Appendix

If we measure a with an error of observation Δa, and b with an error of observation Δb, what will be the effect of these errors on a quantity Q, where Q is some simple expression of the observed values,for example Q= a + b? This topic is described as the confounding or propagation of errors and is discussed in many textbooks concerning applied statistics and experimental measurements (e. g. Topping 1965). First, let us consider how errors propagate through simple arithmetic operations that involve values with errors of observation or measurement. Note that the fractional error in a is given by f= Δa/a. Subsequently, more general situations will be mentioned, including the manner in which variances of samples of observations influence the variance of some derived quantity.