Compositional tables -a continuous counterpart to the contingency tables -carry relative information about relationships between row and column factors; thus, for their analysis, only ratios between cells of a table are informative. Consequently, the standard Euclidean geometry should be replaced by the Aitchison geometry on the simplex that enables decomposition of the table into its independent and interactive parts. The aim of the paper is to find interpretable coordinate representation for independent and interaction tables (in sense of balances and odds ratios of cells, respectively), where further statistical processing of compositional tables can be performed.Theoretical results are applied to real-world problems from a health survey and in macroeconomics.
Setting of mineral trioxide aggregate (MTA) is affected by various factors. The purpose of this in vitro study was to evaluate the influence of root canal wall thickness on mechanical properties of MTA along the whole apical plug. Bovine bone mold tubes with internal diameter of 2 mm, height of 5 mm, and wall thickness of 0.8 mm, 1.2 mm, and 1.6 mm were filled with 3 mm ProRoot MTA and were kept in 37 °C and relative humidity of 100% for 7 days. The indentation hardness and reduced modulus of elasticity were measured in a large overview matrix and detailed matrix placed 1.5 mm from simulated apical foramen in order to obtain particularized information about gradient of altering mechanical properties. The uppermost layer of material in contact with simulated apical foramen had reduced mechanical properties irrespective of root canal wall thickness. The most distinct decrease of microhardness (32%) and reduced modulus of elasticity (27%) in interfacial layer were present in specimen with thinnest root canal wall. This effect could be observed in detailed measurement up to 190 µm in material. The interfacial layer of MTA, which was in contact during setting with root canal wall thinner than 1.2 mm, had reduced mechanical properties.
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