and then the confidence interval will be from the observed value minus t standard errors to the observed value plus t standard errors For the pefr data s=38.8. The standard error of d is thus 9 4. For the 95% confidence interval we have 16 degrees of freedom and t=2. 12. Hence the 95% confidence interval for the bias is -2.1-(2.12 x9.4)to-2.1+(2.12 x9.4), giving -22.0 to 17.8 I/min. The standard error of the limit d-2s is 16.3 1/min. The 95% confidence interval for the lower limit of agreement is-797-(2.12 x 16.3) to-797+(2. 12 x 16.3), giving -114.3 to 45. 1 I/min. For the upper limit of agreement the 95% confidence interval is 40.9 to 110.1 /min. These intervals are wide, reflecting the small sample size and the great variation of the differences. They show, however, that even on the most optimistic interpretation there can be considerable discrepancies between the two meters and that the degree of agreement is not EXAMPLE SHOWING GOOD AGREEMENT Fig 3 shows a comparison of oxygen saturation measured by an oxygen saturation monitor 0.42 percentage points with 95% confidence interval 0. 13 to 0.70. Thus pulsed oximeter< and pulsed oximeter saturation, a new non-invasive technique. Here the mean differenc saturation tends to give a lower reading, by between 0.13 and 0. 70. Despite this, the limits of agreement(-2.0 and 2.8)are small enough for us to be confident that the new method can be used in place of the old for clinical purposes Mean 2SD 0 Mean 2SD 100 Average of osm and pos Fig 3 Oxygen saturation monitor and pulsed saturation oximeter RELATION BETWEEN DIFFERENCE AND MEAN In the preceding analysis it was assumed that the differences did not vary in any systematic way over the range of measurement. This may not be so. Fig 4 compares the measurement of mean velocity of circumferential fibre shortening(VCF) by the long axis and short axis in M- mode echocardiography. The scatter of the differences increases as the VCF increases. W could ignore this, but the limits of agreement would be wider apart than necessary for smal VCF and narrower than they should be for large VCF. If the differences are proportional to the mean, a logarithmic transformation should yield a picture more like that of figs 2 and 4 and we can then apply the analysis described above to the transformed data5 and then the confidence interval will be from the observed value minus t standard errors to the observed value plus t standard errors. For the PEFR data s = 38.8. The standard error of d is thus 9.4, For the 95% confidence interval we have 16 degrees of freedom and t = 2.12. Hence the 95% confidence interval for the bias is - 2.1- (2.12 ´ 9.4) to - 2.1+ (2.12 ´ 9.4), giving - 22.0 to 17.8 l/min. The standard error of the limit d - 2s is 16.3 l/min. The 95% confidence interval for the lower limit of agreement is - 79.7 - (2.12 ´16.3) to - 79.7 + (2.12 ´16.3) , giving -114.3 to - 45.1 l/min. For the upper limit of agreement the 95% confidence interval is 40.9 to 110.1 l/min. These intervals are wide, reflecting the small sample size and the great variation of the differences. They show, however, that even on the most optimistic interpretation there can be considerable discrepancies between the two meters and that the degree of agreement is not acceptable. EXAMPLE SHOWING GOOD AGREEMENT Fig 3 shows a comparison of oxygen saturation measured by an oxygen saturation monitor and pulsed oximeter saturation, a new non-invasive technique. 5 Here the mean difference is 0.42 percentage points with 95% confidence interval 0.13 to 0.70. Thus pulsed oximeter saturation tends to give a lower reading, by between 0.13 and 0.70. Despite this, the limits of agreement ( - 2.0 and 2.8) are small enough for us to be confident that the new method can be used in place of the old for clinical purposes. Fig 3. Oxygen saturation monitor and pulsed saturation oximeter RELATION BETWEEN DIFFERENCE AND MEAN In the preceding analysis it was assumed that the differences did not vary in any systematic way over the range of measurement. This may not be so. Fig 4 compares the measurement of mean velocity of circumferential fibre shortening (VCF) by the long axis and short axis in M￾mode echocardiography. 6 The scatter of the differences increases as the VCF increases. We could ignore this, but the limits of agreement would be wider apart than necessary for small VCF and narrower than they should be for large VCF. If the differences are proportional to the mean, a logarithmic transformation should yield a picture more like that of figs 2 and 4, and we can then apply the analysis described above to the transformed data