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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 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.

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]

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.

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.

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]

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]

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]

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]

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

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]

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]

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 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]

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]

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]

Develops tests of significance for coefficients in a single equation of a simultaneous system. Approaches to the development of a simultaneous equation econometric model; Derivation of the likelihood ratio test; Distribution of the likelihood ratio statistic.

Compares the power functions of the conventional tests of significance based on an asymptotic theory with alternative tests suggested in several studies. Description of the tests of significance considered in the study; Design of Monte Carlo experiments conducted; Conclusions.

This article presents an analysis of variance techniques for unbalanced data. Some of the more important issues encountered in the analysis of unbalanced data is examined here within a single framework. These issues are broadly defined as solutions to the normal equations for linear models where the incidence or design matrix is not of full column rank, estimable functions of the parameters and tests of hypotheses, and reductions in sums of squares and interpretation of results.

If the research goal in applying classical discriminant analysis techniques is to test for differences in the general characteristics of groups, then standard tests from multivariate analysis of variance are appropriate. Statistically significant differences among group means and dispersions indicate that the groups arose from separate populations. If, however, the goal is to explore group structure in terms of group overlap and the locations of individual observations relative to each other and to the group means, then it can be shown that the significance tests provide incomplete and often misleading representations of the data. Similarly, in problems involving just more that just two groups, the null hypothesis can be rejected, when in fact only one of the several groups arose from a different population.

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]

This article analyzes the relationship between stochastic dominance (SD) and mean-semivariance (ES) criteria. This paper contains two main results. First, there are good conceptual bases for anticipating greater consistency between ES and second SD (SSD) rules than between mean-variance (EV) and SSD rules. In particular, with one possible and relatively minor exception (identical mean and semivariance, the efficient set of portfolios derived from the ES rule with semivariance calculated around a fixed point is a subset of the SSD efficient set.

Examines the graphical display of two-way contingency tables interpreting statistical analyses. Use of chi-squared test for independence; Provision of the confidence region size in determining the large sample size; Concepts of displaying vectors and confidence regions.

This paper presents a follow-up records' study of 773 former marriage counseling clients of 21 marriage counselors. The clients' primary treatment form was compared with six categories of counseling outcome. A chi-square statistical treatment demonstrated that the six forms of counseling resulted in different outcomes significant beyond the .001 level. A rank ordering of the six forms for effectiveness suggested conjoint interviews and conjoint groups to be the most effective forms. Different forms may be helpful to those who divorce as opposed to those remaining married, and some findings are quite different from current supposition. [ABSTRACT FROM AUTHOR]

The standard problem of testing hypotheses begins with the formulation of a model containing one or more unknown parameters. The hypothesis is expressed as some restriction on the possible values of the parameters. In common economic applications, a linear regression model may be specified and the hypothesis usually is that one or more regression coefficients are zero. The standard theory is not applicable if the null and alternative hypotheses are disparate or nonnested. The purpose of this paper is to suggest a general purpose method for coping with this type of problem and to compare it with some leading alternatives. Section II of the article is devoted to some theoretical considerations. Some illustrative computations are discussed in section III. Section IV contains some brief conclusions. Three basic procedures have been considered for testing nonnested hypotheses. First, the development of D.R. Cox's generalized likelihood ratio statistic. Second, Cox's exponential weighting procedure and third, a linear weighting procedure.

W.J. Baumol and J. Tobin applied the principle of profit maximization to the management of money balances. Under fairly restrictive assumptions they obtained the conclusion that the income elasticity of the transactions demand for money should be plus one half and the interest elasticity minus one half. The hypothesis is not directly testable because estimates of the transactions demand for money are not available. However, tests using the total demand for money do not support the Baumol-Tobin (BT) elasticities. Authors show that if profit maximization is assumed and more general assumptions employed the only restriction is that the interest elasticity of the total demand for money is between zero and minus one. This finding offers theoretical justification for many previously published statistical results. A very primitive theory of the demand for money may be obtained by assuming that income is distributed at the beginning of each month and that the individual spends it (all) evenly in the course of the month. The only money he holds is the as yet unspent balance. This model implies that the demand for money is proportionate to income. BT regarded their approach as being relevant only to the transactions demand for money.

This study employed several statistical techniques in testing the hypothesis that classification according to (1) growth, (2) stable, and (3) cyclical characteristics represents a factor for grouping stocks. These techniques showed that the residuals obtained by removal of general market effects from a sample of 100 stocks displayed cross-sectional dependence conforming to four distinct stock categories, including an oil group as well as the three hypothesized groups. In addition, regression analysis results indicated that these stock groupings accounted for an avenge of 14 percent of the variance in rate of return of stocks in the sample in comparison to 31 percent represented by general market effects. It was thus considered appropriate to assign a factor to the explanation of the variance of returns of a common stock additional to market, industry, and company, and based upon a system of classification corresponding to (1) growth, (2) stable, (3) cyclical, and (4) oil stocks. Correspondingly, the presence of stock groupings among the stock return residuals implied a violation of the specification of cross-sectional independence of the residuals for the single-index model. An examination of the residual correlation matrices for the single- and four-index models confirmed the existence of a significant degree of dependence among the residuals from the single-index model, whereas the four-index model showed little indication of a violation of this specification. As a result of the superiority in accounting for systematic effects among securities, the four-index model provided a closer approximation to the true correlation matrix than was provided by the single-index model. Since these analyses indicated significant violation of the specification of cross-sectional independence of residuals, the form of the single-index model was examined for additional departures from model specifications. A test of the intercepts from regressions of the four stock groupings on the S & P market index showed that these parameters were significantly different from zero, thereby indicating that the returns of the indexes were not consistently proportional to their risk as measured by the slope coefficient from the regression equation. Risk and return measures developed in conjunction with the test of the form of the regression equation and a statistical test of these measures indicated a consistency as well as an independence of risk-return relationships among the four groups of stocks. [ABSTRACT FROM AUTHOR]

This paper presents a comparison between similar types of American and Canadian forecasts of annual gross national product for an identical period (1960-69) using the same error measures. It was concluded that on mean, mean absolute, and mean square error bases, American forecasts were significantly more accurate than were the Canadian ones in predicting relative changes in their respective annual gross national products during the period 1960-69. Forecasters in both the United States and Canada were likely to have made the same types of errors on average in forecasting any given year. The general conclusion from the analysis of the errors seemed to suggest that a bias toward underestimating change may be less evident in the American gross national product forecasts than in those made in Canada. The negative mean errors were smaller, the percentage of underestimates was smaller, the covariance components of the mean square errors were larger, and the regression and test statistics were less suggestive. One of the more important points is that when "adjustments" of the predictions for differences in the basic nature of the economies are made, the conclusions as to differences in the "accuracy" of aggregate forecasts made in various countries may change a great deal. That is, conclusions as to differences in forecasting ability based solely on the comparison of "absolute accuracy" could be seriously misleading if the economies are not of approximately similar natures. The method of "adjustment" used here assumes that information as to the nature of the economies is contained in the past history of the variables to be forecast, so that a more worthwhile comparison is obtained when the respective judgmental sets are first "adjusted" by extrapolative predictions from these past actuals. Comparisons of the "relative" accuracy of forecasts showed that the American predictions of annual gross national product percentage changes had larger relative mean square errors than did the Canadian sets. That is, the American sets were only about as accurate as, and probably less accurate then, relative to extrapolative predictions. the forecasts made in Canada. The predictive efficiency of the Canadian gross national product forecasts relative to that of the extrapolative predictions was generally higher than that of the American predictions; the amount of autonomous information and available extrapolative information included was also somewhat higher. However, the extrapolative information actually used in forecasting was quite low in both countries, probably because of the essentially trendless nature of percentage changes in gross national product. [ABSTRACT FROM AUTHOR]

The two-sided bivariate t-test for simultaneous comparison of two treatments with a control is studied. The problem of allocating a given number of observations to the treatments and the control is discussed, and it is concluded that, in the absence of preferences, a general purpose rule would be to choose the sample sizes equal. A table is presented which gives the sample size required to ensure that the null hypothesis will be rejected with at least a prescribed probability, given the significance level and the standardized differences between the treatments and the control. Similar tables are provided for use when the object is to ensure that both treatments means will be found significantly different from the control mean with at least a given probability, or to ensure that a specified treatment will be found significant with at least a given probability. [ABSTRACT FROM AUTHOR]

Analytical and Monte Carlo results are used to investigate the robustness of the exact statistical test suggested by Nelson for testing the hypothesis of equality of two availabilities. A non-parametric test based on a generalized U-statistic is proposed which does not depend on the assumption that the times to failure and times to repair are exponentially distributed. Additional Monte Carlo results are used to point out the strengths and weaknesses of this test. [ABSTRACT FROM AUTHOR]