Exact Unconditional Test For Classification Data And Its Algorithm Research

Hypothesis testing is a statistical analysis method that uses sample information to infer whether a certain assumption made in advance on the overall quantitative charac-teristics is credible.In the analysis of classification data,hypothesis testing is an impor-tant method to deal with the comparison of two classification population parameters.It is widely used in modern biomedical,social science and engineering fields.For ex-ample,in modern medical dual-arm experiments,we use hypothesis testing to compare the effectiveness of new drugs(therapeutics)with placebo(standard treatment);in the social science polls experiment,the hypothesis test method is used to compare whether a new policy brings about the change of support rate;in the industrial product quality experiment of engineering,the hypothesis test method is used to compare whether a new technological improvement improves the quality of products.With the develop-ment of modern biomedicine and social sciences,a large number of classification data makes the research of hypothesis testing methods an important issue.It is well known that in the case of large sample sizes,the test statistic is a good es-timate of the overall parameters(such as coincidence estimation,unbiased estimation,consistent estimation,etc.),and the hypothesis test method has many excellent proper-ties(such as unbiased test,invariant test,consistent optimal test,etc.).However,with the decrease of the total sample size,the instability of the test statistics to the estimation of the population parameters and the distortion of the test process make the hypothesis test results unsatisfactory.In particular,when the sample size is small,the hypothesis test method is likely to get a wrong test conclusion.In theoretical research and practical applications,it is obviously inappropriate to compare the parameter comparison prob-lems of two classification populations with the classical hypothesis test method under large sample size when the sample size is usually small.Therefore,it is of great theo-retical and practical significance in modern statistics to find an accurate test method for the overall comparison of two classifications in the case of small samples.The exact test based on comparison of two classifications is a core and challenging problem in modern statistics..In recent decades,many scholars have devoted them-selves to the problem of exact testing of binomial data under small sample conditions.A number of exact test methods using the true probability distribution of the sample are proposed.Although the Fisher exact condition test method can be used,only the pre-cise and unconditional test method can be used to achieve the unique accurate test form in the more common non-conformance test problem.Based on the differences in the construction forms of sample space and parameter space,common exact unconditional test methods can be divided into standard unconditional test method based on maxi-mization,unconditional test method based on confidence interval and maximization of confidence interval,and unconditional test method based on estimation and maximiza-tion of asymptotic estimation.Although these particular accurate test method has many excellent properties,there is also a significant drawback:complexity of the calculation-s.In this article,we systematically studied a precision exact p value calculation method-Fixed-point Algorithm.This method can uniformly deal with the p-value calculation in the standard unconditional test method and the confidence interval unconditional test method.At the same time,on the basis of ensuring accuracy,the new fixed-point method can calculate accurate statistical inference results faster.In the analysis of classification data,in addition to considering the problem of pa-rameter comparison of two independent binomial classification populations,researchers are also interested in the exact test of parameter comparison of two matched binomi-al distribution populations and two independent multinomial classification populations.Also,due to the small sample size,the asymptotic hypothesis test method results in a lower level of efficacy due to the instability of the asymptotic distribution of the test statistic.Therefore in this paper,we also construct an accurate unconditional test for parameter comparison problems of two matched binomial distribution populations and independent multinomial distribution populations,and compare the performance of sev-eral unconditional test methods in various situations.For the calculation of the p value,we also propose the corresponding fixed point iterative algorithm.The simulation and empirical analysis show that the new fixed point algorithm shows greater attractiveness and can easily obtain accurate test results.