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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]

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]

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]

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]

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]

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]

The present model is applicable when pi[sub Y], the population proportion with a nonsensitive attribute Y, is not known in advance and two samples are required to estimate pi[sub A], the population proportion with a sensitive attribute A. It consists of using the sensitive question and two nonsensitive alternate questions in each sample, yielding two unbiased estimates of pi[sub A]. The optimum estimator, a weighted average of these two estimates, is described and its minimum variance calculated. The efficiency of this estimator is compared with Moors' optimized version of the standard two sample single alternate question model, and with the one sample single alternate question model when pi[sub Y] is known. [ABSTRACT FROM AUTHOR]

Following Riedwyl [8] we generalize some one-sample statistics of the Cramer-von Mises type so that they can be used to test grouped data for goodness of fit. We prove that under the null hypothesis the asymptotic distributions of these statistics, when suitably standardized, coincide with the corresponding classical statistics if the ratio of the sample size to the number of groups (k) remains constant. For k fixed the asymptotic distributions are given under the null hypothesis, and it is shown how to obtain them under any alternative. Some results for finite sample sizes are also derived, [ABSTRACT FROM AUTHOR]

The univariate skewness and kurtosis statistics, square root of b[sub 1] and b[sub 2], and the W statistic proposed by Shapiro and Wilk are generalized to test a hypothesis of multivariate normality by use of S.N. Roy's union-intersection principle. These generalized statistics are invariant with respect to nonsingular matrix multiplication and vector addition. Two univariate test statistics, Kolmogorov-Smirnov and Cramer-Von Mises, are used to test whether transformed vector observations follow a Chi[sup 2] distribution. The significance points, and powers against selected alternatives, of these five test statistics are obtained by Monte Carlo methods. These studies showed that adequate powers may be achieved for small sample sizes. [ABSTRACT FROM AUTHOR]

In paired comparisons of a treatment and control, it frequently happens that the two members of each pair can be classified into distinguishable types. The completely randomized design, which assigns the members of each pair at random to treatment and control, then may by chance assign the treatment primarily to subjects of one type and thereby confound treatment and type. This difficulty can be avoided by restricting the randomization. We find that such restriction is desirable by analyzing several of the standard tests (Wilcoxon, t, and tests for dichotomous response) for efficiency and deficiency. [ABSTRACT FROM AUTHOR]

This study is concerned with deriving the properties of the preliminary test estimator for the general linear normal regression model, ascertaining the characteristics of the risk functions over the parameter space, and determining the conditions necessary for the risk of this estimator to exceed or be less than the conventional one under squared error loss. A test procedure and the problem of choosing an optimal level of significance for the test are discussed. Some theorems and lemmas used in evaluating the risk and some properties of functions of the non-central F distribution are developed in the appendices. [ABSTRACT FROM AUTHOR]

A double sampling plan is derived to test the hypothesis H[sub o]: sigma[sup 2, sub 1] less than or equal to sigma[sup 2, sub 2] where it is assumed the samples are from normally distributed populations. An example is given comparing the double sampling plan with a corresponding single sampling plan. [ABSTRACT FROM AUTHOR]

Consider sampling in two stages for testing a simple hypothesis about a population whose elements may be classified into a finite number of classes. The joint asymptotic distribution of the two Pearson chi[sup 2] statistics based on the first and combined samples is derived and used to construct a two-stage test. The advantage of this test relative to the conventional one-stage test is discussed in terms of its asymptotic power. Tables of critical values for 1 percent and 5 percent level tests for 1-10 degrees of freedom ore given as well as modifications for cases involving unknown parameters. [ABSTRACT FROM AUTHOR]

A class of simple methods of computing asymptotically efficient estimates which ore asymptotically equivalent to centers of the confidence intervals from rank tests for a location parameter is described. Values of the asymptotic efficiencies are given for populations other than that used for construction of a particular estimate. [ABSTRACT FROM AUTHOR]

This article tests the hypothesis against the alternative proposed by E.L. Lehmann. This problem is similar to a number that occur in non-parametric statistics, one is given a parametric model but, because the distributions given in this model are considered only as approximations to the real distributions, one is inclined to use a rank test. When one restricts attention to rank tests the problem reduces to testing a simple hypothesis against a one-dimensional alternative. One then requires a test optimal for this reduced situation. In this article one will see that first that for one or both sample sizes large that Lehmann's tests and Savage's test are asymptotically equivalent and optimal. Then numerical values of the powers of several tests are given for the equal sample size case, sample sizes up to ten being considered. One will see in fact that for most of the cases considered, the first three of these tests have such similar properties that for most purposes each may be considered optimal among rank tests.

It is shown that a test suggested by Bechhofer, Kiefer, and Sobel [1], for selecting the better of two binomial populations, can be formulated and solved when a maximum number of tests is specified. If is assumed that the probability of correctly selecting the better population is specified to be better than P[sup *] when the difference in success probabilities exceeds a specified change[sup *]. The populations are sampled equally and it is assumed that the trial ends either when the difference in the number of successes exceeds a calculated value of s, or when N tests have been made, whichever is sooner. [ABSTRACT FROM AUTHOR]

This article studies the effect that serial correlation of the observations has on the distribution of the mean and two one-sample nonparametric tests, the sign test and the Wilcoxon test. It is shown that relatively slight dependence has a strong influence on the level of these tests. [ABSTRACT FROM AUTHOR]

A measure of variation for categorical data is discussed. We develop an analysis of variance for a one-way table, where the response variable is categorical. The data can be viewed alternatively as falling in a two-dimensional contingency table with one margin fixed. Components of variation are derived, and their properties are investigated under a common multinomial model. Using these components~ we propose a measure of the variation in the response variable explained by the grouping variable. A test statistic is constructed on the basis of these properties, and its asymptotic behavior under the null hypothesis of independence is studied. Empirical sampling results confirming the asymptotic behavior and investigating power are included. [ABSTRACT FROM AUTHOR]

In this article we study the exact finite sample distribution function of a t-statistic that can be used to test hypotheses and construct confidence intervals for structural coefficients in simultaneous equations models. It is shown that the exact distribution function is equal to Student's t-distribution when one of its parameters is zero and converges to Student's t-distribution function as another of its parameters increases without bound. Computations of the exact distribution function and its first three moments indicate the error that might result if Student's t-distribution function is used as an approximation to the exact distribution function. [ABSTRACT FROM AUTHOR]

As is true of any statistical application, testing econometric statistical hypotheses involves constructing critical regions with prescribed probabilities of Type I error and determining probabilities of Type II error under alternative hypotheses. Such constructions and determinations presuppose knowledge of exact statistical distribution functions of econometric estimators and test statistics either directly, or indirectly, as in the case where a statistical distribution function that approximates the exact distribution with known margin of error is used. If this requisite information is not available, econometric statistical inference remains guesswork. Partly because of the complicated nature of systems of simultaneous econometric structural equations and the large numbers of structural constants required to characterize distribution functions of econometric statistics, however, only a few exact marginal distributions of econometric estimators and test statistics have been extracted so far. This article is intended as a contribution to the growing literature of econometric distribution theory and to assist the efforts of econometric statisticians in providing a rational basis for econometric statistical inference. [ABSTRACT FROM AUTHOR]

Cronholm and Revusky [4] have proposed a rank test based on independent subexperiments for the comparison of a treatment effect with a control when the treatment is destructive but the control produces at most a transient effect. This article provides a thorough study of its performance under two sampling situations. With the aid of a computer, the exact small sample power of the test is evaluated for some important alternatives. A modification of the test is proposed for the situation where numerical measurements are available rather than merely the ranks within each stage. The modification is found to substantially improve the power. Both tests are shown to be unbiased. Finally, the Pitman asymptotic efficiencies are obtained and comparisons are made with the appropriate Wilcoxon tests. [ABSTRACT FROM AUTHOR]

The lack of memory property of the exponential distribution plays an important part in the branch of applied probability. This property assumes the information regarding the probability distribution. In the present paper we give a characteristic property of the exponential distribution based on the means of the conditional distributions. Considering a random variable T with finite mean and such that P(T > O) > 0, and denoting by y a positive number such that P(T > y) > 0, we show that T has an exponential distribution if and only if the mean of the conditional distribution, given T > y, exceeds the mean of the unconditional distribution by the quantity y for all y. Also given in the paper is a similar characterization for the geometric distribution. Since the information concerning the expected values is easily accessible, we expect these properties to be useful in dealing with the practical problems. [ABSTRACT FROM AUTHOR]

For Bernoulli random variables sequential tests of the simple hypotheses p = p[SUB o] vs. p = p[sub 1] are considered. In particular a comparison is made between the performance of sequential probability ratio tests (SPRTs) and curtailed single sampling plans (CSSPs), when both tests have the same error probabilities. In [1] it is shown that the CSSP has a strong optimality property. Nevertheless, if one admits randomized SPRTs, the latter are better. Numerical examples are considered in detail for p[sub o] = 1/2 and the CSSP with n = 2. The method of finding the randomized SPRTs with the correct error probabilities is indicated. These rules have positive probability of deciding without taking any observations. [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 double sample test for a hypothesis concerning the mean mu of a normal random variable with unknown variance sigma[sup 2] is presented in this note. This test is an alternative to the usual single sample t test and is made by taking samples at two stages. After the first sample has been observed the hypothesis is rejected, accepted or a second sample is taken. This double sample test is a modification of a double sample test suggested by D. Owen. However, for the test being suggested here if the second sample is taken the information from the first sample is used in making the final decision. A table is included which is a tabulation of the rejection and acceptance points for various sample sizes and alpha = .05 and alpha = .01. Additional tables are included which give some power values and expected sample sizes for the new test and Owen's test. These power values are compared with power values of various single sample t tests. Conclusions about desirable sample sizes are presented for both the new test and Owen's test. [ABSTRACT FROM AUTHOR]

The subsample values of a statistic t are the values of t for subsets of the whole sample. Subsample values may be used as indicators of variability of t. For real valued statistics t, estimating a parameter theta, the subsample values are defined to form a set of typical values if the intervals between the ordered subsample values each include theta with equal probability. The typical value property holds exactly in some cases and approximately in others. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to make the reader aware of the applicability and advantage of a particular mathematical model. The application is typified by an example and the advantage is via confidence intervals; that is, shorter confidence intervals are possible using the model than if one ignores it, providing the applicability is valid. It is also shown that an improved estimate can be obtained through use of the model. Let f(y|mu, sigma) be a normal density with mean mu and variance sigma[sup 2] and let g(mu|lambda, beta) be a normal density with mean lambda and variance beta[sup 2]. A sequence y[sub 1], y[sub 2],..., y[sub n+1] of independent observations from the mixture off and g can be considered as follows: An unobservable mu [sub i] is first drawn from g(mu|lambda, beta) and then y[sub i] which can be observed is drawn from f(y|mu[sub i], sigma). Confidence intervals on mu[sub n+1] are obtained which are based on the observations y[sub 1],..., y[sub n+1] and which are shorter than the standard interval based on y[sub n+1] only for any n. Shorter intervals are obtained for two cases: (i) lambda unknown, sigma, beta known; (ii) only sigma/beta = c known. [ABSTRACT FROM AUTHOR]

Results are given of an empirical sampling study of the sensitivities of nine statistical procedures for evaluating the normality of a complete sample. The nine statistics are W (Shapiro and Wilk, 1965), square root of b[sub I] (standard third moment), b[sub 2] (standard fourth moment), KS (Kolmogorov-Smirnov), CM (Cramer-Ven Mises), WCM (weighted CM), D (modified KS), CS (chi-squared) and u (Studentized range). Forty-five alternative distributions in twelve families and five sample sizes were studied. Results are included on the comparison of the statistical procedures in relation to groupings of the alternative distributions, on means and variances of the statistics under the various alternatives, on dependence of sensitivities on sample size, on approach to normality as measured by the W statistic within some classes of distribution, and on the effect of misspecification of parameters on the performance of the simple hypothesis test statistics. The general findings include: (I) The W statistic provides a generally superior omnibus measure of non-normality; (ii) the distance tests (KS, CM, WCM, D) are typically very insensitive; (iii) the u statistic is excellent against symmetric, especially short-tailed, distributions but has virtually no sensitivity to asymmetry; (iv) a combination of both square root of b[sub 1] and b[sub 2] usually provides a sensitive judgment but even their combined performance is usually dominated by W; (v) with sensitive procedures, good indication of extreme non-normality (e.g., the exponential distribution) can be... [ABSTRACT FROM AUTHOR]

The first part of this note is devoted to some of the simpler series representations of the doubly non-central t-distribution. In the second part, the computational considerations arising from the series representations are discussed. A table showing some of the results of the method is presented. [ABSTRACT FROM AUTHOR]

Some optimum nonparametric procedures for estimating and testing contrasts in two-way layouts are proposed and studied. These procedures are based on the Chernoff-Savage [4] type of rank order statistics which include the Wilcoxon and normal scores statistics among others. In the first three sections, the properties of the proposed point estimators of contrasts, such as symmetry, invariance and asymptotic normality, are studied and their asymptotic relative efficiencies with respect to the corresponding least-squares estimators are obtained. In particular, it is shown that the procedures based on the normal scores statistics are asymptotically at least as efficient as the corresponding procedures based on the method of least squares, whatever be parent cumulative distribution functions. In sections 4 and 5, the corresponding problems of testing and confidence intervals are discussed, and generalized to two-way layouts with several observations per cell. [ABSTRACT FROM AUTHOR]

Balls are drawn one after another from k cells C[sub 1], ..., C[sub k] according to the multinomial distribution. Suppose the ith cell initially contains N[sub I] balls, and sampling stops as soon as any of the k cells, say C[sub alpha], empties first. Let X[sub I] denote the number of balls taken from cell C[sub iota] (all I is not equal to alpha) at stopping time. The joint asymptotic (as N[sub I] arrow right Infinity) distribution of the X[sub iota] (I is not equal to alpha) is derived under the most general configuration of the multinomial cell probabilities p[sub 1], ..., p[sub k]. Conditions on p[sub iota] and N[sub I] are given under which the asymptotic distribution is shown to be either normal or truncated (restricted) normal. An application of the asymptotic distribution theory for N[sub iota] = N[sub 0] (I =1, ..., k) in setting up approximate tests and confidence intervals for the largest p[sub I] is also given. Under certain conditions on pi and N[sub I] it is shown that the asymptotic probability that C[sub I] empties first is equal to the probability content of a positive orthant under a multivariate normal distribution. [ABSTRACT FROM AUTHOR]

Abstract The procedures of Scheffe [4] and Welch [5] for testing equality of means of two normal populations are compared according to the expected lengths of the confidence intervals they yield, and a criterion is developed for deciding which of the two methods is better in any given situation. An expression for the expected length of the confidence interval for the Scheffe procedure was developed by Scheffe. Because of the asymptotic series nature of the Welch procedure, in this case, the analogous expression is more involved. It is developed below. A numerical computation was carried out for the case of a two-sided 90 per cent confidence interval. The results are presented in graphical form. Finally, it is shown that in large samples, the two procedures are equivalent. [ABSTRACT FROM AUTHOR]

This paper compares the Pearson Chi-Square and Kolmogorov goodness-of-fit tests with respect to validity under the following conditions: (1) the N independent observations are tabulated and arranged into k mutually exclusive groups that are equally probable under the hypothesis to be tested; and (2) both N and k are "small"; i.e., not greater than 50. A random sampling experiment was performed, and the results show that in general for the conditions considered, the Pearson test is more valid than the Kolmogorov test. [ABSTRACT FROM AUTHOR]

This paper presents the results of a limited investigation which brings into focus the difficulties encountered in developing exact distribution free methods for stratified simple random sampling. It is shown that exact distribution-free confidence intervals for a population median can be obtained from a stratified sample under very special circumstances. The principal result concerns the order statistics of the combined separate strata samples, where proportional allocation is employed. It is proved that a pair of symmetric order statistics provides a confidence interval for the population median whose confidence coefficient is not less than the confidence coefficient obtained from the corresponding order statistics of a random sample of the same total size drawn from the entire population. Furthermore, it is shown by means of a numerical example that this result necessarily holds only when proportional allocation is employed. [ABSTRACT FROM AUTHOR]

Confidence intervals for the population mean of a normal distribution can be determined from the distribution of the variate H = Square root of n(x - mu)/d, analogue to Student's t-distribution but based on the mean absolute deviation d instead of the standard deviation. The H-distribution is derived: the frequency function is symmetric about zero, with central ordinate (1/pi) Square root of (1-n[sup -1]); asymptotically it is normal, N(0, Square root of (pi/2)). An approximate formula for the calculation of the percent values is developed and numerical factors tabulated by which the mean absolute deviation of a normal sample of size n is to be multiplied in order to obtain 95 percent and 50 percent confidence limits of the mean, for n = 2(1)15(5)30, 40, 60,120. It is shown that the increase in length against confidence intervals from the standard deviation and Student's t is negligible. The usefulness of confidence intervals from the mean absolute deviation for estimating the precision of measurements in Physics is discussed. [ABSTRACT FROM AUTHOR]

The need for data compression, a consequence of the demands made on the telemetry system of a space vehicle, prompts consideration of the use of sample quantiles in estimating population parameters and obtaining tests of goodness of fit for large samples. In this paper optimal unbiased estimators of the mean and standard deviation are given using up to twenty quantiles when the parent population is normal. Moreover, the estimators are relatively insensitive to deviations from normality. A distribution-free goodness-of-fit test is presented based on the sum of the squares of four quantiles after an orthogonal transformation to independent normal deviates. If a frequency function is of the form f(x; p) = pf[sub 1](x) + (1 - p) f[sub 2](x), 0 < p < 1, where f, and f[sub 2] are normal frequency functions, the distribution is likely to be bimodal. Another goodness-of-fit test is obtained using four quantiles, which is likely to have considerable power with a null hypothesis of normality and the alternative hypothesis of bimodality. The "data compression ratios" obtained with the use of a quantile system can be on the order of 100 to 1. [ABSTRACT FROM AUTHOR]

The article focuses on comments given by the author on topics related to 2 X 2 contingency tables. As statistician William J. Conover points out in his article, the evidence he presents against Yates' "correction" is not very convincing. Therefore, the controversy seems likely to continue. The dilemma seems to arise from the contrast between the evidence accrued from two lines of inquiry. The first is directed to the question of whether the correction tends to make the sampling distribution of the test statistic in the null case more consistent with the theoretical model for the distribution so as to secure a more nearly correct level for the test. The second line of inquiry focuses on the question of whether the p-values from the corrected statistic tend to agree better with the corresponding "exact" p-values. Generally speaking, evidence from the first line of inquiry is against Yates' correction, whereas the correction tends to improve the agreement between the asymptotic and exact p-values. This incongruence is particularly confusing when the two approaches to the evaluation are regarded as interchangeable.

In the discussion of hypothesis testing in 2 X 2 contingency tables, Fisher's exact test is often used as the standard against which competing tests are measured. Statisticians should not be led into a semantic trap by the words "exact test." Statistician interpreted the phrase to mean that it yields the exact probability of observing a result identical to a more extreme probability under the assumption that a particular 2 X 2 table was generated by sampling from a four-variable hypergeometric distribution. The result shown by statistician K.D. Tocher shows that the exact test, supplemented by randomization to achieve the desired significance α is the most powerful test against one-sided alternatives when both, one or no margin totals are fixed in advance. Therefore, the randomized exact test should be the standard to which competing tests are compared. Even though most statisticians would not use the randomized test in practice, it could be used for judging the value of competing tests.

A procedure for estimating the zero class from a truncated Poisson sample is developed. Asymptotic normality of the estimator is proved so that a confidence interval for the missing zero class can be obtained. An example is given to illustrate the results obtained. [ABSTRACT FROM AUTHOR]

This article considers the problem of testing a completely specified continuous symmetric distribution against alternatives which are also symmetric about the same point. The symmetry is utilized in obtaining a new distribution-free statistic of the Kolomogorov-Smirnov type which can be used to halve the width of the Kolomogorov-Smirnov confidence band for the unknown distribution function. [ABSTRACT FROM AUTHOR]

An approach to two-sample tests of location may be based on the conditional distribution of the sampling process given that the observations are known constants. The author of this article considers a two-sample problem in which a random sample is drawn and an independent random sample is the cumulative probability functions of two continuous random variables. Tests are constructed for a difference in central tendency of the two distributions where central tendency is indicated in various ways. The test procedures are derived as post-data tests and are based on the Dempster-Shafer theory. The description and methods follow economist Arthur P. Dempster more closely since his work is more related to the problems under study. According to the author, the motivation for this article has been to show that Dempster's theory of inference may be easily applied to nonparametric problems. The presentation is kept to its simplest form, and he does not introduce the multivalued mapping necessary to handle discrete problems.

Eight nonparametric tests of location are examined in a small sample setting. Power functions are presented for samples drawn from the double exponential distribution. The results provide an example where the asymptotically most powerful rank test (the Mood median test) performs poorly for alternatives which are not very close to the null hypothesis. [ABSTRACT FROM AUTHOR]

The standard tables used for the Kolmogorov-Smirnov test are valid when testing whether a set of observations are from a completely specified continuous distribution. If one or more parameters must be estimated from the sample then the tables are no longer valid. A table is given in this note for use with the Kolmogorov-Smirnov statistic for testing whether a set of observations is from an exponential population when the mean is not specified but must be estimated from the sample. The table is obtained from a Monte Carlo calculation. [ABSTRACT FROM AUTHOR]

The article presents a comment on a previous article that appeared in the 1973 issue of the Journal of the American Statistical Association. According to the author comments by economists Arthur P. Dempster, D.A.S. Fraser, and John W. Pratt make interesting reading in that they reflect the committed attitudes of their individualistic approaches to statistical inference. The author find that he can react sympathetically to most of the points they have made and do not feel committed to any one approach sufficiently strongly to have any desire to reject out of hand the others. According to the author, he comments only on points to which he had some objection or to which he had something to add. Both Pratt and Dempster comment adversely on the type of significance test procedure. It was the author's intention to produce something like the usual test of significance, and what he suggested seems reasonable, according to him. The quoting of probabilities may be more informative. In any case, this is a side issue and one in which any difference of opinion could be easily settled.