# VCE Physics/Appendices/Appendix B : Analysis of experimental data

The Study Design provides limited advice in relation to the analysis of experimental data. There is supplementary material that provides more detailed information. It includes, for example, a section on Measurement in Science. However, there are some issues with both the VCAA approach as indicated by this supplementary material, and past exam questions. This section seeks to outline a consistent, coherent and pedagogically motivated approach to measurement in physics / analysis of experimental data, and it will point out where this differs from the VCAA approach. As experimental investigations are School based and school assessed, the suggested variations from the VCAA advice are generally not a problem. However, as there are also examination questions related to experimental analysis, advice will also be provided in relation to those questions.

## Contents

## Validity and Reliability[edit]

The Study Design uses the terms "validity" and "reliability". However, these terms are NOT commonly / widely used in relation to physics, except in a casual sense. Neither do they have specific definitions in relation to physics. They are terms that originate from statistics and while we use statistical analusis in relation to measurmeents in physics, the terms "validity" and "reliability" are more commonly used in the social and / or biological sciences. In physics, in terms of well defined concepts (just as terms such as "energy" and "work" are defined) you should be using the terms "precision" and "accuracy". Approximately, "precision" = "reliability" and "accuracy" = "validity". This equivalance can only be approximate because "validity" and "reliability" do not have such well-defined, internationally agreed meanings. The terms "precision" and "accuracy" (and the associated terms "uncertainty" and "error") will be explained in this appendix at a level suitable for VCE physics - as well as including some comments, and references, for teachers (or interested students) to provide a deeper understanding.

## Precision (and Uncertainty)[edit]

**"Precision" and "accuracy" are two different concepts. Do not use the terms interchangeably.** If you are discussing "precision", the related numerical quantity is "uncertainty".
Precision is a relative term similar to the term "tall". You might say that someone who is 6ft in height is tall. If they are in a room with others who are all over 6ft, you might change your mind!
Say you make a measurement that has an uncertainty of 1%, you might ask "Is this a precise measurement?"... the answer is "It depends". If the quantity you are measuring has only previously been measured with a 5% uncertainty then you might call your measurement precise. If in later years, the quantity you are measuring is commonly measured with an uncertainty of 0.1% then your measurement still might be considered precise for when it was done, but relative to current measruments, it might not be considered precise.
Explain what uncertainty is, why it is important and how it is "used", in reference to some concrete examples. Explain +/- notation. Wny it is recommended you take R / sqrt(n) as a measure of uncertainty (the number after the +/-). Ways to propagate uncertainties in calculations.

## Accuracy (and Error)[edit]

**"Accuracy" and "precision" are two different concepts. Do not use the terms interchangeably.** If you are discussion "accuracy", the related numerical quantity is "error".
Accuracy is a relative term, similar to precision - see the initial discussion under the heading "Precision and Uncertainty".
Do not use "human error"!

## Graphing[edit]

Advice for graphing, including

- Dependent and independent variables.
- Proportionality and linear data.
- The importance of the intercept and any uncertainty in the intercept.
- Drawing a line of best fit (linear case)... and "linearising" non-linear data.
- Displaying uncertainties (error bars - unfortunate name!).
- Determining the gradient of a line of best fit and the related uncertainty in that gradient.

## References[edit]

The standard reference for information relating to the analysis of measurement data, as with the conventions around units of measurement (SI Units), comes from the BIPM. See the introduction to the Appendices for why you should consider the BIPM as the root source for this information. In relation to the analysis of measurement data the most relevant BIPM documents are the Guide to Uncertinaty in Measurement (GUM) and the International Vocabulary of Metrology (VIM).