Solution: A transformation of data values by means of some

Chapter 1, Problem 1.25

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A transformation of data values by means of some mathematical function, such as or 1/x, can often yield a set of numbers that has nicer statistical properties than theoriginal data. In particular, it may be possible to find afunction for which the histogram of transformed values ismore symmetric (or, even better, more like a bell-shapedcurve) than the original data. As an example, the articleTime Lapse Cinematographic Analysis of BerylliumLung Fibroblast Interactions (Environ. Research, 1983:3443) reported the results of experiments designed tostudy the behavior of certain individual cells that had beenexposed to beryllium. An important characteristic of suchan individual cell is its interdivision time (IDT). IDTs weredetermined for a large number of cells both in exposed(treatment) and unexposed (control) conditions. Theauthors of the article used a logarithmic transformation,that is, transformed value log(original value). Considerthe following representative IDT data:IDT log10(IDT) IDT log10(IDT) IDT log10(IDT)28.1 1.45 60.1 1.78 21.0 1.3231.2 1.49 23.7 1.37 22.3 1.3513.7 1.14 18.6 1.27 15.5 1.1946.0 1.66 21.4 1.33 36.3 1.5625.8 1.41 26.6 1.42 19.1 1.2816.8 1.23 26.2 1.42 38.4 1.5834.8 1.54 32.0 1.51 72.8 1.8662.3 1.79 43.5 1.64 48.9 1.6928.0 1.45 17.4 1.24 21.4 1.3317.9 1.25 38.8 1.59 20.7 1.3219.5 1.29 30.6 1.49 57.3 1.7621.1 1.32 55.6 1.75 40.9 1.6131.9 1.50 25.5 1.4128.9 1.46 52.1 1.72Use class intervals 1020, 2030, . . . to construct a histogramof the original data. Use intervals 1.11.2,1.21.3, . . . to do the same for the transformed data. Whatis the effect of the transformation?