关于因子显著性问题的F-信度检验法

THE TESTING METHOD OF F-DEGREE OF CONFIDENCE FOR THE FACTOR SIGNIFICANCE PROBLEM

关键词:  统计显著性  F-统计量  F-检验法  F-信度值  F-信度检验法

Key words:  statistic significance  F-statistic  F-test  the value of F-degree of confidence  the test method of F-degree of confidence

摘要:

在时序方差分析周期外推预测、双重检验逐步回归预测及其他相关问题的分析中,需要从若干因子的F-统计量中选取最大值进行F-检验来确定这类问题的显著性。研究发现这种检验方法是有问题的、不准确的和会影响气候预测的准确性。这是由于F-检验是对F-分布的分位数的检验,其检验标准受到两个自由度的制约而成为变数;存在F-统计量最大的因子与显著性最高的因子不对应问题。为此提出F-信度检验法,它是对F-分布的分布函数的检验。定义因子达到的F-信度为F-分布的分布函数值的百分数:P_i=(1-α_i)×100%,它必须利用F-统计量和两个自由度去计算。设显著性水平为α,则临界F-信度值为:P_α=(1-α)×100%。在理论上这种检验法的临界F-信度值是唯一的,因而可从若干F-信度值中选取最大值进行检验。实践证明这种检验法可明显提高对因子显著性问题的判别能力和气候预测水平。

Abstract:

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.However,this kind of test is in question and inappropriate,which might affect the exactness of climatic prediction.Note that F-test is to examine the quantile of the F-distribution and could be a variable value due to the examination standard limited by the two freedom degrees,thus the most significant factor and factor of maximum F-statistics may not be the same.In other words,it is not an appropriate way to use a maximum statistic value as a criterion to choose a significant factor,as the F-test is not exactly true to some extent.Therefore,a test of F-degree of confidence is proposed.It is a test for a distributional function of F-distribution.The F-degree of confidence of a factor is defined as the percentage of distribution function of F-distribution P_i=(1-α_i)×100%,which needs to calculate by using the F-statistic value and two freedom degrees.Given the significant level α,then the criterion of F-degree of confidence is P_α=(1-α)×100%.Theoretically,the criterion of F-degree of confidence is unique for the test so that it can be tested by choosing the maximum from several values of F-degree of confidence.The practice already proved that this test method could improve the ability for discriminating factor significance and predicting the climate.