PsychStatsWiki

标准误（standard of error）

• 指样本均值分布的标准差，是反映样本均值分布变异性的指标。
• 定义式为σ/√n，σ为总体的标准差，n为样本容量。

• Standard error is the standard deviation of the sample mean distribution, is an indicator that reflects the variability of the sample mean distribution.
• The definition formula is σ/√n, σ is the standard deviation of the population, and n is the sample size.

大数定律（law of large numbers）

• 随样本容量的的增大，样本均值与总体均值之间的误差会减小。
• Law of large numbers: As the sample size increases, the error between the sample mean and the population mean will decrease.

中心极限定律（central limit theorem）

• 对于任何均值为μ，标准差为σ的总体, 样本容量为n的样本均值的分布，随着n趋近无穷大时，会趋近均值为μ，标准差为σ/√n的正态分布 。
• 应用条件：通常在n≥30时，我们认为样本均值的分布满足中心极限定律。
• 中心极限定律综合了样本均值的三个主要特性：形状、均值和方差。

• For any population with a mean of μ and a standard deviation of σ, and a sample size of n, the distribution of the mean will approach a normal distribution with a mean of μ and a standard deviation of σ/√n as n approaches infinity.
• Application conditions: Usually, when n ≥ 30, we believe that the distribution of sample mean satisfies the central limit theorem.
• The central limit theorem combines the three main characteristics of sample mean: shape, mean, and variance.