The concept definition was imitated absurdly

Following the general mathematical methods, He(2009) first defined the zero correlation designs, then the existence and non-uniqueness of the zero-correlation designs are studied. Using the absolute value of the maximum correlation coefficient (mcc) as the optimization objective function, and repeated random sampling from the permutation set, and select the components of the random vector do exchange to achieve the minimization of mcc. If mcc cannot be minimized to 0, then an approximate solution, weak correlation design is obtained, Finally, the properties of the zero-correlation designs and data processing methods were researched.

1. The basic definition of He(2009)

the concept of a set of the vector was used (p.3). This symbol S was used many times when discussing construction methods.

2. The definition system in Lin (2009)

Lin & Tang defined permutation sets and correlation matrices in Lin (2009).

Where, the author used a symbol Γu to replace S, however, after three months, it is S in her doctoral thesis.They defined the correlation matrix by equation (1) instead of classic correlation matrix definition (1.1) in He (2009), and defined the correlation as shown in Figure 3.0. The main purpose of Lin (2009) is preemptively to register OLHD and NOLH, but the author did not define OLHD and NOLH in this article. Three months later, in Lin (2008), they defined LHD and defined zero correlated LHD as OLHD, see Figures 2.9 and 3.0. Their NOLH is weak correlation designs in He(2009). The results published in the third section consist of two parts: 3.1 OLHD and 3.2 NOLH, that were no different from in Lin (2008, 2010), and OLHD is an orthogonal subset of the corresponding NOLH, but it is exactly the same as He (2009).

How to construct a weak correlation experimental design?

Section 2.3 in He (2009) describes the sequential construction method. Sections 2.3.1--2.3.3 describe three specific construction methods. Section 4 describes the construction method and characteristics of the weak correlation matrix. see Fig 2.3. The Figure 2.4 is the construction method described by Lin (2009).

He (2009) has stated (p.9):”At present, a set of weak correlation arrays until 33 ×32 dimensional has been constructed in a laptop-computer.”Figure 2.5 is an example.

Lin (2009) preemptively registered the results with the number of runs in 4 and 22, Figure 2.6 is taken from Table 2 of Lin (2009), the author marked max=0.357, which is the same as Figure 2.5. The whole system is the same as He (2009), and the result is the same.

Figure 2.6 An example in Lin (2009) and report correlation parameters in my way

The weak correlation designs constructed by the He(2009) method has three characteristics, I don't know who has defined and constructed such a kind of designs before:

1. It contains a zero correlation sub-array if it exists;

2. Their correlation are weaker on the whole;

3. As the number of columns is increased, mcc and the correlation confidence probability P_max of the sub-array are increasing without decreasing.

My Weak Correlation Arrays (V.I) was constructed in 2005-2006, see First Edition （Constructed at 2005-2006，or Second Edition （Constructed at 2016）。

Figure 2.7 belongs to me. An example from Lin (2008, 2010) is shown in Picture 2.8, both are the same.

3. Concept definition in Lin (2008)

3.1 Literature Definition of Orthogonal Latin Hypercube Designs

In the Latin (discrete) space, Mckay Beckman and Conover (1979) defined Latin hypercube sampling as: "We can divide the range of each x_k into N strata of equal marginal probability 1/N, and sample once from each stratum." Ye (1998), Steinberg and Lin (2006) have a definition, "A design D_L is a Latin hypercube design (LHD) if each column in the design matrix includes n uniformly spaced levels." An LHD is called orthogonal Latin hypercube design(OLHD) if it satisfying

x_i^Tx_j=0, (for all i,j;i≠j) (2.3.1)

The definition is generalized.

3.2 The Orthogonal Latin Hypercube Design Definition in Lin(2008)

In Lin (2008), the author first defines LHD as shown in Figure 2.9, and then defines correlation and orthogonal Latin hypercube design OLHD (Fig.2.10). Lin's definition process is similar to Figure 2.1.

3.3 The fallacy of the orthogonal Latin hypercube definition of Lin et al.

The stolen clothes do not fit well, and the modification will show flaws.

Defining each column of LHD be a permutation of (1,2,...,n) is contrary to the definition in the literature.which is a special case of LHD defined by the literature whose spacing of 1, but it is not the category. The logic mistake of the author is using special cases to define a category. The uniformly spaced levels means that spacing between the levels can be 1, but may is not 1, and may also not be an integer, and the midpoint may be on 0 and can is not on 0. As a result, some well-known results in the literature are excluded from their definition scope. Such as Steinberg and Lin (2006) constructed a famous 16-run OLHD with 12 orthogonal columns，its level spacing is not 1, and Mckay's LHS is decimal (probability), and the midpoint of the zero correlation design may be not zero. In particular, the result of linear transformation of Lin's LHD is not within its own LHD category.

There is no orthogonal subset in the permutation set of (1,2,...,n), zero correlation is not necessarily orthogonal, and zero correlation cannot be used to define OLHD. LHD of the zero-correlated can only to define zero correlation design, which is precisely the topic of He (2009). The author forces zero correlation design to wear the OLHD hat. This is an ironclad proof to imitate He (2009). This absurd narrative was deleted in Lin (2010). Why did Lin (2010) delete this paragraph? Why did Tang not delete it if he carefully reviews and guides her. The only reasonable explanation is that the author was eager to read out her thesis, so did not carefully organize her own system design and manuscripts, and Tang did not review the manuscript. Why is it so sloppy? They have detained my manuscript for more than 27 months, that cannot be continued to detaine it.

Why do they define LHD in this way? They imitated the theorem for existence of zero correlation designs in He (2009) to establish the existence theorem for OLHD. Such theorem can not be proven and had to define a new LHD (LHD2) to remedy it (see Figure 2.11).

They discovered a new way to prove the existence theorem. However, two different LHD definitions appeared in two adjacent paragraphs. LHD2 is another special case of LHD literature definition, spacing between the levels also is 1. Between LHD1 and LHD2 are not "a slightly different", but a typical ambiguous definition. They did not carefully organize the system and manuscript, and did not even modify the absurd definition 2.1 until Lin (2010).

In this definition, the author uses "Thus" to connect two different things, that Incorrect no matter whether it is mathematics or logic. In Lin (2010), they deleted "Thus", but the context has not changed, proving that they knew their mistakes, but omitting this conjunction does not change anything.

3.4 Their Nearly Orthogonal Was the Result Imitating the Weak Correlation Designs In He(2009)

Nearly orthogonal is a term in Latin space, not a term in real Euclidean space. In Latin space, the numeric features of the vector are not defined, while the relationship between vectors is described using balance as a feature , and to measure the degree of orthogonality between vectors. In real Euclidean space, correlation is used to describe the correlation relationship between vectors.

Lin studies OLHD, assigns numerical property to Latin symbols and assigns numerical characteristics to Latin vectors, including the mean, variance, inner product and correlation coefficient etc. Qualitative variables have been unconditionally quantified. In fact, the authors completely stand in the real Euclidean space to discuss the orthogonal design problem in the Latin space. Many of their propositions use the theories and methods in the real Euclidean space, such as the tensor product theory.

The definition Formula (1) in Lin (2009) is a calculation formula of the correlation matrix of a specific matrix. The correlation in Lin (2008, 2010) (as shown in Figure 9) is only an estimated calculation formula of the correlation coefficient, not also a definition. I have consulted many editions of probability and statistics tutorials, but did not find one that defines the correlation coefficient in this way. There are many examples whose definition and calculation for a concept are different in mathematics courses. For the definition of correlation, it is recommended to refer to pages 425 and 427 of "Introduction To Probability and Statistics, (Third Edition 1995)" (by J.S. Milton, Jesse C. Arnold).

Copied the numerical properties of real Euclidean space into Latin space making Latin space into real Euclidean space, but does not use the critical value for correlation, nor does use confidence probability of the correlation .The direct result is that correlation is independent of degrees of freedom. So, leading to the absurd conclusion that non-orthogonal are all Nearly Orthogonal. The correlation requires a critical value, which should be a nonlinear function of the both confidence probability of the correlation and the degrees of freedom. This is not a new concept, but statistical common sense. Lin & Tang is a doctor of statistics and a doctoral tutor, how can you not understand. The critical value of correlation coefficient can be found in the table of statistical constants. Nowadays, it is easy to find it on the Internet. In accordance with the existing results of computational mathematics, a calculation program is only with dozens of sentences. Lin & Tang only cares about robbing results, neither programming calculations nor looking up statistical constant tables. Without the basic theoretical preparation and tool preparation for the subject, If they say that their conceptual definition and system design did not imitate, so where did it come from?

The threshold of the correlation confidence probability is different from the author’s threshold concept. Statistics stipulate two significance levels of 0.05 and 0.01, which are suitable for the significance test of statistical results. The smaller the correlation between the factors of the experimental design then the better, If backward stepwise regression or other advanced software used to process the experimental data,The correlation between factors of a design can be relaxed no need to be too harsh. When constructing a weak correlation design, I insist on constructing n-1 columns and leave the choice to the user unless the mcc is too large. What reason does Dr. Lin has to exclude designs with max>0.05 from NOLH?

A correlation coefficient=0.05, the correlation is weaker for a smaller sample, but for a larger sample, the P value may be very large. For example, if n = 10, p = 0.1091, the correlation is weaker; if n = 1000, p = 0.8857, if n = 2000, p = 0.9746, these correlations are very strong.Lin (2009) listed NOLH (81,70), NOLH (121,108) and NOLH (169,168), The P values corresponding to r = 0.05 are 0.3423, 0.4140 and 0.4815, respectively. The author said: “In most applications, a maximum absolute correlation of at most 0·05 is acceptable, “ what is unacceptable? NOLH(7,4) in Figure 2.6, after adding the fifth column as shown in Figure 2.45, max=0.1071, P=0.181, not NOLH, what is it?

In Lin (2008), the author abolished the 0.05 limit and wrote an ill-conditioned definition, as shown in Figure 2.12.

This definition cannot be read regardless of mathematics, logic or grammar. There is a word "weaker" in the sentence, which reveals that the author wants to define weak correlation designs but has scruples

Their Nearly Orthogonal was the result of imitating the weak correlation designs In He(2009)..