The ``Spread'' as a Measure of Deviation in Physical Measurements

To compare results of incandescent lamp tests expressed in terms of the spread (maximum difference) observed in sets of various numbers of lamps, factors were required to convert these results to a comparable basis. The average deviation of a single observation was chosen as the basis of comparison. To avoid the necessity of computing the probable error, a table of the probability integral for the argument τ = π^½t is given. Assuming a Gaussian distribution of errors, the factors have been tabulated for numbers of observations up to 100,000. They are given approximately by the semi‐empirical formulas: spread/ave. $\mathrm{deviation}{\text{=f(n)=2π}}^{\frac{1}{2}}{t}_a{\text{≐(5}}_0{\text{296−2}}_0{\text{086/(0}}_0\text{45+}\lg \mathrm{\hspace{0.17em}n))(}\lg {\mathrm{\hspace{0.17em}n)}}^{\frac{1}{2}}{\text{≐5}}_0\text{7\hspace{0.17em}(}\lg {\mathrm{\hspace{0.17em}n)}}^{\frac{1}{2}}{\text{−1}}_{0}75$ . While the average deviation so computed is less precise than that computed from the sum of the residuals, or a fortiori of their squares, the difference seldom exceeds the uncertainty of the more refined measures. Conventions are suggested for the retention of figures and for the statement of measures of deviation. The labor of computing the average deviation from the spread is so slight that an expression of the internal consistency of all results of physical measurements may reasonably be required.