Five-Point Likert Items: t test versus Mann-Whitney-Wilcoxon (Addendum added October 2012)
Open accessAbstract
Likert questionnaires are widely used in survey research, but it is unclear whether the item data should be investigated by means of parametric or nonparametric procedures. This study compared the Type I and II error rates of the t test versus the Mann-Whitney-Wilcoxon (MWW) for five-point Likert items. Fourteen population distributions were defined and pairs of samples were drawn from the populations and submitted to the t test and the t test on ranks, which yields the same results as MWW. The results showed that the two tests had equivalent power for most of the pairs. MWW had a power advantage when one of the samples was drawn from a skewed or peaked distribution. Strong power differences between the t test and MWW occurred when one of the samples was drawn from a multimodal distribution. Notably, the Type I error rate of both methods was never more than 3% above the nominal rate of 5%, even not when sample sizes were highly unequal. In conclusion, for five-point Likert items, the t test and MWW generally have similar power, and researchers do not have to worry about finding a difference whilst there is none in the population.Accessed 61,170 times on https://pareonline.net from October 06, 2010 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Cites
Glass, G. V., Peckham, P. D., & Sanders, J. R. (1972) · Review of Educational Research · doi:10.3102/00346543042003237 · Cited by 1,826 · see citing works
The Importance of the Normality Assumption in Large Public Health Data Sets
Lumley, T., Diehr, P., Emerson, S., & Chen, L. (2002) · Annual Review of Public Health · doi:10.1146/annurev.publhealth.23.100901.140546 · Cited by 1,803 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Using the Student's t-test with extremely small sample sizes
de Winter, J. C. F. (2013) · University of Massachusetts Amherst · doi:10.7275/e4r6-dj05 · Cited by 992 · see citing works
Self-citationUsing AI-generated suggestions from ChatGPT to optimize clinical decision support
Liu, S., Wright, A. P., Patterson, B. L., Wanderer, J. P., Turer, R. W., Nelson, S. D., McCoy, A. B., Sittig, D. F., & Wright, A. (2023) · Journal of the American Medical Informatics Association · doi:10.1093/jamia/ocad072 · Cited by 397 · see citing works
On the Comprehension of Program Comprehension
Maalej, W., Tiarks, R., Roehm, T., & Koschke, R. (2014) · ACM Transactions on Software Engineering and Methodology · doi:10.1145/2622669 · Cited by 180 · see citing works
Assessing the Value of ChatGPT for Clinical Decision Support Optimization
Liu, S., Wright, A. P., Patterson, B. L., Wanderer, J. P., Turer, R. W., Nelson, S. D., McCoy, A. B., Sittig, D. F., & Wright, A. (2023) · doi:10.1101/2023.02.21.23286254 · Cited by 90 · see citing works
Reza, M., Laundry, N. M., Musabirov, I., Dushniku, P., Yu, Z. Y. “., Mittal, K., Grossman, T., Liut, M., Kuzminykh, A., & Williams, J. J. (2024) · Proceedings of the CHI Conference on Human Factors in Computing Systems · doi:10.1145/3613904.3641899 · Cited by 52 · see citing works
Error Message Readability and Novice Debugging Performance
Denny, P., Prather, J., & Becker, B. A. (2020) · Proceedings of the 2020 ACM Conference on Innovation and Technology in Computer Science Education · doi:10.1145/3341525.3387384 · Cited by 50 · see citing works
U.S. Dental Students’ Attitudes Toward Research and Science: Impact of Research Experience
Holman, S. D., Wietecha, M. S., Gullard, A., & Peterson, J. M. B. (2014) · Journal of Dental Education · doi:10.1002/j.0022-0337.2014.78.3.tb05684.x · Cited by 38 · see citing works
Cabrera, C., & Neville, R. (2025) · Perspectives: Policy and Practice in Higher Education · doi:10.1080/13603108.2025.2595453 · Cited by 4 · see citing works
- Authors
- de Winter, J. F. C., & Dodou, D.
- ORCID
- Dodou, D.
- Venue
- University of Massachusetts Amherst
- Publisher
- University of Massachusetts Amherst
- Published
- 2010
- Volume
- 15
- Issue
- 1
- Pages
- 11
- OpenAlex
- W2990318625
- Cited by
- 231
- References
- 2
- Citations by year
- 2026: 16 · 2025: 29 · 2024: 41 · 2023: 42 · 2022: 35 · 2021: 45 · 2020: 20 · 2018: 2 · 2017: 1
- FWCI
- 22.59
- Type
- journal article
- Language
- en
- Open access
- Licence
- cc-by-nc-nd
- Locations
- ScholarWorks@UMassAmherst (University of Massachusetts Amherst) (submittedVersion, cc-by-nc-nd)
- Practical assessment, research & evaluation
- University of Massachusetts (UMass) Amherst
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Social Sciences › Sociology and Political Science › Survey Methodology and Nonresponse
- Keywords
- t-test, Mann-Whitney test, statistical power, type I error rate, type II error rate, parametric vs nonparametric tests, skewed distributions, multimodal distributions, unequal sample sizes, survey data analysis
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
