This lecture gave a general overview of statistics and their role in analysing quantities of data. Most of the technical constructions — mean, median, mode, standard deviation — are probably familiar to many, but the setting for their application and the computational context may not be.
Mathematical statistics turns out to be a tool of exceptional power for distilling information from data, with computer assistance having particular impact where there are large quantities of data, or very thinly-spread information.
One recent notable example is the announcement yesterday from the BICEP2 project of evidence for gravitational waves and inflation in the very early universe, identified by traces in the twisting polarisation of the cosmic microwave background radiation. This is a significant scientific discovery, dependent on sophisticated and computation-heavy resampling analyses of a mass of observational data.
Specific items covered in this lecture were:
- Data scales: qualitative and quantitative; categorical, ordinal, interval and ratio.
- Individual statistics: mode, median, mean, variance, standard deviation. When you really should use a median, and the seductive danger of the mean.
- Sampling: estimating statistics of a large population from a small sample; mean, variance and standard deviation.
Finally, a problem: how to draw this example of self-descriptive statistics? Which frame do you begin with? Could you do it without the aid of a computer?
Two books for learning about statistics, and to refer to when applying them:
- P. Hinton. Statistics Explained: A Guide for Social Science Students. Routledge, third edition, March 2014.
- D. B. Wright and K. London. First (and Second) Steps in Statistics. SAGE Publications Ltd, second edition, 2009.
Two more for reading about statistics in the real world. Both easy to digest and recommended for interest.
- M. Blastland and A. Dilnot. The Tiger That Isn’t: Seeing Through a World of Numbers. Profile, 2008.
Link: Electronic copy available through the University Library, requires EASE login.
- D. Huff. How to Lie with Statistics. W. W. Norton, 1954; and many re-releases since.
Link: Electronic copy on the Internet Archive.
Finding Gravitational Waves at the Start of the Universe
Here are an assortment of links to the BICEP2 announcements yesterday, explanations and analyses.
- BICEP2 project home page
- Technical paper describing the results.
- Full data set. Download the numbers and crunch them yourself.
- Sky and Telescope explain what’s going on.
- Video: BICEP2 researcher goes round to tell proposer of inflationary universe the good news — thirty years after setting out the theory.