By Avella P., Boccia M., Sforza A.
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4 gives more details. The second group of transformations ensures a better fit of the data values to a certain distribution or to a certain model. We know for instance that the responses of many organisms to concentrations of cations is logarithmic. g. H + ions to pH). Other variables also frequently display a logarithmic relation instead of a linear one. Another reason for transformation can be that least-squares regression (Chapter 3) requires that the dependent variable has normally distributed random errors.
Systematic sampling strategies require, however, justification by specification of assumptions about the type of variation in the sampled population to arrive at statistically sound conclusions. In certain cases, for instance in a research project involving treatments or observations that could cause irreparable damage, it is not desirable to sample randomly. Anderson et al. (1980) discuss the possible reasons for non-randomized studies in the field of medicine. Their discussion - translated into ecological terms - is also of interest to ecologists.
Research with a practical/technological aim. Another important dichotomy concerns exploratory objectives vs. confirmatory objectives of a study. The first sort are aimed at the detection of relations that represent a starting point for later research devoted to the testing of hypotheses; the second sort are aimed at obtaining conclusive statements (statistical proof), made possible by the application of hypothesis testing and parameter estimation. Apart from this classification of studies by intended purpose, a typology based on a characterization of the study design is important.
A Branch-and-Cut Algorithm for the Median-Path Problem by Avella P., Boccia M., Sforza A.