For PEFR data, there is no obvious relationship between the difference and the mean. Under these conditions, we can summarize the mismatch by calculating the distortion estimated by the mean difference d and the standard deviation of the differences (s). If there is a consistent distortion, we can adjust it by subtracting d from the new method. For PEFR data, the average difference (large metre minus small metre) is -2.1 l/min and s 38.8 l/min. We would expect most of the differences to be between d- 2s and d+2s (Figure 2). If the differences are normally redistributed (Gauss), 95% of the differences are between these limits (or more precisely between d – 1.96s and d + 1.96s). Such differences probably follow a normal distribution, as we have removed much of the variation between subjects and we remain behind with the measurement error. The measurements themselves do not need to follow a normal distribution, and often do not. We thought that a conference that said that everyone was wrong, and then sat down, would fall a little flat.

We had to come up with a method that was the right one. We thought it was obvious from basic statistical methods. If we want to reach an agreement, we want to know how far the measures with the two different methods could be from each other. So we started with the differences between the measurements on the same subject by two methods. We can calculate the mean and standard deviation of these differences. If the mean and standard deviation are constant and the differences have an approximate normal distribution, 95% of these differences must be between the mean minus 1.96 SD and the mean plus 1.96 SD. Later, we called these limits 95% of the match. In the previous analysis, it was judged that the differences between the measurement range did not vary systematically.

That may not be the case…