Measurement Error

Measurement error can be described as the variability in measurements of the same quantity on the same item. These errors occur for a variety of reasons, including inadequate survey design, sampling variability, inherent biological variation, and laboratory error analysis. Measurement error is often classified into two broad categories: random error and systematic error.

Random error refers to any random influence on the measurement of a variable. Consider, for example, a person whose weight is taken at a hospital. If two different nurses see the patient, they may not record the same weight, or if the same nurse takes two measurements only minutes apart, different eye positions may cause different scale readings. There is no discernible pattern, so the measurement may be higher or lower than the true value. Therefore, the sum of all random error in a series of measurements on the same variable should, in theory, equal zero. Thus, random error does not strongly influence the average value of the measurement. This type of error is sometimes referred to as noise.

Systematic error causes measurements to be consistently higher or lower. For example, suppose that the scale used to weigh patients consistently shows readings that are five pounds heavier than the true value. This suggests that the scale should be recalibrated. Systematic errors can be minimized or completely eliminated by the use of careful planning in an experiment. This type of error is commonly referred to as bias.

The statistical models and methods for analyzing data measured with error are called measurement error models. A typical problem in statistics is to determine the linear relationship between two quantitative variables, say, X and Y, in order to use X to explain or predict Y. In this case, we assume that X cannot be observed, and a substitute variable W is used. Often, we write W = X + U, where U is the measurement error. One problem of interest is how the linear relationship between W and Y differs from the relationship between X and Y. It can be shown that the best-fitting line that relates W to Y is biased toward zero. Thus, using W as a substitute restricts one's ability to accurately assess the true linear relationship between X and Y. Various techniques have been developed to correct for such problems.

It is difficult to completely avoid measurement error; however, one can take several steps to reduce it. First, make sure that any instruments used are tested initially, monitored over time, and recalibrated as needed. Second, if possible, use only one instrument or set of instruments to do all of the measuring in an experiment. Third, use statistical methods that account for the presence of measurement error when analyzing data. Finally, take repeated measurements on the same variable.