The Development Of New Hypothesis Test And Sample Size Estimation Methods For The Comparison Of Spearman Rank Correlation Coefficients

Background:Spearman rank correlation coefficient ρs is a nonparametric correlation coefficient,which is mainly used for the correlation analysis of nonbivariate normal data.Because the non-normal data is very common in practice,ρs is widely used.However,the study on ρs is relatively lacking,especially the study on the estimation of sample size.Objective:The purpose of this study is to systematize the existing test methods for ps,propose the hypothesis test methods for the scenes where there is no test method and give the formula for calculating the sample size of ρs under the one sample and two related samples based on the proposed method.In addition,aiming at complex simulation problems of rank-sum testing data,this study also compared the simulation results of two different simulation strategies under the comparison of one sample rank correlation coefficients.Methods:In this study,the Z-statistic proposed by Fieller et al.was selected and the sample size estimation formula was deduced based on the Z-statistic.Under the case of two related samples,this study simulated the construction idea of variance under the one sample of rank correlation coefficient,and improved the two related samples of Pearson correlation coefficient testing methods proposed by Dunn and Clark.Based on the two related samples of Pearson correlation coefficient testing methods proposed by Dunn and Clark,two new hypothesis testing methods for Spearman’s rank correlation coefficient were proposed(including two cases:comparing rank correlation coefficientρ12 and ρ34 with no common variables;ρ12 and ρ13 with one common variable X1),and the sample size estimation formula is derived based on the hypothesis testing methods.Two simulation strategies.were evaluated for how to generate samples with a given rank correlation coefficient in this study;(1)each sample was generated based on the ImanConover algorithm(the IC sample method);(2)Generate a large sample based on the Iman-Conover algorithm,such as 10,000 samples as the population,and then sample from this population(the IC population method).In this study,the results of two simulation strategies under one sample of rank correlation coefficient were simulated,and their advantages and disadvantages were evaluated based on the bias.The superior one was selected for the simulation study comparing the related sample of two rank correlation coefficients.Results:The simulation results of the comparison of single rank correlation coefficients show that type I errors of the test method of Fieller et al.are small when the rank correlation coefficient is large,but there is no inflated phenomenon.For the two simulation strategies,the simulation results under one sample of rank correlation coefficient showed that the IC population method was better than the IC sample method in bias,type I errors and sample size,so the next simulation studies were based on the IC population method.The simulation results of the two related samples of rank correlation coefficients show that:the improved method,only when the sample size is small(10)and the rank correlation coefficient is large(0.7 or 0.8),there is a slight inflated phenomenon in type I errors,and no inflated in the other cases.The simulation results of sample size estimation show that in most cases,the actual power can reach the power we set.Conclusions:In this study,an approximate estimation formula of sample size forρs of one sample is proposed,and the hypothesis test method and the estimation formula of sample size for two related samples are innovatively proposed.The simulation study shows that the method has good statistical performance,and its calculation is simple,so it is recommended to be used in the application.