理解标准差与均值标准误差之间的差异，以及知道何时使用哪一个。
Understanding the Difference Between Standard Deviation and Standard Error of the Mean, and Knowing When to Use Which.
作者信息
Andrade Chittaranjan
机构信息
Dept. of Clinical Psychopharmacology and Neurotoxicology, National Institute of Mental Health and Neurosciences, Bangalore, Karnataka, India.
出版信息
Indian J Psychol Med. 2020 Jul 20;42(4):409-410. doi: 10.1177/0253717620933419. eCollection 2020 Jul.
Many authors are unsure of whether to present the mean along with the standard deviation (SD) or along with the standard error of the mean (SEM). The SD is a descriptive statistic that estimates the scatter of values around the sample mean; hence, the SD describes the sample. In contrast, the SEM is an estimate of how close the sample mean is to the population mean; it is an intermediate term in the calculation of the 95% confidence interval around the mean, and (where applicable) statistical significance; the SEM does not describe the sample. Therefore, the mean should always be accompanied by the SD when describing the sample. There are many reasons why the SEM continues to be reported, and it is argued that none of these is justifiable. In fact, presentation of SEMs may mislead readers into believing that the sample data are more precise than they actually are. Given that the standard error is not presented for other parameters, such as difference between means or proportions, and difference between proportions, it is suggested that presentation of SEM values can be done away with, altogether.
许多作者不确定是应将均值与标准差（SD）一起呈现，还是与均值标准误（SEM）一起呈现。标准差是一种描述性统计量，用于估计样本均值周围数值的离散程度；因此，标准差描述的是样本。相比之下，均值标准误是对样本均值与总体均值接近程度的估计；它是计算均值周围95%置信区间（以及适用时的统计显著性）过程中的一个中间项；均值标准误并不描述样本。所以，在描述样本时，均值应始终与标准差一起给出。均值标准误仍被报告有诸多原因，但有人认为这些原因都不合理。事实上，呈现均值标准误可能会误导读者，使其认为样本数据比实际情况更精确。鉴于其他参数（如均值之差、比例之差等）并未给出标准误，建议完全摒弃均值标准误值的呈现。
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