# Chi Squared, regression and causation

Tuesday 14 April 2015

## Both tests on the same data?

This is a quick blog post about a couple of discussions I have had recently about students using both Linear regression and independence tests with the *same* data! I wrote this in a correspondence recently and thought it worth sharing. Comments welcomed!

^{2}if one or both of the variables are categorical. Clearly correlation does not imply causation, but a chi² test does not imply causation either. The two tests both look for a relationship between 2 variables. If both variables are numerical then a scatter is appropriate, if either or both are categorical then chi² is appropriate. Clearly a chi² test can be done with 2 numerical variables by categorising and it would not be wrong but I can't see a need for it? The outcome of the chi² test would be entirely dependent on the chosen class intervals used to create the categories which could maybe be adjusted to suit an outcome.

HOWEVER - this does not mean students cant use both.... eg a project might be investigating literacy rates and involve a scatter graph of literacy against GDP, and then a chi² to see if literacy rate is dependent on continent for example. This is great. In this case the student has used both tests to investigate a theme involving literacy rates but not on exactly the same data.

I summary, my advice is that students avoid doing both tests on the same data, but there is no official line that it cant be done. If you want to give students full marks then I would advise noting to the moderator where you see the difference. Otherwise I think the relevance can be questioned.'

......... to be continued

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