Measurement error

Measurement error

29 JUNE 1996 | J Martin Bland, Douglas G Altman
This is the 21st in a series of occasional notes on medical statistics. The article discusses measurement error in repeated measurements of the same quantity on the same subject. Natural variation in the subject and variation in the measurement process can lead to differences in measurements. For example, four measurements of lung function in 20 schoolchildren show variation. The true average value is what we want to know, and repeated measurements vary around this true value due to measurement error. The standard deviation of repeated measurements on the same subject measures the size of the measurement error. The within-subject standard deviation, denoted by ζw, is the common standard deviation for all subjects. To estimate ζw, several subjects with at least two measurements are needed. The within-subject variance is calculated by averaging the variances of the measurements. The analysis of variance method is preferred as it automatically handles subjects with different numbers of observations. A graphical check is recommended to ensure that the standard deviation is unrelated to the magnitude of the measurement. For two measurements per subject, the variance is half the square of their difference. The measurement error can be quoted as ζw, and the repeatability, which is 2.77ζw, represents the expected difference between two measurements for the same subject. For the data in table 1, the repeatability is 60 l/min. The article also mentions that other ways of describing the repeatability of measurements will be considered in subsequent notes.This is the 21st in a series of occasional notes on medical statistics. The article discusses measurement error in repeated measurements of the same quantity on the same subject. Natural variation in the subject and variation in the measurement process can lead to differences in measurements. For example, four measurements of lung function in 20 schoolchildren show variation. The true average value is what we want to know, and repeated measurements vary around this true value due to measurement error. The standard deviation of repeated measurements on the same subject measures the size of the measurement error. The within-subject standard deviation, denoted by ζw, is the common standard deviation for all subjects. To estimate ζw, several subjects with at least two measurements are needed. The within-subject variance is calculated by averaging the variances of the measurements. The analysis of variance method is preferred as it automatically handles subjects with different numbers of observations. A graphical check is recommended to ensure that the standard deviation is unrelated to the magnitude of the measurement. For two measurements per subject, the variance is half the square of their difference. The measurement error can be quoted as ζw, and the repeatability, which is 2.77ζw, represents the expected difference between two measurements for the same subject. For the data in table 1, the repeatability is 60 l/min. The article also mentions that other ways of describing the repeatability of measurements will be considered in subsequent notes.
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