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Wielkość próby a istotność wnioskowania statystycznego

100%
Kośny M., Peternek P.
Didactics of Mathematics
|
2011
|
issue 8 (12)
71-80
EN
Commonly used method of determining the quality of research results is the application of significance tests – both parametric and non-parametric. They enable researchers to eliminate low-quality results, when observed differences are the consequence of too small samples. Therefore relatively little attention – also in didactics – is paid to issues of big samples, when the number of observations amounts up to several thousands. Whereas situations, when significance test is applied to big samples requires no less attention than the situations of too small samples. In this context the main aim of the paper is the analysis of results of the significance test for the correlation coefficient (parametric test) and chi-square test for independence (non-parametric test) for samples exceeding 1000 observations. For these tests it will be shown, how imprecise interpretation could lead to the significant distortion of obtained results.
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The allocation of seats in the European Parliament and the principle of degressive proportionality

100%
Peternek P., Kośny M.
Mathematical Economics
|
2015
|
issue 11(18)
99-113
EN
One of the key issues in the process of preparing for an election to the European Parliament is to determine the number of seats for each country. The Treaty of Lisbon, signed by Member States of the European Union, has obliged the European Parliament to establish rules guaranteeing that the distribution of seats should be done according to, inter alia, the principle of degressive proportionality. The purpose of this paper is to explore how the principle of degressive proportionality is actually implemented, and to propose a compromise – a mathematical solution, guaranteeing that the distribution of seats is consistent with the requirements of the Lisbon Treaty.
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