相关系数显著性检验的几何意义

Geometric Meaning of the Significance Test of Correlation Coefficient

摘要:

从几何学角度阐明了相关系数显著性检验的意义。对于来自正态分布的样本,利用其距平序列对应的随机向量在高维空间中均匀分布的性质,在母体无相关假定下,用几何方法求得了显著性水平α和样本容量n下的临界相关系数r′_α,n的表达式,并验证了它等于由t分布求得的临界相关系数r_α,n,从而给出了相关系数显著性检验的直观理解。

Abstract:

Analysis of correlation coefficient is widely used in the study of short-term climate variation and prediction.The meaning of the significance test of correlation coefficient is elucidated from geometric angle.Based on the character that the stochastic vectors corresponding to the anomaly sequence of the samples with a normal distribution,uniformly distribute in the high dimension space,supposing that the samples come from independent parent populations,the expression of critical coefficient r′_α,n under the conditions of significance level α and sample capacity n was obtained by the methods of geometry.That the r′_α,n equals to the critical correlation coefficient r_α,n obtained from t-distrbution was validated.So the intuitive understanding of the significance test of correlation coefficient is given.