3. There is no trace of critical value in the theoretical system of C.D.Lin and Boxin Tang

Lin & Tang define correlation as Figure 2.1

Latin notation has numerical properties, defining distance, mean, variance, inner product and correlation coefficient in Latin space. However, no trace of critical values and degrees of freedom is seen in the entire OLHD-NOLH theoretical system of Lin & Tang. This leads to systemic errors and confusion. Cannot estimate correlation confidence probability, Near Orthogonal cannot to relate critical values, so that all except Orthogonal are Near Orthogonal.

The correlation critical value is a non-linear function including two parameters which be called as confidence level α and the degree of freedom (n-2). It is an important parameter to accurately evaluate the correlation, and is also a necessary parameter for the F-test when selecting or removing factors in the stepwise regression process or ANOVA. As long as you have done experimental design and data processing once, you should know the meaning of critical values and degrees of freedom.

The formula (2) is an estimation formula rather than a definition formula for correlation coefficient. Lin (2009) used the constant 0.05 to pretend to be the correlation threshold. r=0.05, for small samples it indicates low correlation; for large samples, the P-value may be large. Example,when n=10, P=0.1091, the correlation is weaker； if n=1000, P=0.8857； and if n=2000, P=0.9746, the correlation very strong. Regardless of critical values, what is the basis for adding or deleting columns when constructing the NOLH array? The author is likea blind person gropes for fish. Lin(2009)'s NOLH(7,4) has a weak correlation column with p=0.121 for its fourth column, which the authors discarded.

The correlation of OLH(n,p) determines the correlation of the coupling results, After coupling, the size of the matrix is increased by a factor of n, and the degrees of freedom are increased by a factor of n. The correlation confidence probability has changed dramatically, It is discussed in detail in the section "Several Problems of the Generalization of Coupling Method Theory".