Statistically significant difference between multiple thresholds estimated from constant stimuli method on psychophysical experiments could not be tested by t-test and analysis of variance, because the thresholds are not defined as averages of samples but are estimated from a psychometric function fitted to the subject’s response by maximum likelihood estimation and statistic needed for those statistical tests such as degree of freedom cannot be derived. We proposed a new statistical method to test the statistically significant difference between thresholds estimated from method of constant stimuli using the asymptotical normality of maximum likelihood estimator and the characteristic of multivariate normal distribution. This method can be used like analysis of variance for thresholds defined as the average of samples.