Catalogue of selected experimental plans

Summary There are many works in the literature on the construction of experimental plans based on weighing designs. Hence, it is useful to compile a catalogue of experimental designs with specific properties. In this work, we investigate the properties of experimental plans constructed using the matrices of spring balance weighing designs. Additionally, an even number of experimental objects is assumed. An overview of the construction methods of these designs and classes of design matrices with selected properties are given. The results make it possible to create a catalogue of experimental designs constructed on the basis of spring balance weighing designs.

Cochran’s Q-Test on Soil Helminth Prevalence

Summary A study was made of the prevalence of nine geohelminth egg types in 184 soil samples from 16 recreational parks in Abuja metropolis, Nigeria. Cochran’s Q-test was applied to determine whether the difference in the proportions of the egg types found in the soil samples was significant. At a 5% significance level, it was found that the prevalence of the egg types was significantly different in the 184 soil samples from 16 parks. To identify which of the geohelminth eggs had a significantly larger mean proportional prevalence, a minimum required difference mean comparison technique was applied. The mean comparison test showed that Taenia and Coccocidia eggs were highly prevalent, with significantly larger mean proportions than the other analyzed geohelminth eggs in the 184 examined soil samples.

Influence of different sowing density in two varieties of maize. Part I. Relation to yielding

Summary A study was carried out to determine the effect of sowing density on the yield of maize of two different varieties. The field experiment was carried out in 2012–2014 at the Department of Agronomy of Poznań University of Life Sciences. The first-order factor was the variety: SY Cooky and Drim “stay-green”; the second-order factor was sowing density: 6, 7, 8, 9, 10 plants per m2. Weather conditions during the maize growing seasons significantly influenced the values of the studied traits. Significantly the lowest green mass yield of maize was obtained at the sowing density of 6 plants m−2, and the highest for 10 plants m−2. The “stay-green” variety significantly responded to an increase in sowing density with reduced fresh weight of leaf blades of a single plant compared with the conventional variety. This indicated highly effective photosynthesis with a lower plant density per unit area, which is also the basis for effective absorption of solar radiation for these maize varieties.

Pupil changes in persons aged 8 to 79 during text reading – an eye-tracking study

Summary The Eye Tribe eye-tracker was used to capture pupil sizes and fixation times of 40 people aged 8 to 79 years during text reading. The dependence of the number of readable lines on the participants’ age was determined. A function describing the dependence of the eye surface area on age was also derived. Visual perception of the maximum number of consecutive lines with decreasing text font size is best for people aged 30–40. For the studied age group, the pupil area decreased with age by approximately 300%. An approximately two-fold increase in average fixation times was recorded.

Some notes on planning plant protection research in block designs with nested rows and columns

Summary Factorial experiments in block designs with nested rows and columns are described with suggestions about how they should be planned. In such experiments the importance of interaction and hidden replication are emphasized. Such experiments are carried out on heterogeneous experimental material. Thus, it is reasonable to seek a design that can withstand the loss of observations. The robustness of a block design with nested rows and columns against the loss of whole blocks is presented, along with examples of such designs.

Facing sampling techniques as an optimal design problem

Summary The aim of this paper is to investigate and discuss the common points shared, in their line of development, by both Sampling Theory and Design of Experiments. In fact, Sampling Theory adopts the main optimality criterion of the Optimal Design of Experiments, the minimization of variance, i.e. D-optimality. There is also an approach based on c-optimality, as far as ratio estimates are concerned, in Design of Experiments, and the A-optimality involved in a proposed Sampling technique. It is pointed out that the L2 norm is mainly applied as a distance measure.

On sample size calculation in testing treatment efficacy in clinical trials

Summary Sample size calculation is an integral part of any clinical trial design, and determining the optimal sample size for a study ensures adequate power to detect statistical significance. It is a critical step in designing a planned research protocol, since using too many participants in a study is expensive, exposing more subjects to the procedure. If a study is underpowered, it will be statistically inconclusive and may cause the whole protocol to fail. Amidst the attempt to maximize power and the underlying effort to minimize the budget, the optimization of both has become a significant issue in the determination of sample size for clinical trials in recent decades. Although it is hard to generalize a single method for sample size calculation, this study is an attempt to offer something that might be a basis for finding a permanent answer to the contradictions of sample size determination, by the use of simulation studies under simple random and cluster sampling schemes, with different sizes of power and type I error. The effective sample size is much higher when the design effect of the sampling method is smaller, particularly less than 1. Sample size increases for cluster sampling when the number of clusters increases.

Orthogonal decomposition of the sum-symmetry model for square contingency tables with ordinal categories: Use of the exponential sum-symmetry model

Summary In the existing decomposition theorem, the sum-symmetry model holds if and only if both the exponential sum-symmetry and global symmetry models hold. However, this decomposition theorem does not satisfy the asymptotic equivalence for the test statistic. To address the aforementioned gap, this study establishes a decomposition theorem in which the sum-symmetry model holds if and only if both the exponential sum-symmetry and weighted global-sum-symmetry models hold. The proposed decomposition theorem satisfies the asymptotic equivalence for the test statistic. We demonstrate the advantages of the proposed decomposition theorem by applying it to datasets comprising real data and artificial data.

Orthogonal decomposition of the sum-symmetry model using the two-parameters sum-symmetry model for ordinal square contingency tables

Summary Studies have been carried out on decomposing a model with symmetric structure using a model with asymmetric structure. In the existing decomposition theorem, the sum-symmetry model holds if and only if all of the two-parameters sum-symmetry, global symmetry and concordancediscordance models hold. However, this existing decomposition theorem does not satisfy the asymptotic equivalence for the test statistic, namely that the value of the likelihood ratio chi-squared statistic of the sum-symmetry model is asymptotically equivalent to the sum of those of the decomposed models. To address this issue, this study introduces a new decomposition theorem in which the sum-symmetry model holds if and only if all of the two-parameters sum-symmetry, global symmetry and weighted global-sum-symmetry models hold. The proposed decomposition theorem satisfies the asymptotic equivalence for the test statistic—the value of the likelihood ratio chi-squared statistic of the sum-symmetry model is asymptotically equivalent to the sum of those of the two-parameters sum-symmetry, global symmetry and weighted global-sum-symmetry models.

Influence of different sowing density in two varieties of maize. Part II. Relation to agricultural morphological features

Summary In this paper, we investigate the effect of seeding density on several morphological features such as plant height, height of the production ears, ear length, ear diameter, leaf area, and LAI (leaf area index). Inference is based on a series of three-year two-factor experiments with two hybrid maize varieties – SY Cooky and Drim “stay-green” type – and 5 sowing densities: 6, 7, 8, 9 and 10 plants per m2. The “stay-green” maize variety had production cobs significantly higher on the plant, and had a thicker cob and a larger leaf assimilation area than the conventional variety. Increasing maize sowing density from 6 to 10 plants m−2 resulted in a linear decrease in cob length and diameter, while it increased the LAI. Significantly higher chlorophyll content, expressed in SPAD units, was found in the “stay-green” hybrid at the BBCH 67 stage in a wet (2012) and drier year (2014), compared with the traditional variety. This may indicate that such a variety is more tolerant to stress conditions.