A transformation of data values by means of somemathe

Chapter 1, Problem 25

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A transformation of data values by means of somemathe matical function, such as x or 1yx, can oftenyield a setof numbers that has nicer statistical propertiesthan the orig inal data. In particular, it may bepossible to find a function for which the histogram oftransformed values is more symmetric (or, even better,more like a bell-shaped curve) than the original data.As an example, the article Time LapseCinematographic Analysis of BerylliumLungFibroblast Interactions (Environ. Research,1983: 3443) reported the results of experimentsdesigned to study the behavior of certain individualcells that had been exposed to beryllium. An importantcharacteristic of such an individual cell is its interdivisiontime (IDT). IDTs were determined for a largenumber of cells, both in exposed (treatment) and unexposed(control) conditions. The authors of the articleused a logarithmic transformation, that is, transformed value = log(original value). Consider thefollowing representative IDT data:IDT log10(IDT) IDT log10(IDT) IDT log10(IDT) 28.1 1.45 60.1 1.78 21.0 1.32 31.2 1.49 23.7 1.37 22.3 1.35 13.7 1.14 18.6 1.27 15.5 1.19 46.0 1.66 21.4 1.33 36.3 1.56 25.8 1.41 26.6 1.42 19.1 1.28 16.8 1.23 26.2 1.42 38.4 1.58 34.8 1.54 32.0 1.51 72.8 1.86 62.3 1.79 43.5 1.64 48.9 1.69 28.0 1.45 17.4 1.24 21.4 1.33 17.9 1.25 38.8 1.59 20.7 1.32 19.5 1.29 30.6 1.49 57.3 1.76 21.1 1.32 55.6 1.75 40.9 1.61 31.9 1.50 25.5 1.41 28.9 1.46 52.1 1.72Use class intervals 102,20, 202,30, to constructa histogram of the original data. Use intervals1.12,1.2, 1.22,1.3, to do the same for the transformeddata. What is the effect of the transformation?