Error analysis

Overview

A thorough, correct, and precise discussion of experimental errors is the heart of a superior lab report, and of life in general. This page will help you understand and clearly communicate the consequences of experimental error.

What is experimental error?

When you make a quantitative measurement in the lab, the goal is to measure an unknown quantity that has a true value Q. You will measure a value M that in general differs from Q by some amount. Experimental error, E, is the difference between the two, E = Q - M.

In this context, “error” is not a synonym for “mistake,” although mistakes you make during the experiment can certainly result in errors.

Error sources

Error sources are root causes of experimental errors. Some examples of error sources are: shot noise, electromagnetic interference, and miscalibrated instruments.

Error sources can be categorized as fundamental, technical, or illegitimate. (Inherent is a synonym for fundamental.) Fundamental error sources are physical phenomenon that place a strict lower limit on experimental error. The magnitude of experimental error introduced by technical error sources can at least in theory be reduced by improving the instrument or procedure — a proposition that frequently involves spending money. Illegitimate errors are mistakes made by the experimenter that affect the results. There is no excuse for those.

Pentacene molecule imaged with atomic force microscope.

Classify error sources based on the way they affect the measurement. For example, many measurements are limited by random thermal fluctuations in the sample. In principle, it is possible to reduce thermal noise by cooling the experiment. Physicists cooled the pentacene molecules shown at right to 4°C in order to image them with an atomic force microscope. But not all measurements can be undertaken at such low temperatures. Intact biological samples do not fare particularly well at 4°C. Thus, thermal noise may be considered a technical noise source in some circumstances (pentacene) and a fundamental noise source in others (most measurements of living biological samples). There is no hard and fast rule for classifying error sources. You must think each source all the way through the system: how does the underlying physical phenomenon manifest itself in the final measurement?

Accuracy and precision

Types of errors

Systematic errors affect accuracy. Random errors effect precision.

Sample bias

Quantization error

References