The Central Limit Theorem (CLT) states that when plotting a sample distribution of mean the mean of the sample will be equal to the population mean and the sample distribution will approach normal distribution with variance equal to standard error.
样本均值等于总体均值，样本分布接近方差等于样本方差的正态分布
Assumptions behind the CLT:
The sample data must be sampled and selected randomly from the population.
There should not be any multicollinearity in the sampled data; one sample should not influence the other samples.
The sample size should be no more than 10% of the population. Generally, a sample size greater than 30 (n>30) is considered good.
statistical inference:
Confidence Interval: the sample providing information about the precision and reliability of the estimate concerning the larger population.—-Uncertainty of the sample
Law of Large number
As the number of (identically distributed), randomly generated variables increases, their sample mean (average) approaches their theoretical mean.
随着同分布随机生成变量增加，样本均值接近理论均值
the law of large numbers relates to the peak (the mean) of a curve, while the central limit theorem relates to the distribution of a curve.
If unequal distribution of data into groups and undetected confounding variables are combined in a study, Simpson’s paradox will occur.
suitable experimental design and dispersed between the sample group:
Simple randomization: strewing data into sample groups
Randomized block design: the study data are grouped into subgroups according to their similar characteristics. Reduce the consequences of confounding variables.
Minimization: randomly distributes subjects to equivalent groups and the likely confounding variables are equally distributed
https://yancyli1117.github.io/Mathematical-Statistics/
统计学分为描述性统计和推断统计两大部分。描述性统计可以继续细分为图表法和数值法。而推断统计则包含概率论、抽样理论、估计理论、假设检验这四大组成部分。
some basic theory
Central limit theorem (CLT)
The Central Limit Theorem (CLT) states that when plotting a sample distribution of mean the mean of the sample will be equal to the population mean and the sample distribution will approach normal distribution with variance equal to standard error.
样本均值等于总体均值，样本分布接近方差等于样本方差的正态分布
Assumptions behind the CLT:
The sample data must be sampled and selected randomly from the population. There should not be any multicollinearity in the sampled data; one sample should not influence the other samples. The sample size should be no more than 10% of the population. Generally, a sample size greater than 30 (n>30) is considered good.
statistical inference:
Confidence Interval: the sample providing information about the precision and reliability of the estimate concerning the larger population.—-Uncertainty of the sample
Law of Large number
As the number of (identically distributed), randomly generated variables increases, their sample mean (average) approaches their theoretical mean.
随着同分布随机生成变量增加，样本均值接近理论均值
the law of large numbers relates to the peak (the mean) of a curve, while the central limit theorem relates to the distribution of a curve.
Simpson’s Paradox
https://www.sisense.com/blog/understanding-simpsons-paradox-to-avoid-faulty-conclusions/
If unequal distribution of data into groups and undetected confounding variables are combined in a study, Simpson’s paradox will occur.
suitable experimental design and dispersed between the sample group:
Simple randomization: strewing data into sample groups
Randomized block design: the study data are grouped into subgroups according to their similar characteristics. Reduce the consequences of confounding variables.
Minimization: randomly distributes subjects to equivalent groups and the likely confounding variables are equally distributed