Lecture 19: χ² Testing on Categorical Data

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 χ2 test.

The χ2 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 χ2 testing to student Inf1-DA exam results 2011, bigram frequency in the British National Corpus, and possible gender bias in student admissions to Berkeley in 1973.

Use of χ2 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 meta-analysis can squeeze out significant information from pre-existing 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 meta-analyses, and uses a statistical “blobbogram” demonstrating the effect.


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