By Maria Kateri

Contingency tables come up in various fields, together with lifestyles sciences, schooling, social and political sciences, significantly industry learn and opinion surveys. Their research performs an important position in gaining perception into buildings of the amounts into consideration and in aiding choice making.

Combining either idea and purposes, this ebook offers versions and strategies for the research of 2- and multidimensional-contingency tables. the writer makes use of a threefold strategy, offering basic versions and similar inference, highlighting their interpretational facets, and demonstrating their functional usefulness. Emphasis is on purposes and strategies of becoming versions utilizing general statistical instruments - reminiscent of SPSS, R, and insects - and on interpretation of the consequences.

An first-class reference for complicated undergraduates, graduate scholars, and practitioners in facts in addition to biosciences, social sciences, schooling, and economics, the paintings can also be used as a textbook for a direction on express facts research. necessities comprise easy historical past on statistical inference and information of statistical software program packages.

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The marginal invariance of θ can easily be verified as follows. When multiplying row i (i = 1, 2) and/or column j ( j = 1, 2) of the table by a fixed positive number αi and/or β j , respectively, the cell probabilities for the derived table are πi∗j = ratio. Then, it holds αi β j πi j , i, ∑i, j αi β j πi j θ∗ = j = 1, 2, and θ ∗ is the corresponding odds ∗ π∗ π11 π11 π22 22 = =θ . 13) The sample odds ratio is p11 p22 n11 n22 θˆ (n) = = . 11) is more convenient for meaningful interpretation. 14), respectively, while it is undefined when sampling zeros occur in both cells of a row or column.

For a more detailed overview on categorical data analysis, see in Kateri (2008). Overall, the classical reference book of the 1970s on categorical data analysis is that of Bishop et al. (1975). Other fundamental books of the same period are those of Plackett (1974), Upton (1978), Fienberg (first published in 1977; reprint of its revised 2nd edition in 2007), and Haberman (1979). A classical book adjusted to models and applications for social sciences is by Andersen (1980). In our days, the most comprehensive book on categorical data analysis is that of Agresti, in its recent revised 3rd edition (Agresti 2013) and its introductory counterpart (Agresti 2007).

1 Possible Sampling Schemes Let X and Y be two categorical variables of I ≥ 2 and J ≥ 2 levels, respectively, that are cross-classified in a I × J contingency table and ni j be the observed frequency for cell (i, j), i = 1 . . , I, j = 1, . . , J. The table will be of the following form. n11 n21 · ni1 · nI1 n+1 n12 n22 · ni2 · nI2 n+2 ··· ··· ··· ··· ··· ··· ··· n1 j n2 j · ni j · nI j n+ j ··· ··· ··· ··· ··· ··· ··· n1J n2J · niJ · nIJ n+J n1+ n2+ ni+ nI+ n Regarding the sample size and according to the study design, there are three options: (a) the total sample size n is fixed, (b) one set of marginals is fixed, without 34 2 Analysis of Two-way Tables loss of generality assume the row marginals (n1+ , n2+ , .

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