Kim Tae Kyun
Department of Anesthesia and Pain Medicine, Pusan National University School of Medicine, Busan, Korea.
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.
在统计检验中，统计量的概率分布很重要。当从总体N(µ, σ²)中抽取样本量为n的样本时，样本均值X̄的分布应为正态分布N(µ, σ²/n)。在原假设µ = µ0下，统计量[公式：见原文]的分布应标准化为正态分布。当总体方差未知时，可以用样本方差s²代替。在这种情况下，统计量[公式：见原文]服从自由度为n - 1的t分布。可以进行独立样本t检验以比较两个独立组之间的均值，对于配对数据则进行配对t检验。由于t检验是参数检验，样本应满足某些前提条件，如正态性、方差齐性和独立性。
