Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

APPENDIX 2 413It will be observed that they are more randomly distributed about zero when eachpoint is weighted by the factor a’ than when each point is assigned the same weight.This fact suggests that the procedure in which each point is weighted by the factora’ is the superior of the two, a conclusion which agrees with the author’s judgementthat, in this work, a’(a) would be independent of a. For these two reasons,we shall not discuss in detail the parameters obtained when each point is givenequal weight in the least squares equations although, for interest, we give in Table5 a comparison of the rate coefficients and their standard errors for the two methodsof weighting for each of the six experiments of our set. It can be seen immediatelythat the weighting procedure wlf = elf, improves the consistency of the set.Although we do not need a statistical analysis to tell us that the six values ofthe rate coefficients (listed in column 3, Table 5) constitute an homogeneous set,we give in Table 6 the details of the calculations which would be done if the conclusionwere less obvious. This table also shows how the best value of the ratecoefficient is calculated and how an estimate of its standard error is obtained. Theresult should be written thus: “the mean value of the rate coefficient and its standarderror are given byk(35.1” C) = (7.139k0.069)~ sec-’ (D.F. = 3)”The final bracket containing D.F. = 3 shows the number of degrees of freedomused in estimating the quoted standard error in E; if the number of degrees offreedom is not given, it is impossible to decide upon the significance to be attachedto the value quoted. Alternatively, the rate coefficient and its 90 % confidencelimits could be given. In this case, the result should be written: “the mean valueof the rate coefficient together with the 90% confidence limits are given byE(35.1” C) = (7.14k0.16) xsec-”’The former summary of the calculations is preferred since we may wish to use theestimates s(E) in weighting the rate coefficients in a subsequent calculation (e.g.in evaluating the weighted least squares estimate of the activation energy).Inspection of the calculations in Table 6 shows that the estimate s(k) is determinedalmost entirely by the results of group 1 (runs 1,2 and 3). Furthermore, s@)is considerably greater than the standard error of any individual rate coefficientestimated from the scatter of the experimental values of In a about the fitted straightline. In other words, it is the inability to replicate the experimental conditionsexactly rather than the definition of the straight lines which determines the precisionof the final estimate of the rate coefficient. In fact, we show in the calculationsset out in Table 7 that the replicate experiments in Group 1 differ significantlyfrom one another. It is because these results are so discordant that we have(Text continued on p. 41 7.)