Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

380 TREATMENT OF EXPERIMENTAL DATAeach provide an estimate of the same quantity, namely, the variance of a ratecoefficient of unit weight. Thus, their ratio, F, defined asshould be unity. In practice, this ratio may be less or greater than unity. If it is lessthan unity, the scatter of the group means about the set mean is less than would beanticipated from the scatter of the individual rate coefficients and so the wholeset is homogeneous. (This is exemplified by the data given in Table 3 and Appendix2). If F is greater than unity, the set may still be homogeneous but there are limitsto the value F can take. These limits are determined by the confidence level chosenand by the values (u-1) and (r-u) appearing in the expression for F-the'degrees of freedom' associated with the numerator and denominator. Thus,returning to our example, the maximum value of F which is likely to be obtained in,say, 95' cases out of 100 for 2 degrees of freedom in the numerator and 3 degreesof freedom in the denominator, is 9.55" if there is no difference between the threegroups.If the calculated value of F exceeds the critical value, it is probable that thedata cannot be represented by the expression under examination. However, beforeturning to other rate expressions, the data of the replicate experiments should beexamined to make sure that no hidden or incompletely controlled factors systematicallyinfluence the values of ku, obtained. The procedure is described in thenext section.From this discussion, one very important point with practical consequencesemerges. This concerns the use of replicate experiments. If no replicate experimentsare performed, it is not possible to define the basic error of the measurements, i.e.the distribution of the individual rate coefficients of replicate experiments abouttheir means. In terms of our previous expression for F, the lack of replicate experimentsmeans that there are as many 'groups' as there are experiments in the set(i.e. u = r) and so any value of F is consistent with the whole set being homogeneous;the scatter of the rate coefficients about the set mean merely defines thevariance of the distribution of a rate coefficient of unit weight. It is clear thatreplication of initial conditions is highly desirable.The above calculations are often set out in the form of an Analysis of VarianceTable as shown belowOther confidence levels may be chosen depending on the judgement of the investigator.tt A table of F is given in the Handbook of Chemistry and Physics.