与样本量相关的一些条件与参数

与样本量相关的一些条件与参数
## English Answer:
### Conditions related to sample size.
Central Limit Theorem: The distribution of sample means will be approximately normal, regardless of the shape of
the population distribution, for large enough sample sizes. This is a crucial assumption in many statistical tests.
Standard Error: The standard error of the mean is the standard deviation of the sampling distribution of the mean. It is inversely proportional to the square root of the sample size. A larger sample size leads to a smaller standard error, which in turn makes the sample mean more precise.
### Parameters related to sample size.
Confidence Level: The confidence level is the
probability that the sample mean falls within a specified range around the population mean. A higher confidence level requires a larger sample size.
Margin of Error: The margin of error is the maximum amount by which the sample mean is expected to differ from the population mean. A smaller margin of error requires a larger sample size.
Effect Size: The effect size represents the magnitude of the relationship between variables or the difference between groups. A larger effect size requires a smaller sample size to detect statistically significant results.
Power: The power of a statistical test is the probability of correctly rejecting the null hypothesis when it is false. A higher power requires a larger sample size.
Type I Error: The type I error is the probability of rejecting the null hypothesis when it is true. A smaller type I error requires a larger sample size.
Type II Error: The type II error is the probability of failing to reject the null hypothesis when it is false. A smaller type II error requires a larger sample size.
## 中文回答：
### 与样本量相关的条件。

中心极限定理，对于足够大的样本量，样本均值的分布将近似
于正态分布，而无论总体分布的形状如何。

这是许多统计检验中的
一个关键假设。

标准误差，均值的标准误差是均值的抽样分布的标准差。

它与
样本量的大小平方根成反比。

更大的样本量导致更小的标准误差，
进而使样本均值更精确。

### 与样本量相关的参数。

置信水平，置信水平是样本均值落在总体均值周围的特定范围
内的概率。

更高的置信水平需要更大的样本量。

误差范围，误差范围是样本均值与总体均值预期的最大差异量。

较小的误差范围需要更大的样本量。

效应量，效应量代表变量之间的关系或组之间的差异的大小。

较大的效应量需要较小的样本量才能检测出具有统计学意义的结果。

效力，统计检验的效力是指当零假设为假时正确拒绝零假设的
概率。

更高的效力需要更大的样本量。

第一类错误，第一类错误是在零假设为真时拒绝零假设的概率。

较小的第一类错误需要更大的样本量。

第二类错误，第二类错误是在零假设为假时未能拒绝零假设的
概率。

较小的第二类错误需要更大的样本量。