# Is there an acceptable value for the limits of agreement or the repeatability?

We can estimate the repeatability of a measurement from the within-subject standard deviation, sw, or the repeatability coefficient, 1.96 √2 sw. We can estimate how closely two different measurements agree by the limits of agreement.

The within-subject standard deviation, the repeatability coefficient, and the limits of agreement are all estimates. They estimate the standard deviation of repeated measurements on the same subject, the largest likely size of the difference between two measurements on the same subject, and the largest likely size of the difference between measurements by two different methods on the same subject. They have units, the same units as the observations.

If we change the units in which the observations are measured, we will change the sizes of these estimates. For example, if we have measurements of height in centimetres the estimates of repeatability and limits of agreement will also be in centimetres. If we change our measurement to millimetres, we will multiply the estimates of repeatability and limits of agreement by 10.

For this reason, it is not possible to say how small the repeatability or limits of agreement should be to represent 'good' agreement. The question we have to ask is whether the measures agree sufficiently well, i.e. whether the largest likely difference is small enough, for the particular purpose for which we want the measurements. This may be different for different purposes.

Martin Bland