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The problem of the measurement of association between two attributes is of importance in social sciences [5]. Following Hotelling [6, 7], Lancaster [9], and Kendall [8], the canonical structure of a two-way classification is obtained. Based on the canonical correlations, three measures of association are suggested. Their metric properties are summarized. One of the measures is shown to reduce to the measure suggested by Cramer [1]. Their large sample distributions are approximated on the null hypothesis of independence between the two attributes. [ABSTRACT FROM AUTHOR]

Natural test statistics for the hypothesis that an equation is overidentified have been developed by Anderson and Rubin and by Basmann. If the disturbances are jointly normal, serially uncorrelated, and small, both the above overidentification test statistics have the Fisher variance-ratio distribution asymptotically as the variance of the error terms gets small. This gives an analytic explanation of Monte Carlo results of Basmann. The results given apply to linear models in which predetermined variables are exogenous. [ABSTRACT FROM AUTHOR]

Cochran's Q test for differences between related-sample percentages or proportions has generally been incorrectly presented in secondary sources. The most common mistake results from failure to recognize that rows containing only 1's or only O's, i.e., only successes or only failures, do not affect the value of Q. The F test, however, is affected by such rows. The probabilities from the x[sup 2] and F approximations are compared with the exact probabilities in three sets of data. A rule of thumb, based on extensive study of the distribution of Q in small samples, is given as an aid in judging when the x[sup 2] approximation is satisfactory for practical purposes. [ABSTRACT FROM AUTHOR]

A multiple-choice item is called ideal if all its alternatives are equally attractive to every person who cannot answer the item correctly without guessing. This paper discusses reasons for attempting to construct ideal items, develops methods for testing whether items are ideal or at least more nearly ideal than other items, and presents examples of both ideal and nonideal items. [ABSTRACT FROM AUTHOR]

When the hypothesis H[sub 0]: theta = theta[sub 0] is tested against the alternative H[sub alpha]: theta is not equal to theta[sub 0], theta a real-valued parameter, it would often be more appropriate to make simultaneous tests of the two hypotheses [sub 1]H[sub 0]: theta less than or equal to theta[sub 0] (with alternative [sub 1]H[sub alpha]: theta > theta[sub 0]) and [sub 2]H[sub 0]: theta is greater than or equal to theta[sub 0] (with alternative : [sub 2]H[sub 0]: theta < theta[sub 0]). The criterion of unbiasedness in choosing an optimal test of Ho is inapplicable for choosing an optimal simultaneous procedure for testing [sub 1]H[sub 0] and [sub 2]H[sub 0]. A bidirectional unbiased procedure is defined and its properties enumerated. In many important applications such a procedure for testing [sub 1]H[sub 0] and [sub 2]H[sub 0] is essentially equivalent to an "equal tails" test of H[sub 0]. [ABSTRACT FROM AUTHOR]

This paradox is the possibility of P(A|B) < P(A|B') even though P(A|B) is greater than or equal to P(A|B') both under the additional condition C and under the complement C' of that condition. Details are given on why this can happen and how extreme the inequalities can be. An example shows that Savage's sure-thing principle ("If you would definitely prefer g to f, either knowing that the event C obtained, or knowing that C did not obtain, then you definitely prefer g to f.") is not applicable to alternatives f and g that involve sequential operations. [ABSTRACT FROM AUTHOR]

The article comments on a weakened principle of conditionality. The idea that the principle of conditionality ought to be weakened to because all the data of a! experiment beyond the minimal sufficient statistic are superfluous seems to me like the plausible and frustrating idea of the geometry pupil who, since lines of construction cannot affect the truth of a theorem, concludes that they ought not be referred to in its demonstration. How common and right it is to say that sampling with, and sampling without, replacement are practically equivalent when the finite population is large compared to the sample size. Solid though seems to me, it represents an assumption and must be judged by the reader himself, as must a somewhat less familiar continuity assumption to be introduced a little later. Incidentally some seem to find the notion of a function, Ev, the value of which is the evidential meaning of the outcome x to the experiment B so disturbing as to impede further discussion. They, like me, might prefer to begin with the notion that sometimes the outcome x of experiment B cannot justifiably provoke any different statistical reaction from those provoked by x' and B'. Such a pair might be called evidentially equivalent, though just which pairs are equivalent is still under discussion.

The conditionality (ancillarity) concept is discussed with particular reference to Durbin's proposed reformulation (C') of Birnbaum's formulation (C) and Fisher's original formulations [6, 7]. It is pointed out that (C') is not in general suitable for applications in the usual sense, since it fails to eliminate all ambiguities of choice of the conditional frame of reference in which standard statistical methods may be applied. The alternative formulations of conditionality are discussed in relation to sufficiency, likelihood, and related methodological problems. [ABSTRACT FROM AUTHOR]