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This paper investigates the small sample properties of minimum chi-square estimates of the parameters of stochastic brand choice models. It also describes and evaluates a statistical test which is appropriate for discriminating between two stochastic brand choice models when one is a constrained version of the other. [ABSTRACT FROM AUTHOR]

This article presents comments in response to the article "Toward an Empirical Measure of Materiality," by J. Rose, W. Beaver, S. Becker and G. Sorter. The author's comments are meant to evaluate the researchers' approach to the problem of materiality within financial statements. The author claims that the results offered by Rose, Beaver, Becker and Sorter are incomplete because only one set of experimental data is presented. However, there is a realization that this study will be expanded on over time as more complex situations present themselves for exploration.

The article presents a response to the paper "Observations on Jensen's Experimental Design for Study of Effects of Accounting Variations in Decision Making" by Thomas R. Dyckman and discusses the scale of observation in an analysis of variance (ANOV) model. Dyckman questions Jensen's research in proposing violations in the underlying assumptions of the ANOV model and whether or not these violations would appreciably affect the conclusions of his experiment. An interval scale was used during some of Jensen's data selection for discussion which Dyckman feels is incorrect in its additivity assumption.

This article presents an analysis designed to determine whether consumer cash buying or credit buying has an impact upon consumer liquid savings. The research uses data from the 1955 Survey of Consumer Finances as a basis for study. The statistical analysis considers consumer profile factors such as age, income, marital status, children, the change in liquid savings from the previous year, and the amount of purchase of durable consumer goods. George Katona's theories of consumer spending and saving's patterns are discussed.

The article examines individual risk preferences in portfolio management using a model of individual choice behavior which considers estimated payouts and the probability of a bad year for investment returns. Four hypotheses are tested that relate to wealth-holders' preference for low-risk investments with high returns and premiums that appeal to the gambling instinct. Students at the University of North Carolina and Duke University participated in the survey by selecting either risky or standard portfolio investments on a questionnaire. Research methods include payout matrixes and a geometric measure for delimiting individual risk preference.

The influence of workpiece surface temperature, as also of the cutting velocity, depth of cut and feed, on tool life and surface roughness, in hot-machining, has been investigated, using Factorial Regression Analysis, and a mathematical relationship has been obtained. The equations have been tested for goodness of fit by the Chi-Square Test. Alignment charts have been constructed to evaluate surface roughness and tool life, dependent on other parameters. [ABSTRACT FROM AUTHOR]

A novel idea for the development of statistical sampling plans is presented. The salient feature of this inspection plan is that rejection of lots cannot take place, yet the consumer is indifferent to lot quality. Simple examples are discussed. Advantages and disadvantages of this type plan are suggested. [ABSTRACT FROM AUTHOR]

If decisions of marketing managers are to be influenced by predictions based on theoretical models, it is important that the assumptions in the models be accurate. Marketeers must reformulate concepts in such models to make them empirically meaningful, as the author of this article shows. [ABSTRACT FROM AUTHOR]

The article discusses the use of sales testing to determine the effectiveness of advertising. The author notes that the main purpose of this study is to observe the changes in sales patterns resulting from changes made in advertising methods. Possible changes could include varying the copy, position, color and illustrations in print advertisements, as well as changing the type of advertising media. The author discusses the difficulties of controlling variables and obtaining the right conditions for observation in such a study.

A widespread hypothesis in advertising is that a "hierarchy of effects" follows upon an individual's perception of an advertising message and before he buys (Attention→Interest→Desire→Action). Published empirical evidence on this is examined first; then two sets of commercial research data are analyzed statistically. The emphasis is on sales as the relevant criterion; little support is found for the hypothesis. [ABSTRACT FROM AUTHOR]

The present study, based on 67 personal interviews, attempts to test whether variables cited in the literature actually do influence the span of control of chief executives in marketing. Fifteen hypotheses concerning the influence of independent variables in span of control were tested. In most cases, no statistically significant relationship was found between the independent variable and the span of control. One of the most significant relationships was between span of control and the geographic dispersion of subordinates; however, the relationship was positive, rather than negative as hypothesized in the literature. [ABSTRACT FROM AUTHOR]

This article analyzes the second-order interaction in multidimensional contingency tables in marketing research. THe author examines the introduction of chi-square analysis in marketing research as well as the use of chi-square to study three-dimensional contingency tables. The author also examines the association of the three attributes of multidimensional contingency tables. The author suggests that these complex techniques are needed to examine the more complicated relationships that exist between marketing and consumers.

The article discusses statistical testing methods of comparing advertisements and their overall effectiveness. Worthwhile measuring instruments should satisfy three basic requirements. The first is reliability. Its repeated application under essentially similar circumstances should produce essentially the same results. The second is validity. It should measure what it is supposed to measure. The third is sensitivity. A crude, and not very satisfactory general statement is that portfolio tests should produce a "statistically significant" difference in favor of the better ad most of the time when an important difference exists in the impact of two test ads.

The article focuses on the comment of author on the article by J. Scott Armstrong concerning exploratory analysis of marketing data. The author claimed that Armstrong and his colleagues indicated insufficient emphasis on the superior ability of regression analysis to measure relationship rather than cell means. According to the author, the comparisons found in the article are meaningless despite the invocation of significance testing. The author believes that in selecting a rational subset for investigation, system knowledge is essential.

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]

Monte Carlo methods were used to study the performance of the largest-root test, two trace-type tests and three determinantal tests in the fixed-effects MANOVA model when certain assumptions are violated. Results indicated that for protection against nonnormality and heterogeneity of covariance matrices, the largest-root test should be avoided, while the Pillai-Bartlett trace test may be recommended as the most robust of the MANOVA tests, with adequate power to detect true differences in a variety of situations. [ABSTRACT FROM AUTHOR]

Necessary and sufficient conditions for admissibility are given for test procedures based on a preliminary test of significance. Three types of problems are studied-testing the normal mean, fixed effects models of the analysis of variance and random effects models. Admissibility in this instance is equivalent to the intuitive and practical condition that acceptance regions of the procedures have convex sections in certain variables, while other variables are fixed, It is easy to check when the conditions hold. A discussion of optimality properties of these and other types of pooling procedures is given. [ABSTRACT FROM AUTHOR]

When data are transformed to satisfy a spherical normal linear model, the mean θ of a variate in the original scale is a function of the mean μ and variance σ² of a normal variate. We consider several approximate confidence interval methods for θ, including a new method based on exact confidence intervals for linear functions of μ and σ² Monte Carlo estimates of coverage probabilities demonstrate the suitability of the new method for applications involving a wide range of data transformations, parameter values and sample sizes. [ABSTRACT FROM AUTHOR]

Exact small sample behavior in two-way contingency tables is investigated for Pearson's chi-square statistic (X²), Light and Margolin's C statistic and its related R² measure of association, Kuliback's minimum discrimination information statistic (2&lcirc;), and Goodman and Kruskal's Lambda. R² is shown to be identical to Goodman and Kruskal's tb, leading to a test for independence based on 4. In small samples from a product of multinomials model, the null distribution of C is better approximated by a x² distribution than is the null distribution of X²; both are considerably better approximated by a x² distribution than is the null distribution of 2&lcirc;. It is proved for tables with two columns and any number of rows that if the column totals are equal, then X² ≤ 2&lcirc;; thus, X² is more conservative than 2&lcirc;. Hence, use of 2&lcirc; should be avoided in testing independence in tables with small samples. [ABSTRACT FROM AUTHOR]

This article offers a practical guide to goodness-of-fit tests using statistics based on the empirical distribution function (EDF). Five of the leading statistics are examined-those often labelled D, W², V, U², A²-and three important situations: where the hypothesized distribution F(x) is completely specified and where F(x) represents the normal or exponential distribution with one or more parameters to be estimated from the data. EDF statistics are easily calculated, and the tests require only one line of significance points for each situation. They are also shown to be competitive in terms of power. [ABSTRACT FROM AUTHOR]

The use of Patnaik's [28] chi-square approximation to the noncentral chi-square distribution and the Wilson-Hilferty [321 transformation of chi-square to approximate normality are explored as a simple, efficient means of finding k-order-statistic confidence bounds on parameters and reliability of the one- and two-parameter negative exponential distributions. An important implication of the results leads to obtaining simple closed-form approximations to percentiles of the beta distribution either with integer or noninteger parameters. The general methodology is also used to approximate confidence or prediction intervals for the time of the kth exponential failure based on r

This article presents a data analysis approach consisting of a synthesis of experimental design methods and spectral methods of time series analysis which is appropriate in exploratory situations where the re- cording process generates a long sequence of correlated observations. [ABSTRACT FROM AUTHOR]

Three statistics for testing additivity and making detailed inferences on interactions in a two-way setup are considered. The first method uses the well-known sum of squares for testing and yields Scheffe bounds for all contrasts; the second introduces a maximum characteristic root statistic and Roy bounds, but is restricted to product-type contrasts; the last is limited to tetrad differences and its statistic is the maximum of all such differences. Bounds on percentage points for this maximum are provided in the appendix. Uses of the three methods in inferring various types of interaction contrasts are discussed and illustrated. [ABSTRACT FROM AUTHOR]

Following the results of Bhat and Nagnur [2], the locally asymptotically most stringent test of the hypothesis of no preference in paired comparison experiments is derived for the models of Rao and Kupper [9] and Davidson [3]. It is shown that the asymptotic relative efficiency of these tests when compared to the test based on the likelihood ratio statistic is unity. [ABSTRACT FROM AUTHOR]

It is generally recognized that when deciding on a significance level for a test, its power must also be taken into account. Determination of the optimal significance level, however, is not a straightforward task. It is pointed out here that by use of critical significance level and power we can achieve the usual objective of making a reject-or-accept decision without explicitly determining the optimal significance level. [ABSTRACT FROM AUTHOR]

A method is given for obtaining sequential tests of composite hypotheses for a certain class of distributions. Approximate properties of the tests are derived and the method illustrated. [ABSTRACT FROM AUTHOR]

Mean square errors associated with median response estimates are compared for the normal and logistic distributions, based on both maximum likelihood and minimum chi square analyses. In broad perspective there is little difference among the mean square errors for these four estimates, regardless of sample size and stimulus level spacing. The first three of the median response estimates require an iterative numerical solution, whereas the minimum chi square analysis for the logistic distribution yields an explicit expression for the associated median response estimate. This explicit estimation expression may be particularly convenient when nonuniform spacing of stimulus levels is involved in testing. [ABSTRACT FROM AUTHOR]

In this article the problem of testing for homogeneity of k (k > 3) independent negative binomial distributed random variables with parameters r[sub i], p (for i = 1, ..., k) is studied. The alternative hypotheses which are considered are a p-mixture of negative binomial distributions and a positive trend of the p's. Several cases may be distinguished: (1)p known, (2) p unknown and r[sub 1] =...= r[sub k],(3)p unknown and r[sub 1], ..., r[sub kappa] possibly unequal. The proposed tests are based on explicit optimality criteria. [ABSTRACT FROM AUTHOR]

A test for the hypothesis of zero second-order interaction is proposed. The test is obtained by making use of conditional reference sets which are derived in Zelen [17]. This permits the derivation of an exact conditional test of significance for testing the hypothesis of zero second order interaction. The techniques used, in approximating the large sample distribution of this test, are extensions of those due to Gart [5] and Zelen [17]. The test is applied to a numerical example. [ABSTRACT FROM AUTHOR]

Hypothesis test procedures for tests of separate families of hypotheses are defined. These procedures are then compared using Monte Carlo samples as data for five pairs of invariant distributions. The comparisons are made by calculating an approximate relative efficiency for each procedure with respect to the likelihood ratio procedure, which for three pairs of distributions considered is uniformly most powerful among the class of invariant procedures, [ABSTRACT FROM AUTHOR]

The problem considered is how to compare time-to-response data for different groups when the group membership of an individual can be arbitrarily varied during a study. Modified life tables can be constructed which reflect such changes in an individual's status, and associated measures of relative risk and statistical significance calculated. This is illustrated with survival data for heart-transplant patients, for which a patient can transfer from the nontransplanted to the transplanted group. Alternative procedures are given in which distinctive groups are defined for each transplant day. [ABSTRACT FROM AUTHOR]

The asymptotic method described in an earlier article (Bowman and Shenton [2]) is applied to derive the power of the square root of b[sub 1] test of normality against skewed alternatives. In particular, normal mixtures of two components and Type A distributions, each depending on four parameters, are considered. Comparisons of the assessment of percentage points of square root of b[sub 1] using Cornish-Fisher expansions based on the normal and Monte Carlo simulations are given. [ABSTRACT FROM AUTHOR]

Cochran's Q-test, proposed to test the equality of three proportions for correlated observations, may have a larger asymptotic significance level than the nominal one, unless the admissible family of distributions is restricted to ensure that under the hypothesis the correlations between the observations are also equal. For a large class of such restricted families, optimal C[sup 2](alpha) tests of the hypothesis are obtained, and the family for which the Q-test is an optimal C[sub 2](alpha) test is identified. The use of Q for testing a related hypothesis, suggested by Madansky, is also discussed: it is shown that the Q-test is not consistent against all alternatives to Madansky's hypothesis, while the classical chi[sup 2]-test provides an optimal C[sub 4](alpha) test for it. [ABSTRACT FROM AUTHOR]

Procedures for discriminating between models from separate families of hypotheses are examined, with principal emphasis on procedures invariant under location and scale transformations. The discrimination procedures considered are compared using Monte Carlo samples as data for five pairs of invariant distributions. These comparisons are made with respect to the best invariant procedure, a procedure requiring no knowledge of sampling distributions, using approximate relative efficiencies calculated from the Monte Carlo results. On the basis of these efficiencies and the computational complexities of the procedures, suggestions are made for their use. [ABSTRACT FROM AUTHOR]

A Monte Carlo study of confidence limits for the slope of the major axis of a bivariate normal distribution confirms that, when imaginary limits are interpreted as corresponding to an infinite interval covering all possible values of the parameter, the confidence interval behaves satisfactorily under repeated sampling. The excess of the actual over the nominal significance level is negligible even if samples are small and correlation is moderate. The probability of detecting a relationship correctly is never smaller for the major axis than for ordinary regression. imaginary and exclusive confidence limits do not create problems in practice. [ABSTRACT FROM AUTHOR]

We consider the problem of drawing inferences on the difference of the population means when an incomplete sample from a bivariate normal population is available. Whereas Mehta and Gurland [7] have considered this problem from the sampling theory point of view, we tackle here the same problem from a Bayesian approach. [ABSTRACT FROM AUTHOR]

Procedures are given for testing hypotheses and obtaining confidence intervals for the reliability of systems of k independent parallel components consisting of m < k component types. Assume that there are alpha[sub I] components of the ith component type, I = 1, 2 ..... m and that p, is the failure probability of the ith component type. Then the probability of failure of the system is rho = II[sup m, sub l=1] p[sup alpha, sub l]. If m independent sequences of Bernoulli trials are conducted, one for each component type, techniques which may be employed for statistical inference concerning p are given. These techniques are suitable under those conditions for which the binomial distribution may be satisfactorily approximated by the Poisson distribution. [ABSTRACT FROM AUTHOR]

We derive an asymptotically efficient method of estimating the coefficients of systems of seemingly unrelated regression equations when a first-order vector autoregressive error specification is hypothesized. This error specification is shown to contain several commonly used specifications as special cases. A Monte Carlo experiment was performed to examine the finite sample performance of our estimator in comparison with several other estimators. The general results were that the new estimator performed relatively well. [ABSTRACT FROM AUTHOR]

A family of confidence intervals with endpoints that are simple averages of sample order statistics is defined. In this family the interval with shortest expected length is selected and compared to other confidence intervals for the same parameter. [ABSTRACT FROM AUTHOR]

Suppose that in regression problems the simultaneous confidence intervals of the S-method are used only when a preliminary F-test rejects the null hypothesis that the regression parameters are zero. (Some of Scheffe's work emphasizes this usage [12, p. 87; 13, p. 66].) The probability of coverage should then be conditioned on the rejection. That for sufficiently large critical values and at least two degrees of freedom for error the conditional probability of simultaneous coverage is always smaller than the unconditional probability is established in this article. Also included are Monte Carlo studies of the discrepancy and interpretation. [ABSTRACT FROM AUTHOR]

Analogous conditional and unconditional confidence interval procedures for the two parameter Weibull distribution are discussed. Results of an empirical study are given which suggest that, in many practical situations, the two procedures considered lead to near-equivalent results. Ramifications of the empirical results are also considered. [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]

Procedures for testing the difference of means are obtained in sampling from a bivariate normal distribution with covariance matrix Sigma when some of the observations on one of the variables are missing. A UMP test procedure is obtained when Sigma is known. When Sigma is not known, exact test procedures may be obtained by discarding partial data. To make use of all available data, approximate test procedures are proposed. These procedures are compared to the exact tests, obtained by discarding partial data, using Monte Carlo methods. [ABSTRACT FROM AUTHOR]

Theory of testing hypotheses (see [1]) derives sufficient conditions for the existence of optimum tests. These conditions often require that the class of distributions in question be ordered in some way, e.g., stochastically ordered, monotone likelihood ratio, Polya of some order, or exponential class. This article gives four simple examples which show that the sufficient ordering restrictions cannot be weakened to less stringent ordering restrictions and which thus give some insight into the structure and use of such orderings. A fifth example shows that ordering properties are not necessary for the existence of optimal tests. [ABSTRACT FROM AUTHOR]

Procedures are developed for specifying confidence intervals, from possibly censored data, for any characteristic of a two-parameter Weibull population. Although the methods are formally Bayesian, they have exact relative frequency interpretation for uncensored and Type II censored data. Some simulation results are given to indicate relative frequency behavior for Type I censoring, and for comparison to other methods. [ABSTRACT FROM AUTHOR]

Sequential search procedures are described for determining an optimal dosage in the following biomedical problem. People are subjected to a certain chemotherapeutic treatment. The optimal dosage is the maximal dose for which the proportion of patients whose toxicity level does not cross the allowable limit is gamma. We discuss Bayesian and non-Bayesian sequential procedures for searching the optimal dosage, assuming a linear regression between toxicity and dosage, and normal conditional distribution of the toxicity level at each dose, with a known variance. [ABSTRACT FROM AUTHOR]

The small sample properties of several distributed lag estimators are examined under conditions of misspecified lag structure, such as fitting a geometric estimator to a second order lag distribution. Evaluation includes analyses of the estimated average lags and the adjustment rates. Lag structure misspecification is found to yield large biases in the average lag and adjustment rate, especially compared to the biases resulting from a correctly specified but poorly designed estimator. The test statistics are found to be unreliable and often misleading indicators of lag structure misspecification. [ABSTRACT FROM AUTHOR]