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ERIC Number: EJ1015748
Record Type: Journal
Publication Date: 2013-Aug
Pages: 12
Abstractor: As Provided
ISSN: ISSN-1531-7714
Using the Student's "t"-Test with Extremely Small Sample Sizes
de Winter, J. C .F.
Practical Assessment, Research & Evaluation, v18 n10 Aug 2013
Researchers occasionally have to work with an extremely small sample size, defined herein as "N" less than or equal to 5. Some methodologists have cautioned against using the "t"-test when the sample size is extremely small, whereas others have suggested that using the "t"-test is feasible in such a case. The present simulation study estimated the Type I error rate and statistical power of the one- and two-sample "t"-tests for normally distributed populations and for various distortions such as unequal sample sizes, unequal variances, the combination of unequal sample sizes and unequal variances, and a lognormal population distribution. "N"s per group were varied between 2 and 5. Results show that the "t"-test provides Type I error rates close to the 5% nominal value in most of the cases, and that acceptable power (i.e., 80%) is reached only if the effect size is very large. This study also investigated the behavior of the Welch test and a rank-transformation prior to conducting the "t"-test ("t"-testR). Compared to the regular "t"-test, the Welch test tends to reduce statistical power and the "t"-testR yields false positive rates that deviate from 5%. This study further shows that a paired "t"-test is feasible with extremely small "N"s if the within-pair correlation is high. It is concluded that there are no principal objections to using a "t"-test with "N"s as small as 2. A final cautionary note is made on the credibility of research findings when sample sizes are small. (Contains 4 tables and 4 figures.)
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Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A