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      T test as a parametric statistic

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          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 should be a normal distribution N (µ, σ 2/ n). Under the null hypothesis µ = µ 0, the distribution of statistics z = X ¯ - µ 0 σ / n 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 X ¯ - µ 0 s / n 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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          Most cited references5

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          The generalisation of student's problems when several different population variances are involved.

          B L WELCH (1947)
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            An approximate distribution of estimates of variance components.

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              Standard deviation and standard error of the mean

              In most clinical and experimental studies, the standard deviation (SD) and the estimated standard error of the mean (SEM) are used to present the characteristics of sample data and to explain statistical analysis results. However, some authors occasionally muddle the distinctive usage between the SD and SEM in medical literature. Because the process of calculating the SD and SEM includes different statistical inferences, each of them has its own meaning. SD is the dispersion of data in a normal distribution. In other words, SD indicates how accurately the mean represents sample data. However the meaning of SEM includes statistical inference based on the sampling distribution. SEM is the SD of the theoretical distribution of the sample means (the sampling distribution). While either SD or SEM can be applied to describe data and statistical results, one should be aware of reasonable methods with which to use SD and SEM. We aim to elucidate the distinctions between SD and SEM and to provide proper usage guidelines for both, which summarize data and describe statistical results.
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                Author and article information

                Journal
                Korean J Anesthesiol
                Korean J Anesthesiol
                KJAE
                Korean Journal of Anesthesiology
                The Korean Society of Anesthesiologists
                2005-6419
                2005-7563
                December 2015
                25 November 2015
                : 68
                : 6
                : 540-546
                Affiliations
                Department of Anesthesia and Pain Medicine, Pusan National University School of Medicine, Busan, Korea.
                Author notes
                Corresponding author: Tae Kyun Kim, M.D., Ph.D. Department of Anesthesia and Pain Medicine, Pusan National University School of Medicine, 20, Geumo-ro, Mulgeum-eup, Yangsan 50612, Korea. Tel: 82-51-360-2129, Fax: 82-51-360-2149, anesktk@ 123456pusan.ac.kr
                Author information
                http://orcid.org/0000-0002-4790-896X
                Article
                10.4097/kjae.2015.68.6.540
                4667138
                26634076
                75885e1f-2e8e-487a-87de-69e557040066
                Copyright © the Korean Society of Anesthesiologists, 2015

                This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( http://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 10 July 2015
                : 19 August 2015
                : 07 September 2015
                Categories
                Statistical Round

                Anesthesiology & Pain management
                biostatistics,matched-pair analysis,normal distribution,probability

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