Statistical Artifacts in the Ratio of Discrete Quantities |
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| Authors: | Roger G. Johnston Shayla D. Schroder A. Rajika Mallawaaratchy |
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| Affiliation: | 1. Los Alamos National Laboratory , Los Alamos , NM , 87545 , USA;2. Computer Sciences Department , Eastern New Mexico University , Portales , NM , 88130 , USA;3. Electrical Engineering Department , Iowa State University , Ames , IA , 50012 , USA |
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| Abstract: | The ratio is a familiar statistic, but it is often misused. One frequently overlooked problem occurs when ratioing two discrete (digitized) variables. Fine structure appears in the histogram of the ratio that can be very subtle, or can sometimes even dominate the histogram. It disappears when the numerator and/or denominator become continuous. This statistical artifact is not a binning error, nor is it removed by taking more data. It is important to be aware of the artifact in order to avoid misinterpretation of ratio data. We provide examples of the statistical artifact (including one from baseball) and discuss ways to avoid or minimize the problems it can cause. |
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| Keywords: | Analog-to-digital conversion Binning errors Digitization Histogram Ratio Statistical artifacts |
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