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In this article we propose two minimum chi-square estimators for a bivariate probit model. We call one estimator the Full Information and the other Limited Information Minimum Chi-Square because the first takes account of all the a priori information while the second does not. Both estimators are shown to be consistent. Moreover, the first is shown to be asymptotically as efficient as the maximum likelihood estimator and yet is computationally much simpler. For illustration, estimates are computed for the data used by Ashford and Sowden [1970.] [ABSTRACT FROM AUTHOR]

The asymptotic non-null distribution is obtained for the modified form of the Pearson chi-square statistic studied by Dahiya and Gurland [3]. By utilizing this result the power is obtained for specific alternative distributions in testing for normality, This enables recommendations to be made as to the number of class intervals to be employed in applying the aforementioned modification of the Pearson chi-square test of normality. [ABSTRACT FROM AUTHOR]

This article shows that information partitioning in contingency tables is a very general property of exponential families, One partitioning scheme occurs when the hypotheses of interest are stated as linear expressions in the natural parameters, A second partitioning scheme is possible when the hypotheses are stated as linear in the parameter which is the expectation of the statistic in the exponent. [ABSTRACT FROM AUTHOR]

A step-by-step method is presented herein far partitioning a certain kind of hypothesis H about the m-way contingency table into (a) a series of hypotheses about marginal tables formed from the m-way table by ignoring one or more of table's m dimensions; and (b) a hypothesis about independence, conditional independence, or conditional equiprobability in the m-way table. This step-by-step method facilitates both the testing of H and the calculation of F, the estimated expected frequencies in the m-way table under FI. The method introduced herein for calculating F is easier to apply than the usual iterative-scaling method in many cases. [ABSTRACT FROM AUTHOR]

The article focuses on an inequality for a class of bivariate chi-square distributions. A recurrent problem in simultaneous inference is discussed in the article. While the joint distributions of test statistics may be known in form, these frequently depend on parameters, values of which are unknown. In such cases it is not possible to give simultaneous procedures, which hold exactly with specified probability; instead, it is expedient to give approximate procedures for which useful probability bounds can be established. Considerable effort has been expended in this direction, particularly in connection with simultaneous inference regarding means. The study is concerned with the construction of two-sided simultaneous confidence limits for variances in the bivariate case. In the p-variate normal case, researcher C.G. Khatri has given a lower bound to the simultaneous confidence coefficient associated with one-sided lower confidence limits and with additional assumptions regarding the covariance matrix, Khatri has similarly bounded the simultaneous confidence coefficient in the case of one-sided upper limits; however, two-sided limits was not examined.

If the parameters are estmated independently of the sample, the chi-square test statistic for a goodness of fit test has a limiting distribution that is stochastically larger than that of the test of fit for a completely specified distribution. Thus, if the critical values for the test of fit for a completely specified distribution are incorrectly used, the probability that we will reject the null hypothesis when it is true is greater than the desired level of significance. [ABSTRACT FROM AUTHOR]

Offers a nomogram or an alignment chart for chi square. Probability values given by the nomogram; Applications of the nomogram. [ABSTRACT FROM AUTHOR]

The article focuses on comments given by the author on topics related to 2 X 2 contingency tables. In the article two ideas are proposed. The first is that the Yates continuity correction should not be used in 2 X 2 contingency tables unless row and column totals are nonrandom. The second idea is that if row totals, or column totals, are not fixed in advance of the experiment, the Yates correction should not be used for two reasons. First, it provides poor estimates of the desired probabilities. Second, it sometimes exchanges points inside the critical region for points outside the critical region, thus providing a different test. Statistician Olli S. Miettinen points out that much of the controversy over use of a continuity correction is due to a lack of distinguishing between two distinct situations. The first situation involves estimating the exceedance probability associated with a known possible value of a discrete random variable. The second situation involves estimating the exceedance probability associated with an arbitrary real number, such as a quantile from the chi-square' distribution.