All books

Professional

Apps About Coach Log in Start reading

Chemistry · Glossary

What is Measurement uncertainty?

Also known as: standard uncertainty · type A evaluation · type B evaluation · expanded uncertainty · relative uncertainty

Definition 29.5 University Chemistry — Year 1 · Chapter 29 — Lab Techniques I: Safety, Measurement and Separation
  • The measurement uncertainty is a parameter that characterises the dispersion of the values that can reasonably be attributed to the quantity measured.
  • The standard uncertainty u(x)u(x) is that uncertainty expressed as a standard deviation.
  • A type A evaluation obtains uu by the statistical analysis of a series of repeated measurements; a type B evaluation obtains it by any other means: the graduation of an instrument, the tolerance stated by its maker, a calibration certificate, the number of digits of a tabulated value.
  • The expanded uncertainty U=k uU = k\,u is the standard uncertainty multiplied by a coverage factor kk, usually k=2k = 2; for a normal distribution the interval x±2ux \pm 2u contains the true value with a probability of about 95 %95\,\%.
  • The relative uncertainty is u(x)/∣x∣u(x)/|x|, often given in per cent.
Left: twenty readings of the same titration end point (illustrative data), read to 0.05\, mL, with the normal curve of the same mean V = 12.455\, mL and standard deviation s = 0.071\, mL. Right: the rectangular distribution of a type B evaluation, a value known only to lie between x_0 - a and x_0 + a; its standard deviation is a/√3. Left: twenty readings of the same titration end point (illustrative data), read to 0.05\, mL, with the normal curve of the same mean V = 12.455\, mL and standard deviation s = 0.071\, mL. Right: the rectangular distribution of a type B evaluation, a value known only to lie between x_0 - a and x_0 + a; its standard deviation is a/√3.
Left: twenty readings of the same titration end point (illustrative data), read to 0.05 mL0.05\,\mathrm{mL}, with the normal curve of the same mean Vˉ=12.455 mL\bar V = 12.455\,\mathrm{mL} and standard deviation s=0.071 mLs = 0.071\,\mathrm{mL}. Right: the rectangular distribution of a type B evaluation, a value known only to lie between x0−ax_0 - a and x0+ax_0 + a; its standard deviation is a/3a/\sqrt3.
Read in context →