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Korean J Anesthesiol > Epub ahead of print
DOI: https://doi.org/10.4097/kja.d.18.00292    [Epub ahead of print]
Published online April 1, 2019.
More about the basic assumptions of t-test: normality and sample size
Tae Kyun Kim1, Jae Hong Park2
1Department of Anesthesia and Pain Medicine, Pusan National University School of Medicine, Busan, Korea
2Department of Anesthesiology and Pain Medicine, Haeundae Paik Hospital, Inje University College of Medicine, Inje, Korea
Corresponding author:  Jae Hong Park, Tel: +82-51-797-0422, Fax: +82-51-797-0422, 
Email: H00150@paik.ac.kr
Received: 11 October 2018   • Revised: 6 March 2019   • Accepted: 25 March 2019
Abstract
Background
Most of parametric statistics starts with the basic assumptions on the distribution of populations. Preceding conditions required to analyze t-test include the measured values in ratio scale or interval scale, simple random extraction, normal distribution of data, appropriate sample size and homogeneity of variance. Normality test is a kind of hypothesis test which has the type I and II errors as like the other hypothesis tests. It means that the sample size must influence the power of the normality test and its reliability. It is hard to find an established sample size for satisfying the power of normality test. In current article, the relationship between normality, power, and sample size is discussed. Materials and
Methods
In independent t-test, the change of the power according to sample size and ratio of the sample sizes between groups was observed.
Results
As the sample size decreased in the normality test, sufficient power was not guaranteed even under the same significance level. When the sample size of one group was fixed and the sample size of another group was increased, power was increased to some extent. However, it was not more efficient than increasing the sample sizes of both groups equally. Discussions and Conclusion: To ensure the power in normality test, sufficient sample size is required. And the power is maximized when the ratios of sample size between the two groups is 1: 1.
Key Words: Biostatistics; Normal distribution; Power; Sample size
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