598-021-99299-5
Wang, R., & Xu, W., 2021. An approximate randomization test for the high-dimensional two-sample Behrens–Fisher problem under arbitrary covariances. Biometrika. https://doi.org/10.1093/biomet/asac014
Wilcox, R., 2022. Comparing Two Groups. Introduction to Robust Estimation and Hypothesis Testing. https://doi.org/10.1016/B978-0-12-386983-8.00005-6
Chapman, C., & Feit, E., 2020. Comparing Groups: Statistical Tests. Python for Marketing Research and Analytics. https://doi.org/10.1007/978-3-319-14436-8_6
