Cumulative Confidence Limits in Reporting the Results of Volumetric Analyses I t is common practice today for students in undergraduate analytical courses to calculate standard deviations and confidence limits in reporting the results of a quantitative analysis. An extension of this practice has been introduced recently by the author, in the case of volumetric analyses, to recognize the fact that the standard deviation in the analysis per se, as calculated from data on sample weights and titration volumes, does not include any contribution from the uncertainty in normality of the titrant. In order to include this uncertainty in normality in the statistical treatment of the data, a cumulative confi~, for the normality of the dence limit, Cum. C.L., is ca.Iculated. The relative confidence limit, C . L . S , ~calculated titrant from standardization data, is combined with the relative confidence limit for the analysis of the sample, C.L.r,.s,i,, using the square root of the sum of the squares ss in the propsgationof errors:'
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Cum. C.L. = Q \ / ( C . L . ~ M ~(C.L.m.tvais)Z )~ This is roughly equivalent to adding the variances of the two experiments, with due regard for possible differences in the number of trials in the two cases. In our la.boratory these cdculations are performed on a parts per thousand basis, at the 95% confidence level. A tentative average, obtained by the student directly from the experimental data a,n the various portions analyzed, may contain more figures than are warranted by the overall precision of the data. The cumulative confidence limit offers the student a statistically valid basis for rounding off (if necessary) to the number of figures that are significant in the final average.
' LAITINEN,H. A., "Chemical Analysis," MoGraw-Hill Book Co., New York, 1960, pp. 544-5.
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Journal o f Chemiccrl Education
