统计常见问题

楼主整理了一些统计高频问题及答案，缸里没米了，卖艺求米

第一题
Type I and Type II Error

• Type I error (false positive): the probability of rejecting a true null hypothesis
• Type II error (false negative): the probability of failing to reject a false null hypothesis
  

第二题
p value

• The p value is the evidence against a null hypothesis. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.
  

how to explain to non-technical person?

• Differences happen as a result of chance. A small p-value means that the observed results are so unusual assuming that they were due to chance only. How likely is it that you see something as extreme as an elephant walking down a city street?
• a low p-value that is less than significance level, indicates that it is not very likely and thus the occurrence of such an event is significant.
  

第三题
Confience interval

• CI is an interval of numbers which shows how likely it covers the true value. For example, we can be 95% confident that the sample mean lies within there two values.
  

How to interpred CI?
•        narrower CI means less uncertainty of samples, which means the results is more reliable.
•        more uncertainty of samples, wider CI
•        less data, wider CI
•        higher confidence level, wider CI
•        bad user segmentation results in high standard error, then wider CI
How to explain CI to non-technical person?
•        CI measures level of uncertainty when estimating a value. CI is a range of values with a lower and an upper bound such that if you were to sample the parameter of interest a large number of times.
•        the 95% confidence interval would contain the true value of this parameter 95% of the time. For example, the CI of 168~185 cm cover true value of average of men height in U.S. 95% of the time

第四题
What is PMF, PDF, CDF?
•        PMF is probability mass function that is discrete
•        PDF is probability density function that is continuous, which describe the probability of the value of a continuous random variable falling within a range.
•        CDF is cumulative distribution function that calculate the cumulative probability for a given value

第五题
When to use z-test versus t-test?

• in a z-test, your test statistic follows a normal distribution under the null hypothesis. Alternatively, in a t-test, you employ a student’s t-distribution rather than a normal distribution as your sampling distribution.
• considering the population mean, we can user either z-test or t-test only if the mean is normally distributed, which is possible in two cases: the initial population is normally distributed, or the sample size is large enough (n≥30) that we can apply the Central Limit Theorem
• if the condition above is satisfied, then we need to decide which type of test is more appropriate to use. In general, we use z-test if the population variation is known, and user t-test if the population variation is unknown.
• additionally, if the sample size is very large (n>200), we can user the z-test in any case, since for such large degrees of freedom, t-distribution coincided with z-distribution up to thousands
• considering the population proportion, we can use z-test where np_0≥10 and n(1-p_0)≥10, i.e. when each of the number of successes and the number of failures is at least 10.
• 
  

第六题
What is Simpson’s Paradox?
•        a trend appears in several groups of data but disappears or reverses when the groups are combined.
•        To avoid Simpson's Paradox leading us to two opposite conclusions, we need to choose to segregate the data in groups or aggregate it together.

huichen2012 发表于 2022-02-05 11:03:42
谢谢楼主， 想讨论一下type I error.....总觉得说 false positive 不好理解， 这里 positive 指代什么呢？ 我也没有找到相应的书。。 按照 type 1 erro

positive指的是发现结果significant，就是拒绝了H0。

谢谢楼主， 想讨论一下type I error.....总觉得说 false positive 不好理解， 这里 positive 指代什么呢？ 我也没有找到相应的书。。 按照 type 1 error 的定义， 这里的 positive 就是指 null hypothesis positive, 可是。。。。希望有人能明白我意思。。。。