| Experimental design is an important branch of statistics,through which people can better understand nature.Experimental design has been widely applied in agricultureforestry,biology,medicine,machinery manufacturing and other fields.For example,in medicine,two-level factorial testing is often used to screen the best treatment options and drug formulations,greatly reducing research time and costs.The main research content of this paper is the repeated regular two-level factorial experiments,each factor has only two levels,and each experiment is repeated for many times to get multiple responses.Based on the experimental results,we test the null hypothesis of the factor coefficients of the response mean and variance,and analyze whether each factor has an effect on the response.Several existing methods for testing the null hypothesis is too conservative or radical,this article use the Bootstrap inference and Fiducial inference methods,and studentized maximum modulus test,z test,t test,F test method to test the null hypothesis of the model,this article uses the Bootstrap inference and Fiducial inference methods,and z test,t test,F test method to test the null hypothesis,and we compare the accuracy and stability of these methods by numerical simulation.The simulation results show that in the position models,each method has a good test effect.When the sample size is smaller,the t test method is more robust than the Bootstrap method.The results of student maximum modulus test and F test are not stable.In general,the Bootstrap method has better inspection effect.In the dispersion models,the test results of Bootstrap and Fiducial are satisfactory. |
