A Research On The Principle Of Fixed Step Method

The fixed-step-size method(FSS method)is an important method in psychophysics,and it has a natural affinity with markov chains.Based on markov chain,our study uses 3 method(theoretical derivation,numerical analysis,and simulation in R programming language)to discuss the FSS method.4 facts are clarified in this research:(1)In this research,we analyzed the sufficient condition about the existence of the estimation calculated by the FSS method,and further give the distribution of the estimation value.(2)We compared the cost of all the 6 kind of estimator,and based on this,the method selection proposal was given.(3)We illuminated 2 kind of basic priciple on building variable type of tradition up-down method,proved the existence of the estimate,gave the distribution of the estimate and proposed a new variable type of the Levitt method.(4)We compared the cost of all the 18 kind of estimator(3 method: Levitt,Derman and WUD × 6 kind of calculation).This study found that:(1)For any monotone,continuous psychometric function with range of values [0,1],if the threshold exists then it can be estimated by any kind of FSS method.(2)Regardless of any kind of FSS method,the estimated value is always biased,and that bias is determined by the psychometric function,starting point and step length.(3)When using the simple staircase method to estimate the threshold,the mean of the sequence value is more better than that of other values in estimation precision.(4)In the three variant of simple steps method: Levitt method has the smallest estimation precision,but it also has the lowest efficiency of sampling and the expanding of the threshold scope is small;Derman method has a large scope of threshold,but its estimation precision is large and the validity of estimator is poor;the WUD method is the average,in many cases,its estimator is not bad,but in the case of insufficient test times the estimator is influenced with the number of trails.