This lecture covered more on hypothesis testing, with a brief review of the apparent correlation between exercise and lack of sleep in the survey data from earlier this term, and working through three examples of the χ^{2} test.
The χ^{2} test is a tool for assessing potential correlations in categorical data, where it is not possible to apply the correlation coefficient measures used on quantitative data. The three examples presented today applied χ^{2} testing to student Inf1DA exam results 2011, bigram frequency in the British National Corpus, and possible gender bias in student admissions to Berkeley in 1973.
Use of χ^{2} follows the standard pattern for statistical tests: we have a null hypothesis that there is no correlation between different possible categories of data, and the test estimates the probability p that if this were true then we would observe data similar to that actually seen. If p is very low, we reject the null hypothesis and may conclude that there is a correlation.
Of course, as usual, correlation does not imply causation, but a correlation may lead us to investigate possible mechanisms of causation, which might in turn give rise to predictions that can be repeatedly tested.
I also gave an outline of an example where appropriate statistical metaanalysis can squeeze out significant information from preexisting datasets: specifically the results of Lau et al. on heart attack treatments where they discovered that strong evidence for certain treatment had been already present in the data fifteen years before the results of individual large trials brought the treatment into common use. The Cochrane Collaboration now routinely carries out large and influential medical metaanalyses, and uses a statistical “blobbogram” demonstrating the effect.
References

Ben Goldacre. Bad Pharma: How Medicine is Broken, and How We Can Fix It. Fourth Estate, 2013.
Links: Bad Pharma at Blackwell’s; Bad Science blog; Ben Goldacre; All Trials campaign

Lau et al. Cumulative MetaAnalysis of Therapeutic Trials for Myocardial Infarction. New England Journal of Medicine 327:248–254, July 1992.
DOI: 10.1056/NEJM199207233270406Link: Full text via EASE login

The Cochrane Collaboration and the story behind their blobbogram logo.

P. J. Bickel, E. A. Hammel, and J. W. O’Connell. Sex bias in graduate admissions: Data from Berkeley. Science, 187(4175):398–404, 1975. DOI: 10.1126/science.187.4175.398.
This closely analyses the admissions data to conclude that it does point at serious issues of discrimination, although not quite in the places first indicated.
The bias in the aggregated data stems not from any pattern of discrimination on the part of admissions committees, which seem quite fair on the whole, but apparently from prior screening at earlier levels of the educational system. Women are shunted by their socialization and education toward fields of graduate study that are generally more crowded, less productive of completed degrees, and less well funded, and that frequently offer poorer professional employment prospects.
Link: Full text via EASE login
 Wikipedia page on Simpson’s Paradox, of which the Berkeley admissions is a wellknown example.