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Korean J Anesthesiol. 2015 Dec;68(6):540-6. doi: 10.4097/kjae.2015.68.6.540. Epub 2015 Nov 25.

T test as a parametric statistic.

Author information

1
Department of Anesthesia and Pain Medicine, Pusan National University School of Medicine, Busan, Korea.

Abstract

In statistic tests, the probability distribution of the statistics is important. When samples are drawn from population N (µ, σ(2)) with a sample size of n, the distribution of the sample mean X̄ should be a normal distribution N (µ, σ(2)/n). Under the null hypothesis µ = µ0, the distribution of statistics [Formula: see text] should be standardized as a normal distribution. When the variance of the population is not known, replacement with the sample variance s (2) is possible. In this case, the statistics [Formula: see text] follows a t distribution (n-1 degrees of freedom). An independent-group t test can be carried out for a comparison of means between two independent groups, with a paired t test for paired data. As the t test is a parametric test, samples should meet certain preconditions, such as normality, equal variances and independence.

KEYWORDS:

Biostatistics; Matched-pair analysis; Normal distribution; Probability

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