Measurement error is the difference between a value we measure and the true value we are trying to measure. Measurement error happens because measurements are rarely perfectly exact.
A scale gives slightly different weights each time
A student guesses on a survey question
A stopwatch is started a little too late
A person accidentally types the wrong value into a dataset
In each case, the recorded value may not perfectly match reality.
Measurement error can come from many sources, including:
Imperfect measuring tools
Human mistakes
Unclear survey questions
Rounding or recording errors
Natural variation in repeated measurements
Suppose a person’s true height is 68 inches, but a measurement is recorded as 67 inches.
Measurement Error = 67 - 68 = -1
The measurement is off by 1 inch.
Measurement error is important to consider because models depend on data. If measurements are inaccurate, predictions and conclusions may also become less accurate.
Measurement error can:
Increase unexplained variation
Make relationships harder to detect
Reduce the accuracy of models
Lead to misleading conclusions
For example:
A shaky scale may create random error
A broken scale that always adds 5 pounds creates systematic error
Models try to explain variation in data, but some variation may come from measurement error rather than meaningful patterns.
This means:
Not all variation can be explained
Even good models usually have some error remaining
Researchers try to reduce measurement error by:
Using reliable instruments
Standardizing procedures
Training observers carefully
Repeating measurements
Cleaning and checking data