Measurement Error

TL;DR

Measurement error is the difference between a true value and the value produced by a measurement process.
It arises from instrument limitations, the skill of the person measuring, and the conditions of measurement.
Measurement error affects accuracy and precision, can introduce bias, and is reduced by proper instruments, correct procedures, and repeated measurements.

Definition

Measurement error is the difference between the true value of a quantity and the value obtained from a measurement. It is an inherent part of the measurement process and can arise from various sources, including the limitations of the measuring instrument, the skill of the person taking the measurement, and the conditions under which the measurement is taken.

Explanation

Measurement error results when the measured value deviates from the true value because of factors intrinsic to the measurement process. Common sources are imperfect instruments, incorrect use or reading by the measurer, and varying environmental or situational conditions during measurement. Measurement error influences both:

Inaccuracy (the difference between the measured value and the true value) and
Precision (the repeatability of the measurement).

A systematic measurement error that consistently pushes results in one direction introduces bias, producing consistent overestimation or underestimation of the true value.

Examples

Ruler measurement

Using a ruler to measure an object’s length can produce measurement error if the ruler’s markings are not perfectly spaced, if the ruler is not aligned correctly, or if the reader misreads the markings. These factors can cause the measured value to differ from the object’s true length.

Thermometer measurement

Using a thermometer to measure body temperature can produce measurement error if the thermometer has a limited accurate range, if it is not placed correctly (in the mouth, under the arm, or in the ear), or because body temperature varies with time of day and activity level. These factors can cause the measured value to differ from the true body temperature.

Systematic reading error (mm vs cm)

If a person consistently measures length with a ruler marked in millimeters but interprets the markings as centimeters, the measured values will be consistently too high, introducing bias that systematically overestimates the true length.

Notes or pitfalls

Measurement error is inherent to measurements and cannot be entirely eliminated.
Bias is a systematic error that leads to consistent over- or underestimation of the true value.
Random error affects precision; taking multiple measurements and averaging can reduce the effect of random error.
To reduce measurement error: use appropriate instruments, follow proper procedures (align rulers, place thermometers correctly, wait for stable readings), and take multiple measurements.

Accuracy / Inaccuracy
Precision
Bias
Random error