Uncertainties and errors in measurement and results

Nature of science:

Making quantitative measurements with replicates to ensure reliability—precision, accuracy, systematic, and random errors must be interpreted through replication. (3.2, 3.4)

• Qualitative data includes all non-numerical information obtained from observations not from measurement.
• Quantitative data are obtained from measurements, and are always associated with random errors/uncertainties, determined by the apparatus, and by human limitations such as reaction times.
• Propagation of random errors in data processing shows the impact of the uncertainties on the final result.
• Experimental design and procedure usually lead to systematic errors in measurement, which cause a deviation in a particular direction.
• Repeat trials and measurements will reduce random errors but not systematic errors.

Applications and skills:

• Distinction between random errors and systematic errors.
• Record uncertainties in all measurements as a range (+) to an appropriate precision.
• Discussion of ways to reduce uncertainties in an experiment.
• Propagation of uncertainties in processed data, including the use of percentage uncertainties.
• Discussion of systematic errors in all experimental work, their impact on the results and how they can be reduced.
• Estimation of whether a particular source of error is likely to have a major or minor effect on the final result.
• Calculation of percentage error when the experimental result can be compared with a theoretical or accepted result.
• Distinction between accuracy and precision in evaluating results.

• As a result of collaboration between seven international organizations, including IUPAC, the International Standards Organization (ISO) published the Guide to the Expression of Uncertainty in Measurement in 1995. This has been widely adopted in most countries and has been translated into several languages.

Theory of knowledge:

• Science has been described as a self-correcting and communal public endeavour. To what extent do these characteristics also apply to the other areas of knowledge?

Utilization:

• Crash of the Mars Climate Orbiter spacecraft.
• Original results from CERN regarding the speed of neutrinos were flawed.

Syllabus and cross-curricular links:
Option D.1—drug trials
Aims:

• Aim 6: The distinction and different roles of Class A and Class B glassware could be explored.
• Aim 8: Consider the moral obligations of scientists to communicate the full extent of their data, including experimental uncertainties. The “cold fusion” case of Fleischmann and Pons in the 1990s is an example of when this was not fulfilled.

• The number of significant figures in a result is based on the figures given in the data. When adding or subtracting, the final answer should be given to the least number of decimal places. When multiplying or dividing the final answer is given to the least number of significant figures.
• Note that the data value must be recorded to the same precision as the random error.
• SI units should be used throughout the programme.