Bland Altman analysis for weights

The table presents a comparison of two sets of weight measurements, wgt0 and wgt4. For each pair of measurements, the following statistics are calculated:

Mean

The average of the two weight measurements ((wgt0 + wgt4) / 2).

Difference

The absolute difference between wgt0 and wgt4 (wgt0 - wgt4).

Difference/Mean

The ratio of the difference to the mean, indicating the relative difference between the two weight measurements.

Key observations

• Consistent Positive Differences: The differences between wgt0 and wgt4 are generally positive across the 10 records, indicating that wgt0 tends to be slightly higher than wgt4. For example, in record 1, wgt0 (198) is higher than wgt4 (192), resulting in a positive difference of 6. Similarly, in record 2, wgt0 (237) is 12 units higher than wgt4 (225).
• Relative Differences (Ratio): The Difference/Mean column reveals that the relative differences between the two weight measurements are small. For instance, in record 2, the ratio is 0.052, suggesting that the difference is 5.2% of the mean weight. Overall, the ratios are small (close to zero), indicating that wgt0 and wgt4 are relatively close to each other in most cases.

Confidence Intervals of Mean Differences (wgt0 and wgt4)

This table provides the mean difference between wgt0 and wgt4 along with its confidence intervals:

Mean Difference

The average difference between wgt0 and wgt4 is 8.063 units, indicating that, on average, wgt0 is 8.063 units higher than wgt4.

95% Confidence Interval (CI)

The CI for the mean difference ranges from 6.525 to 9.600, indicating that the true mean difference between wgt0 and wgt4 in the population lies within this range 95% of the time. This interval does not include zero, suggesting a consistent positive difference between the two measurements.

Ratio (Difference/Mean)

The mean of the ratios is 0.041, with a 95% CI from 0.034 to 0.049. This indicates that, on average, the difference between wgt0 and wgt4 is around 4.1% of their mean, pointing to a small but consistent proportional difference.

Interpretation:

• The confidence intervals for the mean difference suggest a relatively consistent and positive bias where wgt0 tends to be slightly higher than wgt4.
• The small mean ratio (0.041) and its narrow confidence interval indicate that the differences between wgt0 and wgt4 are minor relative to the magnitude of the measurements, implying a good level of agreement between the two weight measurements.

Confidence Intervals of Agreement Limits (wgt0 and wgt4)

This table summarizes the agreement limits and their confidence intervals for both absolute differences and ratios:

Agreement Limits

• Lower Limit: For the differences (wgt0 - wgt4), the lower limit is 2.406 units, and the upper limit is 13.719 units. This means that 95% of the differences between wgt0 and wgt4 are expected to fall within this range.
• Ratios: For the ratio of differences to the mean, the lower limit is 0.012 and the upper limit is 0.071. This indicates that 95% of the relative differences between wgt0 and wgt4 are expected to lie within this narrow range, reflecting a relatively high degree of agreement.

Confidence Intervals of Agreement Limits

• For the absolute differences (wgt0 - wgt4), the confidence intervals for the limits are:
  • Lower Limit CI: -0.279 to 5.091
  • Upper Limit CI: 11.034 to 16.404
  • These intervals indicate some variability in the precision of the agreement limits, especially for the lower limit.
• For the ratios ((wgt0 - wgt4)/Mean), the confidence intervals for the agreement limits show:
  • Lower Limit CI: -0.001 to 0.026
  • Upper Limit CI: 0.057 to 0.084
  • These narrow confidence intervals suggest a high level of precision in estimating the agreement limits for the ratios.

Interpretation

• The agreement limits for the differences show a narrow range, indicating that the differences between wgt0 and wgt4 are relatively small and consistent. The fact that the lower limit is positive suggests that wgt0 is generally higher than wgt4.
• The ratios' agreement limits indicate that the proportional differences between the two weight measurements are consistently small, reinforcing the notion of strong agreement.
• The narrow confidence intervals, especially for the ratios, point to a high level of precision in these estimates, suggesting reliable and consistent agreement between wgt0 and wgt4.