# Search Results

###### Canonical correlation analysis for functional data

References Krzyśko M. (2009): Podstawy wielowymiarowego wnioskowania statysty- cznego [Foundations of multidimensional statistical inference]. Wydawnictwo Naukowe UAM, Poznan. Leurgans S.E., Moyeed R.A., Silverman B.W. (1993): Canonical correlation analy- sis when the data are curves. Journal of the Royal Statistical Society B 55(3): 725{740. Ramsay J.O., Danzell C.J. (1991): Some tools for functional data analysis. Journal of the Royal Statistical Society B 53: 539-572. Ramsay J

###### Remarks about a construction method for D-optimal chemical balance weighing designs

bipartite weighing designs under the certain condition. Colloquium Biometricum 34a, 17-28. Ceranka B., Graczyk M. (2016). New construction of D-optimal weighing design with non-negative correlations of errors. Colloquium Biometricum 46, 31-45. Ceranka B., Graczyk M. (2017). Some D-optimal chemical balance weighing designs: theory and examples. Biometrical Letters 54(2), 137-154. Ceranka B., Graczyk M. (2018). Regular D-optimal weighing design with non-negative correlations of errors constructed from some block designs. Colloquium Biometricum 48, 1

###### Entropy as a measure of dependency for categorized data

## Summary

Data arranged in a two-way contingency table can be obtained as a result of many experiments in the life sciences. In some cases the categorized trait is in fact conditioned by an unobservable continuous variable, called liability. It may be interesting to know the relationship between the Pearson correlation coefficient of these two continuous variables and the entropy function measuring the corresponding relation for categorized data. After many simulation trials, a linear regression was estimated between the Pearson correlation coefficient and the normalized mutual information (both on a logarithmic scale). It was observed that the regression coefficients obtained do not depend either on the number of observations classified on a categorical scale or on the continuous random distribution used for the latent variable, but they are influenced by the number of columns in the contingency table. In this paper a known measure of dependency for such data, based on the entropy concept, is applied.

###### Determination of robust optimum plot size and shape – a model-based approach

R eferences Bhatti A.U., Mulla D.J., Koehler F.E., Gurmani A.H. (1991): Identifying and removing spatial correlation from yield experiments. Soil Sci. Soc. Am. J. 55: 1523-1528. Cressie N.A.C. (1993): Statistics for Spatial Data. John Wiley, New York. Cressie N., Wikle C.K. (2011): Statistics for Spatio-Temporal Data. Pub. A John Wiley & Sons. Inc. Faground M., Meirvenne M. Van (2002): Accounting for Soil Spatial Autocorrelation in the design of experimental trials. Soil Sci. Soc. Am. J. 66: 1134-1142. Matheron G. (1963): Principles

###### On the relevance of the 3D retinal vascular network from OCT data

. Sci. 46: E-Abstract 3467 Kwa, V.I.H., van der Sande J.J., Stam J., Tijmes N., Vrooland J.L. (2002): Retinal arterial changes correlate with cerebral small-vessel disease. Neurology 59: 1536-1540. Laatikainen L. (2006): Adverse e ects of uorescein angiography Acta Ophthalmologica Scandinavica 84(6): 720-721. Parikh A.H., Smith J.K., Ewend M.G., Bullitt E. (2004): Correlation of MR Perfusion Imaging and Vessel Tortuosity Parameters in Assessment of Intracranial Neoplasms. Technology in Cancer Research & Treatment 3

###### An alternative methodology for imputing missing data in trials with genotype-by-environment interaction: some new aspects

## Abstract

A common problem in multi-environment trials arises when some genotypeby- environment combinations are missing. In Arciniegas-Alarcón et al. (2010) we outlined a method of data imputation to estimate the missing values, the computational algorithm for which was a mixture of regression and lower-rank approximation of a matrix based on its singular value decomposition (SVD). In the present paper we provide two extensions to this methodology, by including weights chosen by cross-validation and allowing multiple as well as simple imputation. The three methods are assessed and compared in a simulation study, using a complete set of real data in which values are deleted randomly at different rates. The quality of the imputations is evaluated using three measures: the Procrustes statistic, the squared correlation between matrices and the normalised root mean squared error between these estimates and the true observed values. None of the methods makes any distributional or structural assumptions, and all of them can be used for any pattern or mechanism of the missing values.

###### Application of longitudinal analysis to the analysis of height increment of pine stands – simulated data

References Assmann E. (1968): Nauka o produkcyjności lasu [Forest yield science]. PWRiL, Warszawa. [in Polish]. Graczyk M., Kaźmierczak K., Zawieja B. (2010): The longitudinal analysis applied to the analysis of height increment of pine stands. Biometrical Letters 47(2): 199-128. Kaźmierczak K., Zawieja B. (2008): An attempt to assess the correlation between lengthwise growth of the main shoot in 24-year old Scots pines ( Pinus sylvestris L) on the growth of lateral branches. Biometrical Letters 45

###### The LMS for testing independence in two-way contingency tables

.G. (1954): Some methods for strengthening the common χ 2 tests, Biometrics 10(4): 417–451. Cohen, J., Nee, J.C. (1990): Robustness of Type I Error and Power in Set Correlation Analysis of Contingency Tables, Multivariate Behav. Res. 25(3): 341–350. Cressie, N., Read, T. (1984): Multinomial Goodness-of-Fit Tests, J R Stat Soc Ser B Stat Methodol 46: 440–464. Cressie, N., Read, T.R. (1989): Pearson’s χ 2 and the log likelihood ratio statistics G2: a comparative review, International Statistical Review/Revue Internationale de Statistique: 19

###### On modeling and analyzing barley malt data in different years

effects by a simulation study. Euphytica 202: 459-467. Caliński T. (1967): Doświadczenia wielokrotne i wieloletnie (in Polish). In: Training Materials of the Research Centre for Cultivar Testing, Part 1 – Basic problems of agricultural experimentation, Słupia Wielka, 1967. Caliński T., Krzyśko M., Wołyński W. (2006): Multivariate analysis. A comparison of some tests for determining the number of nonzero canonical correlations. Communications in Statistics – Simulation and Computation 35: 727-749. Elandt R. (1964): Statystyka matematyczna w zastosowaniu

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Copper and manganese acquisition in maize (*Zea mays* L) under different P and K fertilization

## Summary

The paper demonstrates the influence of different mineral fertilization with phosphorus and potassium on the concentration of copper (Cu) and manganese (Mn) in the ear leaf of maize at the stage of flowering (BBCH 65) as well as the contents and accumulation of the nutrients studied in maize when fully ripe (BBCH 89). A single factor experiment was carried out in 5-year-cycle (2007-2011), in the randomized complete block design. The experiment was conducted as a part of a long-term stationary trial. The investigation comprised 8 different P and K treatments: the absolute control, exclusive of one of the main nutrients (P - WPN or K - WKN), reduced amount of phosphorus and potassium (to 25% - W25 and to 50% WP50, WK50) as well as recommended amounts of basic nutrients (NPKMg - W100 and NP*KMg, P* - P* as PAPR - W100 PAPR). Evaluation of the nutriational status, performed in the ear leaf of maize at flowering stage, showed that regardless of fertilization treatment applied, the concentration of copper was lower than normative values, whereas that of manganese ranged within the optimal scope. At the same time, there was found a significant relationship between the grain yield obtained and acquisition of both copper and manganese by maize at flowering stage (stronger for manganese, r = 0.614). The total accumulation of copper and manganese in fully ripe maize was significantly differentiated as a result of mineral fertilization. The total uptake of Cu and Mn was reduced under the conditions of 10-year lack of P fertilization. Uptake reduction was considerably more advanced when K fertilization was absent for 10 years. Regardless of the experimental factor effects, more than 50% of the total copper uptake was accumulated in grain, whereas the majority of manganese was accumulated in maize leaves (50-64% of the total uptake). Correlation analysis showed a significant relationship between maize grain yield and the total accumulation of copper, whereas that of manganese was observed only in 3 of 8 treatments tested (WPN, WP50 and W100 as PAPR).