Objective To construct a new index(abbreviate FQ statistic) for testing the balance of covariates among 3 groups;to compare the power of hypothesis testing,standardized difference and FQ statistics to test the balance of covariates among 3 groups.Methods Using pooled variance to build FQ Statistic;Calculating propensity score for each individual by using ordinal logistic regression and multinomial logistic regression;Comparing the power of hypothesis testing,standardized difference and FQ statistics to test the balance of covariates among 3 groups by Monte Carlo simulation.Results The distribution of a covariate can be considered balanced among the 3 groups if FQ statisticsis less than 0.2.The power of hypothesis test is affected by sample size but FQ statistics and standardized difference.The power of FQ statistics and standardized difference to test the balance of covariates among 3 groups are higher than hypothesis testing,and both highly consistent.Conclusion FQ statistics and standardized differences are valid methods to test the balance of covariates among 3 groups.With more convenient calculating step than standardized difference,FQ statistic has more advantages in applications.