On C-Property in Block Designs

Block designs having a property described in Caliński (1971) and Saha (1976), referred to herein as C-property, are considered. A necessary and sufficient condition for a block design to have C-property is derived, and some methods of construction of such block designs are presented.     

Construction of Equi-replicated Balanced Block Designs with Block Sizes Exceeding the Number of Treatments

In this note it is shown that the block design with incidence matrix Ñ = [NN… N], where N = c_1hN_h + c_oh (11′–N_h). c_oh and c_1h are any non-negative integers and N_h,h = 1, 2,…,p, are incidence matrices of balanced incomplete block designs with the same number of treatments t, is a balanced block design with the block sizes exceeding the number of treatments. In derivation the matrix M₀, introduced by CALIński (1971) is utilized.     

A model-independent approach to the theory of experimental designs and a special discussion of bib. i general definition and designs with one or two block factors

Experimental designs are definded by introducing an assignment matrix Z. It is shown by block designs and double block designs that using Z or an operator on Z otherwise defined, well known designs can be got as special cases. Till now we didn' find an experimental design which could not be defined by our matrix Z. The definitions of properties of experimental designs can be given independently of the model of the statistical analysis. This is shown for the property of balance of block designs.     

Randomization Analysis of Incomplete Data in Some Basic Designs

The first two randomization moments of W = Tt.S.S./(Tt.S.S. + Error S.S.) are derived in case of (a) a completely randomized design with one observation missing using (I) Yates method of fitting constants and (II) the available observations only and in case of (b) a randomized block design in which one treatment is tested twice by mistake in a block and another treatment is not tested at all in that block using (I) all the available observations and (II) the data after deleting the observation due to the treatment tested by mistake in place of another treatment in a block. It is concluded that in each of the two cases for a completely randomized design, the F-test is unbiased whereas in each of the two cases for a randomized block design the F-test is in general not unbiased. However, if one treatment is tested twice by mistake in randomly chosen plots of some block, the F-test is unbiased in both cases for a randomized block design. For a completely randomized design the F-test is found to be a good approximation to the corresponding randomized test if N ≧ 80 in case (I) whereas in case (II) this approximation is of the same accuracy as that of case (I) if N ≧ 90. For a randomized block design it is seen that in case (I), the F-test provides a good approximation to the corresponding randomization test if v≧r≧7 and in case (II) this approximation is of the same accuracy if r≧6 and r(v-1)≧45. The analysis of several uniformity trial data shows that for values of “N” in the neighbourhood of 50 the agreement of the first two moments of “W” under the randomization theory and normal theory are reasonably close in all the four cases considered.     

A Simple Construction Procedure for Eesolvable Incomplete Block Designs for any Number of Treatments

A simple, straightforward procedure, which requires no special tables or generators, is presented for constructing resolvable incomplete block designs for v=pk, v=p²k, …, treatments, for k≥p, in incomplete blocks of size k. Also, it is shown, how to obtain incomplete block designs for any v in blocks of size k and k+1. The procedure allows construction of balanced incomplete block designs for p = k a prime number. For p = n not a prime number, incomplete block designs can be obtained by the procedure, but are not balanced. However, for p_s being the smallest prime factor of n, p_s + 1 for v = n², p_s²+ p_s + 1 for v = n³, …, arrangements can be obtained for which the occurrence of any treatment pair in the blocks is either zero or one. This is called a zero-one concurrence design. Procedures are described for obtaining additional zero-one concurrence arrangements. It is shown that the efficiency of these designs is maximum. Both intra-block and inter-block analyses are described.     

Equi-replicated balanced block designs generated by a balanced matrix

In this paper it is shown that if N= \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^{S_h} $\end{document} c_ihN_ih, where c_ih are some non-negative integer numbers and N_ih are such incidence matrices that A_h = \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^{S_h} $\end{document} i N_ih is a balanced matrix defined by SHAH (1959), for h = 1, 2,…, p, then a block design with an incidence matrix Ñ = [N, N,…,N] is an equi-replicated balanced block design. Here the balance of a block design is defined in terms of the matrix M₀ introduced by CALI?SKI (1971).     

Fractional Plans to Estimate Main Effects and Two Factor Interactions Inclusive of a Specific Factor

Balanced incomplete block designs are used to construct non‐geometric 2ⁿ fractional factorial plans to estimate all n main effects and n – 1, 2 factor interactions with a specific factor included in each interaction. When the balanced incomplete block design is of Family (A), the resulting fractional factorial plan has the same number of runs as a fold‐over Hadamard matrix giving same variances for the estimates; however, some new designs are shown to be non‐isomorphic to the fold‐over Hadamard matrix plans.     

On the E-Optimality of Block Designs with Unequal Block Sizes

In this paper an inequality for the smallest positive eigenvalues of the C-matrix of a block design are derived. This inequality is a generalization of a result by Constantine (1982) to the case of unequal block sizes. On the basis of the above result a certain E-optimality criterium of block designs is given. Furthermore coefficient e_d has been introduced which permits to assess how close the block design is from the optimal one.     

On the Construction of Balanced and Partially Balanced Ternary Design

A method of constructing balanced and partially balanced ternary designs from balanced and partially balanced incomplete block designs, respectively, and two methods of constructing partially balanced ternary designs from association schemes are obtained. Two new and efficient balanced ternary designs having K < V and R ≦ 20 are obtained by the first method.     

Sequentially Generated Designs

Procedures for sequential generation of nearly D-optimal designs are described. Two kinds of designs can be obtained: symmetrical block designs and nonsymmetrical ones. It is shown that in a special case when the number of the support points of a continuous D-optimal design equals to the number of regression coefficients the sequential designs can be constructed very easy without use of a computer. A Catalogue containing 135 designs has been developed by use of these procedures. 34 of them can be used for experiments in cuboidal factor space and the remaining for experiments with mixture and process variables. Comparison with other designs is done.     

Optimality of Some Class of Incomplete Block Designs

A class of incomplete block designs called C-design, was considered by Caliński (1971), Saha (1976), Ceranka (1983) and Ceranka , Kozłowska (1983, 1984). In this paper we extend the theory of block designs having the C-property. We consider optimality of C-designs with respect to any criterion of a described form. Das and Kageyama (1991) considered a class of E-optimal proper efficiency balanced designs (strictly speaking, Das and Kageyama considered E_R-optimality of some class of block designs). Hence we consider E_R, A_R, D_R optimality of C-designs.     

A Simple Procedure for Constructing Experiment Designs with Incomplete Blocks of Sizes 2 and 3

In order to maximize control of heterogeneity within complete blocks, an experimenter could use incomplete blocks of size k = 2 or 3. In certain situations, incomplete blocks of this nature would eliminate the need for such spatial types of analyses as nearest neighbor. The intrablock efficiency factors for such designs are relatively low. However, with recovery of interblock information, FEDERER and SPEED (1987) have presented measures of design efficiency factors which demonstrate that efficiency factors approach unity for certain ratios of the intrablock and interblock variance components. Hence with recovery of interblock information, even incomplete block designs with k = 2 or 3 have relatively high efficiency factors. The reduction in the intrablock error variance over the complete block error variance in many situations will provide designs with high efficiency. A simple procedure for constructing incomplete blocks of sizes 2 and 3 is presented. It is shown how to obtain additional zero-one association confounding arrangements when v = 4 t, t an integer, and for v = pk, k ≤ p. It is indicated how to do the statistical analysis for these designs.     

Application of Partially Balanced Block Designs to Factorial Experiments

In this paper we present partially balanced block designs with F_p and C_p association schemes. These designs play a great role in the experimental theory since they can be applied to factorial experiments. A particular stress is put on the formulation of association schemes _p and C_p, presentation of exemplary constructions of these designs and their analysis of variance. The presented considerations are abundantly illustrated with examples.     

Designs Suited for Varietal Trials with Multiple Basals

DAS (1960) gave a method of construction of confounded balanced asymmetrical factorial designs of the type v × 2² by using BIB designs. In the present paper a method has been given for construction of balanced asymmetrical factorial designs of the type (v–t) × 2² by using truncated balanced incomplete block designs obtainable by omitting t treatments. Likewise, partially balanced asymmetrical factorial designs can also be obtained by omitting any particular treatment alongwith its first or second associate treatments from the v treatments of a PBIB design. We can get a large number of new designs not available in literature through this technique. These designs are well suited for varietal trials with multiple basals.     

The Exact Distribution of the Anderson-Kannemann Statistic

The Anderson-Kannemann test is a rank test for treatment effects in a randomized block design with K treatments and N blocks. In this paper, an algorithm for computing the exact distribution of the Anderson-Kannemann test statistic under the null hypothesis is deduced. Then, the exact distribution is compared with the asymptotic χ²-distribution, and it is shown that the exact distribution is approximated fairly well by the asymptotic distribution. Tables of the exact distribution are given for K = 3, N = 3(1)15; K = 4, N = 3(1)11; K = 5, N = 3(1)7; and K = 6, N = 3(1)5.     

A model-independent approach to the theory of experimental designs and a special discussion of bib. II. properties and construction of bib

In addition to the first part we prove independently of the model some theorems on properties of balanced block designs. Then we propose nine methods of construction of BIB and prove theorems in connection with these methods. In a table we give a survey on block designs with v$25 and possibilities of their construction with these methods. Further follow theorems with the number of nonisomorphic BIB for some fixed v and k.     

Interactions of a few azole derivatives with a transport protein: role of heteroatoms

The interaction of a few azole derivatives, 2‐(4′‐N,N‐dimethylaminophenyl)benzimidazole, 2‐(4′‐N,N‐dimethylaminophenyl)benzoxazole, 2‐(4′‐N,N‐dimethylaminophenyl)oxazolo[4,5‐b]pyridine with bovine serum albumin (BSA) were examined by absorption and fluorescence spectroscopy. The results were compared with the previously studied imidazopyridine derivative 2‐(4′‐N,N‐dimethylaminophenyl)imidazo[4,5‐b]pyridine. Displacement studies were carried out with site selective probes to locate the binding site of these ligands. The spectral shifts and the binding constant vary depending on the nature of the ligand. The fluorescence intensity of both oxazole derivatives 2‐(4′‐N,N‐dimethylaminophenyl)benzoxazole and 2‐(4′‐N,N‐dimethylaminophenyl) oxazolo[4,5‐b]pyridine increases substantially in the presence of BSA, whereas the intensity of 2‐(4′‐N,N‐dimethylaminophenyl)benzimidazole decreases. However, hypsochromic shift is observed in presence of BSA. The results obtained from the docking studies are also in good agreement with the experimental results. The location and orientation of binding depend upon the nature of the ligand. The studies revealed that apart from hydrophobic interaction, hydrogen bonding also plays a vital role in the molecular binding. Oxazoles have higher binding affinity than imidazoles and substitution of extra nitrogen further increases the binding affinity. Copyright © 2015 John Wiley & Sons, Ltd.     

A comparison of four experimental designs for the estimation of heritability

Summary The partial diallel cross, the complete diallel cross, and the designs known as North Carolina Experiments 1 and 2 are compared for their usefulness in estimating heritability. It is first shown that reliable values for the sampling mean and variance of heritability estimates are obtained from approximate expressions based on the moments of the chi-square distribution. These expressions are then applied to determine the optimum experimental designs for a range of situations.The main basis for discrimination is the amount of information per unit, defined as i = 1/(N var( ²)), where ² is the estimate of the heritability h ² and N is the number of units in the experiment, either individuals or families.The two parameters considered were the heritability of individuals and the heritability of full-sib families, and for each of these the partial diallel cross was the most preferred, followed in decreasing order of preference by design NC2, the complete diallel, and design NC1.It is first shown that there is no optimum number of parents for a partial diallel cross or male parents for designs NC1 and NC2. The number of crosses per parent for a partial diallel or dams per sire for designs NC2 and NC2 should generally be six or less. Any expansion should be in the direction of using more parents in the case of the partial diallel, or more male parents in the case of designs NC1 and NC2. For the two heritability parameters considered in this study it is inefficient to increase the number of replicates beyond two.     

Examples of non-trivial efficiency-balanced designs with b=v+1

This note provides examples of binary efficiency-balanced block designs with b=v+1, having no complete blocks, which are unequal-replicated and unequal-blocksized from a biometrical and agricultural standpoint.     

Translesion Synthesis across 1,N6-(2-Hydroxy-3-hydroxymethylpropan-1,3-diyl)-2′-deoxyadenosine (1,N6-γ-HMHP-dA) Adducts by Human and Archebacterial DNA Polymerases

The 1,N⁶-(2-Hydroxy-3-hydroxymethylpropan-1,3-diyl)-2′-deoxyadenosine (1,N⁶-γ-HMHP-dA) adducts are formed upon bifunctional alkylation of adenine nucleobases in DNA by 1,2,3,4-diepoxybutane, the putative ultimate carcinogenic metabolite of 1,3-butadiene. The presence of a substituted 1,N⁶-propano group on 1,N⁶-γ-HMHP-dA is expected to block the Watson-Crick base pairing of the adducted adenine with thymine, potentially contributing to mutagenesis. In this study, the enzymology of replication past site-specific 1,N⁶-γ-HMHP-dA lesions in the presence of human DNA polymerases (hpols) β, η, κ, and ι and archebacterial polymerase Dpo4 was investigated. Run-on gel analysis with all four dNTPs revealed that hpol η, κ, and Dpo4 were able to copy the modified template. In contrast, hpol ι inserted a single base opposite 1,N⁶-γ-HMHP-dA but was unable to extend beyond the damaged site, and a complete replication block was observed with hpol β. Single nucleotide incorporation experiments indicated that although hpol η, κ, and Dpo4 incorporated the correct nucleotide (dTMP) opposite the lesion, dGMP and dAMP were inserted with a comparable frequency. HPLC-ESI-MS/MS analysis of primer extension products confirmed the ability of bypass polymerases to insert dTMP, dAMP, or dGMP opposite 1,N⁶-γ-HMHP-dA and detected large amounts of −1 and −2 deletion products. Taken together, these results indicate that hpol η and κ enzymes bypass 1,N⁶-γ-HMHP-dA lesions in an error-prone fashion, potentially contributing to A→T and A→C transversions and frameshift mutations observed in cells following treatment with 1,2,3,4-diepoxybutane.