统计类面试基本概念总结 （有需要进）

花了一些时间自己做了一些统计基本概念的总结，来应对面试可能会问到的问题。根据自己理解的角度做的总结，可能有理解和表达不精准的地方，可以一起探讨下
. Waral dи,
有需要的同学可以当作一个参考:



Sampling distribution/ sample mean/ how to compare the means of two samples
                i. Sample mean is an estimate of the 'true' mean for the population
                ii. Choose a p-value and run t-test and compare to threshold value to decide if we should reject Null hypothesis.

Confidence interval
                i. Confidence interval always comes with bootstrap sampling>10000, for each sampling we got a sample mean.
                ii. CI is a range, in which a certain percentage of the sample means fall in.
                iii. If the confidence level is 95%, it means 95% of the sample means fall into that range, which can be further explained that we are 95% sure that true population mean fall into that range.

P-value
                i. P-value is a measure of statistical confidence. A measure of how confident you are that the model will still be valid if you have a lot more data.
                        a. The lower the p-value, the greater the statistical confidence.
                ii. P-value is used in the hypothesis testing when comparing two sample data and is the evidence against the null hypothesis.
                        a. If the p-value is lower than the threshold value(0.05), we would like to reject the null hypothesis which supports two samples coming from the sample distribution.
                        b. There are only 5% of chance (too small) to get this extreme observation if the null hypothesis is true.
                        c. There are only 5% for the statistical test to be False Positive (too small) if the two samples do come from the same distribution (null hypothesis is true).

Multi-hypothesis testing
                i. The multiple hypothesis testing occurs when a number of individual hypothesis tests are considered simultaneously.
                ii. In this case, the significance of individual tests no longer represents the combined sets.

P-hacking
                i. P-hacking
                        a. In multi-hypothesis testing , P-hacking means the misuse of the analysis techniques so the results are misled by false positive.
                        b. Take the single result/observation to draw conclusion or adjust sample size during the experiment to achieve statistical significance.
                        c. If the  two samples do come from the same distribution (null hypothesis is true), there are still 5% chance that the statistical tests will result in False Positive.
                ii. How to prevent P-hacking
                        a. False Discovery Rate method usually prevent P-hacking in multi-hypothesis testing by inputting every single p-value and output the adjusted p-value that is usually greater than the original ones.
                        b. Bonferroni Method (Reduce the threshold of P-value so we can reduce the false positive rate).

Power Analysis
                i. The power analysis determines what sample size will ensure the higher probability to correctly reject a null hypothesis
                ii. We can't adjust the sample size during the experiment because it will lead to P-hacking and only can do that before the experiment.
                iii. Effect size (metric to show the overlap of two distributions)/ desired power level / confident level

Central limit theorem
                i. No matter what distribution from which the sample means were calculated, the means of the collected samples (sample mean) are normally distributed
                ii. When doing experiment , we don't know the distribution where the group data come from, but CLT doesn't care since the sample means are always normally distributed
                iii. On top of that we conduct t-test and ANOVA to see If the means of two groups are statistically different.
                iv. Sample size > 30

Bias/Variance/Underfitting/Overfitting
                i. Bias (under-fitting) - The inability for a machine learning method to capture the true relationship
                ii. Variance (overfitting) - the difference of the performance in fitting among different  datasets.
                iii. The high variance means the hypothesis line fit the training set so well, but it did a terrible job in fitting the test set.
                iv. Overfitting - the function line fits the training set well but not the testing set.



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