Fenvalerate data sets

Thanks are due David Kurtz for providing the Fenvalerate data and stimulating my interest in the detection-calibration problem. Helpful discussions with John Mandel concerning the Fenvalerate data set are also gratefully acknowledged. 

The various Datasets A-F were all of fenvalerate. We chose to transform the response values of these sets to the same power as required for the fenvalerate data set since we wished to use these data sets as examples of "unknown" data sets or as examples of poor quality standard sets. If the compound has an inherent analysis quality relating to the response variance, the quality of the poor sets is reflected in differences in the error bands. The acceptable ranges for the Datasets A-F, as shown in Table V, did include the 0.13 power eventually used in all cases where an acceptable H value was found. 

Four datasets are taken as examples for discussion, those for chlorothalonil. Dataset B (a general fenvalerate data set). 

In the text which follows we shall examine in numerical detail the decision levels and detection limits for the Fenval-erate calibration data set ( set-B ) provided by D. Kurtz (17). In order to calculate said detection limits it was necessary to assign and fit models both to the variance as a function of concentration and the response (i.e., calibration curve) as a function of concentration. No simple model (2, 3 parameter) was found that was consistent with the empirical calibration curve and the replication error, so several alternative simple functions were used to illustrate the approach for calibration curve detection limits. A more appropriate treatment would require a new design including real blanks and Fenvalerate standards spanning the region from zero to a few times the detection limit. Detailed calculations are given in the Appendix and summarized in Table V. 

Fenvalerate Detection Limits. To the extent that detection limits require knowledge of the calibration curve and random error (for x) as a function of concentration, all of the foregoing discussion is relevant — both for detection and estimation. However, curve shape and errors where x x, are relatively unimportant at the detection limit, in contrast to direct observations of the initial slope and the blank and its variability. (It will be seen that the initial observation in the current data set exceeded the ultimate detection limit by more than an order of magnitude )... 

Transformation Power of Selected Data Sets. Hartley statistic values are shown in Tables I-III for fenvalerate, chlordecone, and chlorothalonil. In each case a power transformation was found of sufficient size at a 93% probability which satisfied the H criterion. For fenvalerate the power of 0.15 was satisfactory for constant variance. For chlordecone the whole range of powers from 0.30 to 0.10 satisfied the critical H value (listed in order of increasing transformation power). Despite apparent non-constancy of data for chlorothalonil shown in Table III, the critical H was satisfied for the range in power transformation from 0.23 to 0.10. 

The Bandwidth is essentially a normalized half confidence band. The confidence interval bandwidths for 9 data sets using inverse transformed data are given in Table X. The bandwidths are approximately the vertical widths of response from the line to either band. The best band was found for chlorpyrifos, 1.5%, at the minimum width (located at the mean value of the response) and 4.9% at the minimum or lowest point on the graph. Values for fenvalerate and chlorothalonil were slightly higher, 2.1-2.2% at the mean level. The width at the lowest amount for the former was smaller due to a lower scatter of its points. The same reason explains the difference between fenvalerate and Dataset B. Similarly, the lack of points in Dataset A produced a band that was twice as wide when compared to Dataset B. Dataset C gave a much wider band when compared to Dataset B. 

Differences in calibration graph results were found in amount and amount interval estimations in the use of three common data sets of the chemical pesticide fenvalerate by the individual methods of three researchers. Differences in the methods included constant variance treatments by weighting or transforming response values. Linear single and multiple curve functions and cubic spline functions were used to fit the data. Amount differences were found between three hand plotted methods and between the hand plotted and three different statistical regression line methods. Significant differences in the calculated amount interval estimates were found with the cubic spline function due to its limited scope of inference. Smaller differences were produced by the use of local versus global variance estimators and a simple Bonferroni adjustment. 

Fenvalerate "unknown data sets were used as examples in this study. See Appendix A for the complete listing of the data. 

Each of the Datasets A-F were also of fenvalerate and were obtained from an extensive study of fenvalerate residues in chickens and eggs. They show how much variability in data quality can be obtained in practice. Table VII describes the number of calibration levels, replicates at each level, and ranges in ng of amounts injected into the gas chromatograph. Dataset A is an "ideal" set, a set that looked ideal at the time it was recorded. Dataset B is a set of data taken over two days under constant... 

There is one final observation using the bandwidth information The data of Tables IX and X suggest that the flame photometric detector (chlorpyrifos) produces more consistent data than the electron capture detector. The chlorpyrifos data clearly had the narrowest bandwidth yet both the range and sample size of this set were comparable to the others studied. The range of chlorpyrifos was 500 to 1 whereas those of fenvalerate and chlorothalonil were 2000 to 1 and 1000 to 1, resp. Chlorpyrifos had 30 samples whereas the other two had 36 and 30, resp. Chlorpyrifos had 5 analysis levels while the other two had 6 each. More data of this sort is needed to compare various detector systems. 

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