THE USE OF CHI-SQUARE IN SMALL SAMPLES.

Empirical studies by sociologists rely frequently upon Chi-Square analysis to indicate existence and nature of association between variables. A cursory glance through the 50 issues of the 1949 issues of the "The American Journal of Sociology" and the journal "American Sociological Review," discloses at least half a dozen reports utilizing this tool. As an analytical tool, Chi-Square has much to recommend it. It is readily understood, is easily calculated, conveniently summarizes many categories of data simultaneously and is not so high powered as to outreach the refinement of most of the data to which it is applied. Certain difficulties are encountered, however, in determining independence. When each of the expected cell frequencies exceeds ten this test gives quite acceptable results. But if one or more of the expected cell frequencies is less than ten, the Chi-Square test tends to underestimate the small probabilities with the result that many hypotheses of independence are rejected, and relationship assumed, at a particular level which would not have been so if the true probability had been known.