The usage specifications of p-value statistic were stimulated by highly visible discussions in the field of Statistics over the last few years. It is generally considered that a p-value can indicate how incompatible sample data are with the alternative hypothesis model. To explore the connection between the p-value of correlation analysis and spectral independence, the deductive reasoning and example verification were carried out. Compared with correlation coefficient(r-value statistic), results show that the band independence can be directly expressed by p-value statistic of correlation analysis. And p-value matrix has a kind of high-level self-sparsity, which can be used to model easily. And then an unsupervised band selection method(p-value sparsity matrix band selection, pSMBS) through p-value statistic modeling independence was proposed, based on the histogram frequency statistics of p-value matrix. Using two typical hyperspectral images (HSI) data, the experiments of supervised classification were carried out. The results indicate that, on Kappa coefficient, overall accuracy(OA) and average accuracy(AA), pSMBS is superior to three kinds of methods, adaptive band selection(ABS), infinite feature selection (InfFS) and Laplacian score feature selection(LSFS). Therefore, the effectiveness and the practicability of pSMBS were verified on HSI band selection, and the characterization ability of p-value of correlation analysis on expressing band independence was evidenced.hyperspectral image