I am trying to test the equality of two covariance matrices based on articles from Srivastava, M.S. and Yanagihara, H., 2010 and Ishii, Yata and Aoshima 2016. I am not a statistician but a programmer. I implemented test formulas from above articles and trying to verify their effectiveness. In order to do so I created two sample matrices X and Y (sampled from a 5000-dimension N(0, S) distribution. X has 200 observations and Y has 800 respectively. X ~ N(0, I) and Y ~ N(0, 50*I). When I run Srivastava's Q2 test or Ishii's F3 test, they both return a p-value that show X and Y are not significantly different even the traces of their covariance matrices are far apart. I am not sure whether I misunderstood conditions and formulas in both papers or my samples are indeed non-distinguishable. It will be much appreciated if anyone can shed a light for this question or point me to a good test method. Thanks.
Ref: Srivastava, M.S. and Yanagihara, H., 2010. Testing the equality of several covariance matrices with fewer observations than the dimension. Journal of Multivariate Analysis, 101(6), pp.1319-1329.
Ishii, A., Yata, K., Aoshima, M., 2016. Asymptotic properties of the first principal component and equality tests of covariancematrices in high-dimension, low-sample-sizecontext. J.Statist.Plann. Inference(ISSN:0378-3758)170,186–199.http://dx.doi.org/10.1016/j.jspi.2015.10.007.