Measures of association - download pdf or read online


By Albert M. Liebetrau

In actual fact experiences the homes of vital modern measures of organization and correlation. Liebetrau devotes complete chapters to measures for nominal, ordinal, and non-stop (interval) info, paying exact recognition to the sampling distributions had to ensure degrees of value and self belief periods. precious discussions additionally concentrate on the relationships among a number of measures, the sampling homes in their estimators and the comparative benefits and downsides of alternative ways.

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Cohen's k and Weighted k Let pij denote the probability that an item is classified into category i by one judge and category j by another, where i and j range from 1 to I, inclusive. Then represents the proportion of cases on which the judges agree. If the judges work independently, the proportion of times they agree purely by chance is so q1q2 is a measure of agreement corrected for chance. To make this measure independent of the marginal totals, it is normalized by 1 q2, the maximum possible value of q1q2 for the given sets of marginal totals and The resulting measure, was proposed by Cohen (1960) as a measure of agreement, corrected for chance, between the classifications of a group of objects by two judges.

41 is well defined if at least two cells of the table contain nonzero probabilities. Page 33 The maximum likelihood estimator of k under the multinomial sampling model is When pij is replaced by = nij / n, statements about the range of k apply also to . For n sufficiently large, is approximately a normal variable with mean k. 43 are obtained as usual by substituting = nij / n for pij. 42 can be used to establish confidence intervals for k. The calculations of and its variance are illustrated in the next example.

The measure t is well defined if at least two cells, not both in the same row or column of the table, contain nonzero probabilities. The value of t lies between the values of tA|B and tB|A; consequently 0 £t£ 1. If the table has exactly one nonzero probability in each row and column, then t = 1, while t = 0 when A and B are independent. Under the multinomial sampling model, tA|B, tB|A, and t have maximum likelihood estimators Page 27 and respectively. 29, respectively. If any one of the measures is either 0 or 1, the corresponding estimator has the same value.

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