I am wondering if there is a reference for the Pearson's chi-squared test suitable for technically-sophisticated audience that simply presents when the test (in its various forms) is appropriate and how it is carried out (i.e., construction of the test statistic, etc.)

The reason I ask is that I am using Pearson's chi-squared tests for independence (in a simpe 2x2 contingency table) and homogeneity in a paper that describes some experimental results in physics. The tests are used to confirm the "minor" phenomena and are thus relegated to the footnotes. However, I would still like to provide a reference in case the audience wants to look up the test and confirm my claims (either on my data or their own data).

Many of the stats books that I looked at either don't discuss Pearson's chi-square, or have a very limited discussion of it (I saw relegated to a homework problem in one of the books I looked at). However, I think that "A Guide to Chi-Squared Testing" by Greenwood and Nikulin is very hard to read. Is there a better text? Perhaps a chapter or two in a good textbook? Any suggestions?


3 Answers 3


One possible reference might be to section 2.4 of Alan Agresti's "An Introduction to Categorical Data Analysis"[1]. It might be worth checking if that has enough of what you need.

[1]: Agresti, A. (2007),
An Introduction to Categorical Data Analysis,
John Wiley & Sons Hoboken, NJ


What about simply going to the roots:

Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine Series, 5, 50 (302): 157–175.

  • 1
    $\begingroup$ Two problems with this suggestion: (i) Pearson doesn't get everything right; (ii) neither Fisherian nor Neyman Pearson hypothesis testing frameworks exist -- you can see some hints of the ideas, but the full structure isn't there. If a single reference is desired, I don't think this would do. (As part of a collection of references, there would be an argument to include it.) $\endgroup$
    – Glen_b
    Dec 19, 2014 at 15:37
  • $\begingroup$ I have considered Pearson's original paper, but decided against it based on item (ii) in @Glen_b's comment. The dearth of references to the literature describing a chi-squared test is rather surprising that, considering that there is a myriad of chi-squared testing tutorials on the web. I am not a statistician, but is it something considered "common knowledge" in the stats community? (like you don't reference calculus books when claiming that the first derivative of location is the velocity) $\endgroup$
    – M.B.M.
    Dec 19, 2014 at 17:08
  • $\begingroup$ MBM -- IMO, basically that's it - much of the development is relatively simple, well within the capability of a reasonably able undergrad. In many places, you'd typically learn enough about the test to be able to perform them in a first statistics course (at least ones of a general nature - though you might not tackle the theory the first time you see the test). I'd at least expect that for the chi-square goodness of fit test, a reasonably able stats student would be able to show the derivation of the asymptotic chi-square approximation in second year (though there's variation across programs) $\endgroup$
    – Glen_b
    Dec 19, 2014 at 23:29
  • $\begingroup$ ... But there are some more or less classic texts one might refer to. Give it another day or two. I have some suggestions myself, but I don't want to hog all the easy questions. Give me a nudge and I'll mention some if you don't get an answer. $\endgroup$
    – Glen_b
    Dec 19, 2014 at 23:31
  • $\begingroup$ (One might at least mention chapter 4 of Fisher's Statistical Methods for Research Workers, 1925, for a reasonably early reference, but I think there are perhaps better suggestions) $\endgroup$
    – Glen_b
    Dec 19, 2014 at 23:38

Ludbrook clarifies the evolution of analysis of 2x2 tables including the problems and improvements; see Int. J. Epidemiol. (2008) 37 (6): 1430-1435. doi: 10.1093/ije/dyn162 found at http://ije.oxfordjournals.org/content/37/6/1430.short

Citing is open to your intent, so be careful. Choose an original publication to honor precedence - the first mention in print (1900), or how the testing is viewed today in a more professionally acceptable form. These are not the same and you should be clear in what you write which is being cited.


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