Statistical inference is a method of inferring the performance of the population from the information of the sample. It can be divided into two types of problems, namely parameter estimation and hypothesis testing . In actual production and scientific experiments, a large number of problems are to estimate and test a certain parameter of the mother body after obtaining a batch of data .
For example, we measured the fracture toughness of 45 steel , obtained a batch of data, and then required the average value of the 45 steel fracture toughness, or required the unilateral lower limit of the 45 steel fracture toughness, or required the dispersion of the 45 steel fracture toughness Degree (ie coefficient of dispersion ), this is the problem of parameter estimation .
For another example, after long-term accumulation, we know the average value and standard deviation of the fracture toughness of a certain material , and after improved heat treatment, a batch of data is measured. How can the new process be significantly different from the old process? This is the hypothesis The question of inspection .
It can be seen that parameter estimation is the first step of hypothesis testing. Without parameter estimation, hypothesis testing cannot be completed.