Supposing that the effectiveness of different safety measures has abstract function relation,the function was extended into power series by normalization,introduced all possible mathematical relativity,and eliminated redundant relativity by F-statistic and Gram-Schmidt orthography algorithm.

In the prediction of time series by using the periodic extrapolation of the variance analysis,and in double-test stepwise regression prediction,or in other analysis of related problems,there is a need to find the maximum from the F-statistics of several factors to be F-tested significant.

Established a method evaluating the fuzzy cluster validity with F-statistics of multivariable statistics and changing levels of significance,and constructed a Validity funtction of cluster with the minimal level of significance.

According to the theory of difference analysis in statistics and entropy theory in information theory, two functions-F statistics and fuzzy division entropy were constructer, the F statistics was mainly used to determine the optimal division number and the fuzzy division entropy was used to verify the validity of division.

Sliding window least square method is used with U statistics and F statistics to quantitatively analyze the variance of innovations.

Using the information of F-statistics,GST,gene flow(Nm),DS genetic distances,the genetic structure and differentiation were evaluated.

Pointing to the optimal category for comprehensive water use level in a river basin,the paper put forward a knew method used a multi-statistical analysis F-statistics and significant change level for the research of optimization category and established a way to seek the optimal classification.

The clustering scheme with the largest F-statistics is chosen.

In addition,we have also introduced pseudo F-statistics,on the one hand,some of the overlapping points in space realizes effective classification;on the other hand,it can give the best clustering number,thereby making up for the shortage of k-modes clustering method.