On the distribution of quadratic forms and applications in the analysis of repeated measurements

In this paper a unified approach is given to the distribution of scalar quadratic forms for dependent variables. Necessary and sufficient conditions are found for the sums of squares of the various hierarchical layers in ANOVA to be distributed as multiples of chi-square variables. Results concerning the usual univariate F-tests in ANOVA of repeated measurements are derived as a special case.27112625264

Application of the split-plot experimental design for the optimization of a catalytic procedure for the determination of Cr(VI)

A kinetic catalytic procedure for the determination of Cr(VI), based on the o-dianisidine oxidation reaction with hydrogen peroxide in a weakly acid medium was optimized with respect to both reactants [HCl, o-dianisidine and H2O2] and solvent composition [mixtures of water, acetone and N, N-dimethylformamide], in order to achieve higher sensitivities. This was accomplished by making use of a split-plot experimental design which permitted simultaneous variations in both mixture and process variables, using a response surface approach. Ten mixture experiments were randomized at each one of the 23 factorial levels and error analysis was performed using a split-plot approach. The optimal mixture [water-acetone 70-30% m/m] and process variables [HCl: 6.0 x 10(-4) mol/l, o-dianisidine: 1.9 x 10(-2) mol/l and H2O2: 0.79 mol/l] values resulted in a significant sensitivity increase compared with a similar procedure described in the literature. (C) 1998 Elsevier Science B.V. All rights reserved.369326927