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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]

Departures from statistical independence are conjoined with an assessment of predictive accuracy' in a coefficient of association for nominal-level 2 x 2 contingency tables which is both interpretable as a PRE measure and consistent with research hypotheses of manifold forms. Measurement assumptions and operating characteristics o[ the measure are delineated; definitional and computational formulate are derived from classical probability theory; comparisons with other relevant statistics are made' and The test of significance is shown to be the traditional chi-square test. [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.

The article focuses on the task of a psychologist to discover the rules or laws governing mental activity. It examines three experiments in which a set of targets, equiprobable to the experimenter, are treated by the subjects as non-equiprobable. In one of the experiments, for the experimenter, the elements constitute a uniform display. The same feature characterized a further preliminary experiment. A subject is told that to each square has been assigned a number, and this number is recorded on a ticket in an urn. Three tickets will be successively drawn at random from the urn, with replacement after each draw. Before each draw, the subject indicates the square, which he thinks will be located by the ticket drawn. A Chi-square test shows that the first and third choices depart significantly from a uniform distribution, but not the second choice. The responses constitute a way of patterning the display, this patterning presumably being shaped by experience. The variation of pattern as between the three experiments suggests that the pattern or structure imposed is sensitive to the display and to the task.

This article presents information regarding parole prediction variables and the time factor in violations by burglars. Parole prediction studies have shown that it is possible to determine, before an inmate is released from prison under parole supervision, what are his relative chances for making a successful extramural adjustment. The original data were set up in 23 contingency tables with the number of months before violation as the independent variable in each case and one of the 23 parole prediction factors as the dependent variable. The Chi-square test was undertaken to test the probability that differences between the actual and the theoretical frequencies would occur by chance. In these instances where the probability that the differences were due to chance was very small the coefficient of mean square contingency was determined in order to measure the amount of the relationship that exists between the variables. Whether the relationship is a positive or a negative, one was determined by inspection of the data and the signs of the differences.

The implications of replacing the assumption of normal distribution of the parameters (A, b, c) by chi-square and other related nonnegative distributions are discussed here in the framework of chance-constrained linear programming. [ABSTRACT FROM AUTHOR]

A "blowup factor" is defined for the measurement of the effect on forecast error variance of two types of misspecification which may be implicit in the choice of a particular adaptive forecasting scheme: (1) misspecification of the number of non-zero parameters of the stationary linear stochastic process generating the observed time series, and (2) misspecification arising from postulating stationarity when in fact the generating process is non-stationary in mean. [ABSTRACT FROM AUTHOR]

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]

Periodically, the uses and misuses of probability statistics in social and behavioral science research have been reviewed. The frequently used chi-square test, and the interpretations given to data analyzed by this statistic will serve to illustrate the problem. To avoid these errors of confusing significance with strength of association and of misinterpretating form of relationship, two elementary safeguards can be exercised in reporting results. One is routinely to compute and report a measure of degree of association in addition to the statistical test whenever this is possible. The second safeguard is the introduction of care and caution in the verbal interpretation of data tables and the inferred association of variables.

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.