Number of distinctly different factor combinations

If / is the number of distinctly different factor combinations at which experiments have been carried out (also called design points), then the sum of squares due to lack of fit has f — p degrees of freedom associated with it. 

Because the number of distinctly different factor combinations is seven (/ = 7), and because the number of experiments is eight (n = 8), there is only one degree of freedom for lack of fit f—p = 7 — 6 = 1) and only one degree of freedom for purely experimental uncertainty n-f-S-7= 1). 

A second feature of the book is its emphasis on degrees of freedom. We have tried to remove the magic associated with knowing the source of these numbers by using the symbols n (the total number of experiments in a set), p (the number of parameters in the model), and / (the number of distinctly different factor combinations in the experimental design). Combinations of these symbols appear on the tree to show the degrees of freedom associated with various sums of squares (e.g., n-/for SS ). 

For the derivation of the PNEC several approaches have been proposed. Generally these can be categorised into three distinct assessments a conservative, a distributional, and a mixture toxicity approach. In conservative approaches, usually the most (realistic) sensitive endpoint such as LC50 or the known no observed effect concentration (NOEC) is taken and divided by an uncertainty factor (10-100). The selected uncertainty factor value depends on the type of endpoint and the number of available data, and is applied to account for laboratory to field extrapolations, species differences in sensitivities, and similar uncertainties. In distributional approaches, a series of, or all available, literature data are taken and a selected cut-off value is applied to the distribution of these data. The cut-off value may be, e.g., the concentration value that will protect 95% of the species (tested). In general, again an uncertainty factor (usually of 10) is then applied to take into account species differences. In the mixture toxicity approach, a similar mode of action is assumed for the assessment of the combined (additive) effect of the mixture. All relevant mixture components are scaled relative to the most potent one. This results in relative potencies for each component. The total effect of the mixture is then evaluated by... 

Bates [3] discussed the role of molecular architecture in polymer-polymer phase behavior. There are a number of molecular configurations available to a pair of chenucally distinct polymer species. Star polymers with a specific arm number with predeternuned molecular weights and with narrow molecular weight distribution can be synthesized using anionic polymerization. Diblock and multiblock arrangements are possible. Different polymers can be combined into a single material in several different ways that can lead to a variety of phase behaviors. Four factors control the phase behavior of polymer-polymer systems [3]. These are... 

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