Uncertainties and errors

Nature of science:

Uncertainties: “All scientific knowledge is uncertain… if you have made up your mind already, you might not solve it. When the scientist tells you he does not know the answer, he is an ignorant man. When he tells you he has a hunch about how it is going to work, he is uncertain about it. When he is pretty sure of how it is going to work, and he tells you, ‘This is the way it’s going to work, I’ll bet,’ he still is in some doubt. And it is of paramount importance, in order to make progress, that we recognize this ignorance and this doubt. Because we have the doubt, we then propose looking in new directions for new ideas.” (3.4) Feynman, Richard P. 1998. The Meaning of It All: Thoughts of a Citizen-Scientist. Reading, Massachusetts, USA. Perseus. P 13.

1. Random and systematic errors
2. Absolute, fractional and percentage uncertainties
3. Error bars
4. Uncertainty of gradient and intercepts

Applications and skills:

• Explaining how random and systematic errors can be identified and reduced
• Collecting data that include absolute and/or fractional uncertainties and stating these as an uncertainty range (expressed as: best estimate ± uncertainty range)
• Propagating uncertainties through calculations involving addition, subtraction, multiplication, division and raising to a power
• Determining the uncertainty in gradients and intercepts

• “One aim of the physical sciences has been to give an exact picture of the material world. One achievement of physics in the twentieth century has been to prove that this aim is unattainable.” – Jacob Bronowski. Can scientists ever be truly certain of their discoveries?

Utilization:

• Students studying more than one group 4 subject will be able to use these skills across all subjects

• Analysis of uncertainties will not be expected for trigonometric or logarithmic functions in examinations
• Further guidance on how uncertainties, error bars and lines of best fit are used in examinations can be found in the Teacher support material

Data booklet reference:

• Aim 4: it is important that students see scientific errors and uncertainties not only as the range of possible answers but as an integral part of the scientific process
• Aim 9: the process of using uncertainties in classical physics can be compared to the view of uncertainties in modern (and particularly quantum) physics