T test as a parametric statistic

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 sta...

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Bibliographic Details
Published in:Korean journal of anesthesiology Vol. 68; no. 6; pp. 540 - 546
Main Author: Kim, Tae Kyun
Format: Journal Article
Language:English
Published: Korea (South) The Korean Society of Anesthesiologists 01.12.2015
Korean Society of Anesthesiologists
대한마취통증의학회
Subjects:
biostatistics
matched-pair analysis
normal distribution
probability
Statistical Round
마취과학
Probability
Biostatistics
Matched-pair analysis
Normal distribution
ISSN:2005-6419, 2005-7563
Online Access:Get full text
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Summary: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.
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G704-000679.2015.68.6.003
ISSN:2005-6419
2005-7563
DOI:10.4097/kjae.2015.68.6.540