23 Other Methods of Reporting Uncertainty*

Sometimes scientists report as percentages of the result. For Tyler’s example we would divide the uncertainty by the result and the multiply by 100 to find the percent uncertainty before writing it behind the result:

    \begin{equation*} \Average\, PD = 56\, \bold{mm}\, \pm\left(\frac{2\,\bold{mm}}{56\,\bold{mm}}\right)\times100=56\,\bold{mm}\pm 4\% \end{equation*}

Finding percent uncertainty is an important step in some of the more sophisticated methods of determining the total uncertainty in the result of a calculation that uses several numbers that each have uncertainties themselves. This text won’t get into those sophisticated methods, but if you are curious you can read about some of them in Section 1.3 of OpenStax College Physics.

In addition to the methods we just discussed, Scientists sometimes report uncertainty in other ways, such as confidence intervals. Typically this method states 95% confidence that an actual value lies within the interval between two values. For example, this 25-year and 7-country study on cigarette smoking and mortality risk found that the hazard risk for all causes of death was 1.3x higher for smokers than non-smokers with a 95% confidence that the value was between 1.2x and 1.4x. (The risk was 1.8x higher for smokers of more than 10 cigarettes a day and even higher for death caused by coronary heart disease, all stroke, other arterial disease, lung cancer, other cancer, chronic obstructive pulmonary disease, and other disease in smokers[1].


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