Power transformation fenvalerate

Constant Variances. Response values from the electron capture chromatographic analysis of the insecticide fenvalerate, were transformed by the process described above. The six response values at each of six different amount levels were transformed by a series of powers, and the variances calculated at each level (Table I). For a transformation power of 0.5 the value of the variances increased from 0.001 to 0.338 as the response increased. When the logarithm of the response was used, the value of the variances decreased from 0.00085 to 0.00008 as the response increased. Raising the responses to the 0.15 power gave calculated variances that remained roughly constant across the range of amounts. 

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. 

Table I. Comparison of Transformed Response Variances for Several Powers of Transformation. Fenvalerate Data on the Electron Capture Detector.

For fenvalerate the minimum H statistic was found to be at a transformation power of 0.15. The power range of 0.15 to 0.10 gave an H statistic less than or equal to the critical H value. 

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. 

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See also in sourсe #XX -- [ ]

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