Library / Some Difficulties of Interpretation Encountered in the Application of the Chi-Square Test

Reference

Joseph Berkson “Some Difficulties of Interpretation Encountered in the Application of the Chi-Square Test” (1938) // Journal of the American Statistical Association. Publisher: JSTOR. Vol. 33. No 203. Pp. 526. DOI: 10.2307/2279690

Bib

@Article{berkson1938,
  title = {Some Difficulties of Interpretation Encountered in the Application of the Chi-Square Test},
  volume = {33},
  issn = {0162-1459},
  url = {http://dx.doi.org/10.2307/2279690},
  doi = {10.2307/2279690},
  number = {203},
  journal = {Journal of the American Statistical Association},
  publisher = {JSTOR},
  author = {Berkson, Joseph},
  year = {1938},
  month = {sep},
  pages = {526}
}

Quotes (3)

No Black and White Balls

I have a considerable interest in mathematical statistics, but very little competency in it. You will not hear anything about cards or black and white balls from me. I shall speak as a practitioner who has frequently applied the test to real observations, made seriously for the solution of concrete scientific problems.

Any Series of Real Observations Does Not Actually Follow a Normal Curve

For we may assume that it is practically certain that any series of real observations does not actually follow a normal curve with absolute exactitude in all respects, and no matter how small the discrepancy between the normal curve and the true curve of observations, the chi-square P will be small if the sample has a sufficientlylarge numberof observationsin it.

P-Value Beyond Any Usual Limit of Significance

I believe that an observant statistician who has had any considerable experience with applying the chi-square test repeatedly will agree with my statement that, as a matterof observation, when the numbersin the data are quite large, the P’s tend to come out small. Having observed this, and on reflection, I make the following dogmatic statement, referring for illustration to the normal curve: “If the normal curve is fitted to a body of data representingany real observations whatever of quantitiesin the physical world, hen if the number of observationsis extremely large - for instance, on the order of 200,000-the chi-square P will be small beyond any usual limit of significance.”

Backlinks (1)

1. Testing the Approximate Validity of Statistical Hypotheses (1954) by J. L. Hodges et al. 2 2