A Statistical Technique for Historians: Standardizing Tables of Counts
Stephen E. Fienberg · The Journal of Interdisciplinary History · 1971
A Statistical Technique for Historians: Standardizing Tables of Counts A great deal of historical data is summarized by counts of the number of individuals or objects falling into certain categories, which can be arranged in a row, in a rectangle, or in an array of higher dimensions. If, for example, one wishes to investigate the relationship between a congressman's geographic origin and his voting behavior, one might display the available data in a rectangular or two-way array similar to Table I. One may or may not wish to think of each of the classifications in a two-way table as arising from an underlying continuum or as having some underlying order. For example, age may be divided into three categories, but it clearly arises from an underlying continuum. By contrast, the categories for voting position used in Table I clearly do not correspond to a continuum and may not even have an underlying order if abstain means something other than undecided between yea and nay. In several situations, it may be desirable to summarize the relationship between the two classifications by a single number, index, or correlation-type coefficient. (This approach to measuring association or interaction is of special interest when both variables or classifications have underlying continua.) An excellent discussion of a large number of such measures of association can be found in a series of articles by Goodman and Kruskal.I For the present discussion it will be assumed that there is no definite reason to summarize the relationship between the classifications by a single index.