I have just broken up for Christmas and managed to successfully complete five deadlines over the last two weeks! I’ve spent the weekend climbing and generally being outside, something that has become pretty rare over the last month! Now it’s time to do all that Christmas shopping I’ve put off until now, and send off the PhD applications I started at the beginning of term!
I thought I’d talk briefly about the ‘Scientific Inference’ assignment I handed in this Friday. ‘Scientific Inference’ is a module run by Dr Simon Vaughan on the statistical analysis procedures behind every great experiment. You will have no doubt heard the term ‘5 sigma confidence level’ associated with particle physics and in particular the Higgs Boson discovery; this is just one example of the statistical analysis behind every scientific result.
When regarding the use of statistics in Physics, the subject ultimately boils down to a simple fact: experimental measurements are not perfect, therefore we will never be able to prove a universal physical law, we can just say it fits the data we have collected. Take the force of gravity as an example; we can never be completely certain that when a ball is released from a height it will fall to the ground. Though we can say every observation we have made up to this point fits with this hypothesis or ‘model’. Mind-bending right? An example given to us by Dr Vaughan was this: a chicken is fed every morning at precisely 10am for every day of its life. It wakes up one morning and has no reason to expect anything different from this day. Except on this day the farmer kills it. As far as the chicken is concerned this is a totally random event and does not fit any existing model it has of the universe.
So maybe one day that ball you drop will fly upwards instead, or remain completely still in midair!
Statistical analysis often begins with a theoretical model with an unknown parameter. This parameter is often estimated using a statistical method called ‘Maximum Likelihood’. This method involves finding the variable that maximises the likelihood of the model as a fit for the data you collected. This can be done with relative ease using R programming. If you are thinking of coming to study here at Leicester, you will learn R during your first year. It is a very useful tool for plotting graphs and analysing data. Don’t worry if you’ve never programmed before since it is pretty easy to get the hang of!
Once you have estimated your unknown parameter there are many ways of testing how well your model fits the data. You could simply plot the data and the model on the same graph or perhaps you could find something called a p-value for your model. A p-value is a way of quantifying the significance of the relationship between your model and the data. It can be converted to a sigma level, which is where the ‘5 sigma’ expression used by CERN is from.
Statistics is a pretty complicated topic but I’ve definitely enjoyed learning about it. Plus it is one of the most vital tools a physicist has in understanding our universe!