Error calculations in practice

We are now in a position to estimate the standard errors for a large class of experiments. Let us briefly recapitulate. The final quantity Z is a function of the primary quantities A, B, C, … which are either measured directly or are the slopes or intercepts of straight lines drawn through points representing directly measured quantities.

If the quantity is measured directly, we take the mean of several values to be the best value and obtain its standard error by the method given in chapter 3. (During the present chapter we shall drop the word ‘standard’ in ‘standard error’. We shall not be considering the actual error in a measured quantity, and the word ‘error’ will refer to the standard error, i.e. the standard deviation of the distribution of which the quantity is a member.) If the quantity is the slope or intercept in a straight line, its value and error are obtained either from the method of least squares or from the method of taking the points in pairs.

The best value of Z is calculated from the best values of the primary quantities, and its error is obtained from their errors by the rules given in Table 4.1, or in general from (4.17) and (4.18).

There are often a large number of primary quantities to be measured, and it might be thought that the calculation of the error in each one and the subsequent calculation of the error in Z would be a laborious process.