T test as a parametric statistic

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


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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