Factorial design experimental standard deviation

The experimenter often chooses the smallest design consistent with his objectives and resources. Effects are estimated with a certain precision. For example, we have seen with the Plackett-Burman designs (and it is the same for the 2-level factorial designs of the following chapter) that the standard error of estimation of an effect is where ct is the experimental standard deviation (repeatability) and N is the number of experiments in the design. 

Abstract A preconcentration method using Amberlite XAD-16 column for the enrichment of aluminum was proposed. The optimization process was carried out using fractional factorial design. The factors involved were pH, resin amount, reagent/metal mole ratio, elution volume and samphng flow rate. The absorbance was used as analytical response. Using the optimised experimental conditions, the proposed procedure allowed determination of aluminum with a detection limit (3o/s) of 6.1 ig L and a quantification limit (lOa/s) of 20.2 pg L, and a precision which was calculated as relative standard deviation (RSD) of 2.4% for aluminum concentration of 30 pg L . The preconcentration factor of 100 was obtained. These results demonstrated that this procedure could be applied for separation and preconcentration of aluminum in the presence of several matrix. 

Any experimental design that is intended to determine the effect of a parameter on a response must be able to differentiate a real effect from normal experimental error. One usual means of doing this determination is to run replicate experiments. The variations observed between the replicates can then be used to estimate the standard deviation of a single observation and hence the standard deviation of the effects. However, in the absence of replicates, other methods are available for ascertaining, at least in a qualitative way, whether an observed effect may be statistically significant. One very useful technique used with the data presented here involves the analysis of the factorial by using half-normal probability paper (19). 

Assume that you have run experiments by a factorial design (with Np runs) with a view to assessing the significance of the experimental variables fi om estimates, hj, of the coefficients in a linear response surface model. Assume also that you have made Nq repeated runs of one experiment to obtain an estimate of the experimental error standard deviation. From the average response, J, in repeated runs, an estimate of the experimental error standard deviation, Sq, with (Nq - 1) degrees of freedom is obtained as... 

Van Dooren and Muller investigated in great detail by factorial designs the effects of apparatus, test substance, reference material, atmosphere (152), as well as heating rate and particle size (153,159,160) on results in quantitative DSC. The former set of experimental factors are called baseline-related characteristics if the curve is described using these parameters, large standard deviations should be taken into account. A baseline equation, based on heat balance considerations, is... 

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