This page will support you in satisfying Writing Learning Outcome: 
ANALYSIS - Analyze lab data by quantifying error.

Learning Objectives

You should be able to

What is Error?

Error is a difference between an expected value and a measured value and is categorized as either systematic (meaning it is repeatable) or random (not following a pattern). From the perspective of the statistics we have discussed previously (see Figure 1), a difference between a mean and expected value is a systematic error. The standard deviation is a measure of the random error. 

Systematic errors can be attributed to problems in calibration or test configuration that can often be addressed or explained. They can also be the result of a bias introduced in a published value to ensure safety, as when the design strength of a material is specified at the low end of the distribution of tested strengths. 

Random errors are often associated with the precision of instruments or operators (humans!) used in measurement and can be addressed only by improving the precision of equipment and standardization of procedures.

Figure 1. Depictions of accuracy and precision and relationships to statistical measures of mean and standard deviation. 

Why Does the Technical Audience Value Error Analysis?

Quantifying the error in reported values provides an indication of the precision of the result. This is conveyed commonly by correctly reporting significant figures. For example, a value of 5.3 mm indicates a precision of ± 0.1 mm (± 2%). However, a rigorous error analysis might show that the uncertainty is actually ± 0.7 mm (± 13%), which significantly impacts the confidence the audience might have in the result. If an error analysis is not provided, the audience will likely take the results at face value, or worse, question the work for lack of rigor.

How is an Error Analysis Performed?

An error analysis can be conducted on either univariate or bivariate data. For univariate data, the analysis is simple:

For bivariate data, the analysis is similar, but rather than comparing to a single expected value, you are comparing data to expected values estimated by a trendline.

This is all better explained with an example:

Error Analysis Example

What Expectations Does the Technical Audience Have for an Error Analysis?

Common Mistakes