Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

382 TREATMENT OF EXPERIMENTAL DATAand so s(E), the standard error of the weighted mean, is given by eitherwhichever is the larger. Conlidence limits can be calculated, as explained previously,from the value oft appropriate to (a) the chosen confidence level and (b)the number of degrees of freedom used in estimating ms, or ms,. The examplein Appendix 2 should make this clearer.(iu) Homogeneity of the rate coeficients of the replicate experimentsIt is important to test the rate coefficients obtained from a group of replicateexperiments for homogeneity. Such a test can provide information as to whetheror not all factors influencing the rate of the reaction are completely controlledthroughout the group. For this purpose, we compare the distribution of the k;values (not the rate coefficients themselves) about their mean with the distributionof the experimental values of f(aij) about the fitted straight linef(aij) = li-k;(tij-tio)In the case of the oth group of replicate experiments, we shall have ru separatevalues of k;.Firstly, we calculate a weighted average of the ru values of k; using the expressionwhere the weighting factors W(k;) are given byW(kf) = -Dij=nij= 1The quantity Di is given by e-qn. (60) and ci=1( wij can be calculated from theweights wij assigned to each of the ni points in the ith run.If the ru values of the rate coeffi.cients are derived from a single set of f(aij)values characterized by the same value of Q (the standard deviation of a point ofunit weight), and if the rate coefficients are distributed normally about some truevalue, it can be shown that