Measurement error

Topic of Studies, data, and evidence, part of Data analysis · Also in Introduction to generalised linear models

Measurement error

Type	Topic
Taught in	Studies, data, and evidence · Introduction to generalised linear models
Part	Data analysis · Generalised linear models

Variation in recorded values that comes from the measuring process rather than from the units measured. It adds to the residual variability a model cannot explain, and in an explanatory variable it biases a fitted slope toward zero.

In Studies, data, and evidence

From Studies, data, and evidence

Measurements vary for more than one reason. Most of the variation in heights is natural diversity between people, from genetics, diet and environment. Some is measurement error. Later models try to explain part of the variation by other variables, such as sex or shoe size. What no variable in the model explains is the residual variability, and a good model leaves little of it while still predicting new data well. One or more measurements are taken on each experimental unit: a person, a plant, a plot of land, a household, a star or a manufactured object.

In Introduction to generalised linear models

From Introduction to generalised linear models

The normal model is used for three good reasons, and then it is used too often. Some measurements really are normal: measurement error is the usual example. Even when the individual responses are skewed, a group average is approximately normal for a large enough group, by the central limit theorem, and sometimes the data we receive are already averages. And a great deal of exact theory has been built for the normal, so people reach for it because they know what the inference will look like. That last reason is also why it is overused. A five-point or seven-point agreement scale is an ordered category. Averaging “strongly disagree” through “strongly agree” and calling the result normal pretends that the gaps between categories are equal numbers. A grade of 7 is not a number of which a grade of 1 is one seventh. Treat the labels as an ordered categorical response, not as a normal measurement.¹

Used in

• Taught in Studies, data, and evidence · Introduction to generalised linear models
• Also used in Introduction to generalised linear models
• All 6 questions on Studies, data, and evidence

See also

Explanatory variable · Regression slope · Observational study · Designed experiment · Randomised controlled trial · Confounding variable · Blinding and placebo · Simple random sample

Glossary and index

Footnotes

1. The same habit shows up in grade-point averages. The point of the example is the scale.