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Additional info for Analyzing Tabular Data: Loglinear and Logistic Models for Social Researchers
Thus, amongst the sample, a respondent's occupation does make a difference to the probability that he or she has an income below $10,000, and this shows that there is association. These two ways of viewing association are statistically equivalent. Both show the existence of association between income and occupation in these data. e is another, quicker, way of telling whether there is association in a table of two variables when each variable has only two categories. ) Multiply the top left-hand frequency and the bottom right-hand frequency, and divide the result by the product of the top right-hand and bottom left-hand frequencies.
1. We shall construct a model table which shows no interaction and then compare this table with the Banbury data. If the model and data tables are similar, we shall have developed a simpler model than the original study assumed was necessary. Moreover, we shall have shown that there is in fact no interaction in the data and that the study was wrong in arguing that occupational class and tenure have a joint effect on voting behaviour over and above their separate influences. In Chapter 4, a model of "no-association" was constructed by fixing the marginals to be the same in both data and model tables.
An observed data table was compared with another table constructed on the assumption of a specified simple model. The model was arranged to mirror the data in all respects, except that it did not include any association between the variables. This was achieved by ensuring that the model table's marginals were kept the same as those of the data table. An inferential test, the i test, was used to decide whether the model fitted the data. The magnitude of the association was measured with cP, which expressed the extent of the deviation of the observed table from the model table.