For small samples, the prerequisite is that the entire population must obey a normal distribution.

signed test, signed rank test (Statistical thinking, if there is no change in the population between pre- and post-test, Then the difference between the two samples mainly comes from random error, is randomly generated, so n =n-, positive rank sum = negative rank sum) The purpose of testing is achieved by comparing the consistency of the distribution of two measurements. Inspection total construction quantity: T=min(T , 丨T-丨)

t-test Use the difference between the eigenvalues ​​of the two samples to Test the difference between the eigenvalues ​​of two populations

Statistical thinking: two populations have the same distribution, The sample distribution will not be much different, After mixed ranking, the results of the two samples will appear alternately, so there will be a journey, The rank sum will not be too large or too small

rank sum test

run test

cumulative frequency test

Classical concepts, probability addition formula, multiplication formula, conditional probability

Probability distribution of discrete random variables

Probability distribution of continuous random variables

Law of large numbers: ①When n is large enough, frequency ≈ probability ② When n is large enough, the sample mean can be used to estimate the population mean μ

Central limit theorem: n is large enough, the mean of all sample combinations forms a normal distribution The normal distribution has mean μ and variance σ²/n.

Sampling distribution of sample mean

Sampling distribution of sample frequencies

Sampling distribution of sample variance

point estimate

interval estimate

According to the principle of small probability

Hypothesis testing two types of errors

Chi-square test

H0:πi=πi0 H1:πi≠πi0 πi0, is based on the distribution to be tested The overall features calculated for each category frequency, so as to find the expected frequency, Find the test statistic

When conducting a two-sample t-test, Analysis of variance and regression analysis The premise is that the entire population obeys the normal distribution.

H0:X～N (x pull out, s²) H1: The population does not obey the normal distribution Calculate sample cumulative frequency and expectation The maximum absolute value of the distribution function difference Large value,D. Compare with Dα

Contingency correlation coefficient

rank correlation coefficient

hypothetical test

r (correlation coefficient)

R goodness of fit R²=r²

F-test (overall test of linear regression equation)

t-test (test of regression coefficients)

e (normality, homogeneity of variances, mean=0)

Test statistic, F=BSS/(m-1)/WSS/(n–m) H0: μ1=μ2=μ3=···μm H1: There is at least one category corresponding to the mean of the scale variable. Value is not equal to other categories

Equiskedasticity normality

Non-parametric test

One-way rank analysis of variance

Median test

two-way rank analysis of variance

kendall'sW test