###### A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans

## Abstract

This paper considers main effects plans used to study *m* two-level factors using *n* runs which are partitioned into *b* blocks of equal size *k* = *n/b*. The assumptions are adopted that *n* ≡ 2 (mod 8) and *k* > 2 is even. Certain designs not having all main effects orthogonal to blocks were shown by Jacroux (2011a) to be D-optimal when (*m* − 2)(*k* − 2) + 2 ⩽ *n* ⩽ (*m* − 1)(*k* − 2) + 2. Here, we extend that result. For (*m* − 3)(*k* − 2) + 2 ⩽ *n* < (*m* − 2)(*k* − 2) + 2, the D-optimality of those designs is proved. Moreover, their D-efficiency is shown to be close to one for 2(*m* + 1) ⩽ *n* < (*m* − 3)(*k* − 2) + 2, indicating their good performance under the criterion of D-optimality.

###### Evaluation of experimental designs in durum wheat trials

References Abd El-Shafi M.A. (2014): Efficiency of classical complete and incomplete block designs in yield trial on bread wheat genotypes. Research Journal of Agriculture and Biological Sciences 10(1): 17-23. Akaike H. (1974): A new look at the statistical model identification. IEEE Transactions on Automatic Control 19: 716-723. Bose R.C., Nair K.R. (1939): Partially balanced incomplete block designs. Sankhya 4: 337-372. CropStat for Windows ver.7.2 (2007): International Rice Research Institute

###### Incomplete split-block designs constructed by affine α-resolvable designs

of the Royal Society. London A 283, 147-162. Nelder J.A. (1965b): The analysis of randomized experiments with orthogonal block structure. II. Treatment structure and the general analysis of variance. Proceedings of the Royal Society. London A 283: 163-178. Ozawa K., Jimbo M., Kageyama S., Mejza S. (2002a): Optimality and constructions of incomplete split-block designs. Journal of Statistical Planning and Inference 106: 135-157. Ozawa K., Jimbo M., Kageyama S., Mejza S. (2002b): Optimality and efficiency of incomplete

######
The comparison of three models applied to the analysis of a three-factor trial on hybrid maize (*Zea mays* L.) cultivars

R eferences Ambroży K., Mejza I. (2012): Modeling data from three-factor experiments with split units set up in designs with different block structures (in Polish). Biul. IHAR 264: 23-31. Ambroży K., Mejza I., Mejza S. (2014): On the relative efficiency of split-split-plot design to split-plot × split-block design. Colloquium Biometricum 44: 69-78. Federer W.T., King F. (2007): Variations on Split Plot and Split Block Experiment Designs. Wiley. New Jersey. LeClerg E.L., Leonard W.H., Clark A.G. (1962): Field plot technique. Burgess

###### An evaluation of the efficiency of plant protection products via nonlinear statistical methods – a simulation study

## Abstract

A nonlinear statistical approach was used to evaluate the efficiency of plant protection products. The methodology presented can be implemented when the observations in an experiment are recorded as success or failure. This occurs, for example, when following the application of a herbicide or pesticide, a single weed or insect is classified as alive (failure) or dead (success). Then a higher probability of success means a higher efficiency of the tested product. Using simulated data sets, a comparison was made of three methods based on the logit, probit and threshold models, with special attention to the effect of sample size and number of replications on the accuracy of the estimation of probabilities.

######
Use of *α*-resolvable designs in the construction of two-factor experiments of split-plot type

## Abstract

We consider an incomplete split-plot design (ISPD) with two factors generated by the semi-Kronecker product of two *α*-resolvable designs. We use an *α*-resolvable design for the whole plot treatments and an affine *α*-resolvable design for the subplot treatments. We characterize the ISPDs with respect to the general balance property, and we give the stratum efficiency factors for the ISPDs.

###### Control treatments in designs with split units generated by Latin squares

in Statistics, 170, Springer-Verlag, New York. Ceranka B., Mejza S. (1987): Merging of treatments in certain partially efficiency balanced block designs with two different numbers of replications. Calcutta Statist. Assoc. Bull. 36: 49-55. Clatworthy W.H. (1973): Tables of Two-Associate-Class Partially Balanced Designs. NBS Applied Mathematics Series 63. Washington, D.C, USA. Hering F., Mejza S. (2002): An incomplete split-block design generated by GDPBIBD(2)s. Journal of Statistical Planning and Inference 106: 125

######
X^{−1}-balance of some partially balanced experimental designs with particular emphasis on block and row-column designs

## Summary

This paper considers block designs and row-column designs where the information matrix **C** has two different nonzero eigenvalues, one of multiplicity 1 and the other of multiplicity *h*−1, where *h* is the rank of the matrix **C**. It was found that for each such design there exists a diagonal positive definite matrix **X** such that the design is **X**
^{
−1}-balanced.

###### Biometric characteristics of interspecific hybrids in the genus Secale

-149. Mackiewicz D., Broda Z. (2004): Ocena przydatności hodowlanej mieszańców żyta uprawnego Secale cereale L. z dzikimi gatunkami z rodzaju Secale [Estimation of breeding suitability of hybrids of rye (Secale cereale L.) with wild species from the genus Secale]. Biul. IHAR 231: 265-277. Mackiewicz-Karolczak D., Broda Z. (2002): Ocena efektywności krzyżowań międzygatunkowych w rodzaju Secale [Estimation of the efficiency of interspecific crosses in genus Secale]. Biul. IHAR 221: 73-82. Mahalanobis P. C. (1936): On the generalized distance in

###### A variant of gravitational classification

## Summary

In this article there is proposed a new two-parametrical variant of the gravitational classification method. We use the general idea of objects' behavior in a gravity field. Classification depends on a test object's motion in a gravity field of training points. To solve this motion problem, we use a simulation method. This classifier is compared to the 1NN method, because our method tends towards it for some parameter values. Experimental results on different data sets demonstrate an improvement in efficiency and that this approach outperforms the 1NN method by providing a significant reduction in the mean classification error rate.