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Estimators for finite population parameters and their variances in two-stage sampling have been developed by using the linear least-squares prediction approach in a recent article by Royall (1976). This article considers a special case of the superpopulation model assumed by Royall and uses a new technique involving linear combinations of the sample observations to estimate the variances of these estimators. An exact confidence interval for the finite population total is calculated for the case in which all clusters have an equal number of elements and an equal number of elements are sampled from each selected cluster. [ABSTRACT FROM AUTHOR]

This article comments on frequintist theory. A procedure justifiable by frequentist theory must be "anticipatory" as well as frequentist. For example, considering statistician Abraham Wald's sequential probability ratio test for testing between two simple hypotheses. It does not suffice merely to look at conditional properties of the terminal decision rule given the stopping time-even though these possess a valid (conditional) frequentist interpretation. Instead, all possible consequences of the actions must be anticipated from the outset. Thus the sequential test procedure consists of both a stopping rule as well as a terminal decision rule; and various procedures are compared according to the combined frequency properties of their stopping and terminal decision rules. To some, it had seemed to pose an irresolvable paradox to have a theory of conditional confidence which also possessed this anticipatory frequentiest property. Jack Kiefer has decisively demonstrated that this is not so. The key step is to anticipate from the outset the class of conditioning statements which will later be made. In this fashion the apparent paradox can thus be resolved.

For tests of a single parameter in the binomial logit model, Wald's test is shown to behave in an aberrant manner. In particular, the test statistic decreases to zero as the distance between the parameter estimate and null value increases, and the power of the test, based on its large-sample distribution, decreases to the significance level for alternatives sufficiently far from the null value. [ABSTRACT FROM AUTHOR]

Comments on the study `Conditional Confidence Statements and Confidence Estimators,' by J. Kiefer, published in the December 1977 issue of the `Journal of the American Statistical Association.' Focus on foundational issues; Arguments on the proposed inference procedures; Limitations of the study. [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.

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 rejoinder by authors to comments made by scholars B. Efron, Joe R. Hill and C.N. Morris on their article " Empirical Bayes Confidence Intervals Based on Bootstrap Samples." Our article has several goals, introducing an empirical Bayes (EB) bootstrap, investigating the properties of one method of using the bootstrap for computing EB confidence intervals and generating discussion on philosophical and technical approaches. Discussants have contributed enormously to our efforts both by elucidating many important points of our article and making specific suggestions for modifications or alternate approaches that are likely to improve our method. Efron, Hill and Morris observe that our bootstrap uses the sampling distribution as a posterior distribution. Although there is no philosophical basis for this substitution, this bootstrap successfully adjusts for variation in estimating the prior. Its potential merit lies in EB properties and its true test will come in more complicated settings and in competition with other approaches. Efron suggests using the bootstrap samples in a different way, namely, to calibrate the naive intervals to have the appropriate EB coverage.

This article comments on the topic of confidence interval. Statistician Jack Kiefer has tackled the problem of conditional inference head on in a new way. It is fitting that this should be done, and it is a pleasure to see both the mathematics and the presentation handled so skilfully. The notion of correct decision provides a unifying theme for bringing together hypothesis testing, confidence intervals, ranking, and selection. There are formidable problems. One is the selection of criteria by which procedures should be evaluated and the second is the choice of how conditional one should be. The choice of reference set is, of course, the central issue. Three possibilities are considered: (i) The coarsest conditioning (none at all); (ii) the finest conditioning; (iii) intermediate conditioning. The word "confidence" traditionally suggests confidence intervals, and the author has used the word in a broader context. Here (i) corresponds to standard widely used Neyman-Pearson procedures. As the opposite extreme, it is arguable that (ii) has comparable claims to objectivity, and is perhaps not too much harder to comprehend or explain. Alternative (iii) is interesting to contemplate mathematically, but it is hard to picture it in widespread practical use.

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.

Test statistics from the weighted log-rank class are commonly used to compare treatment with control when there is right censoring. This paper uses saddlepoint methods to determine mid-p-values from the null permutation distributions of tests from the weighted log-rank class. Analytical saddlepoint computations replace the permutation simulations and provide mid-p-values that are virtually exact for all practical purposes. The speed of these saddlepoint computations makes it practicable to invert the weighted log-rank tests to determine nominal 95% confidence intervals for the treatment effect with right-censored data. Such analytical inversions lead to permutation confidence intervals that are easily computed and virtually identical to the exact intervals that would normally require massive amounts of simulation. [ABSTRACT FROM AUTHOR]

This article responds to Professor Berry's points about the appropriate test of significance of gamma. His remarks do not alter the findings or conclusions of the author's paper. The crucial question involves those relationships which the author reported as nonsignificant and which therefore led the author to explore alternatives. Professor Berry suggests that an appropriate test of significance may have revealed a significant relationship between occupational and religious mobility. But clearly the chi-square is the appropriate test in the case, for the categories are mobility and nonmobility. The former category can be broken down further into upward and downward mobility. No relationship was found between occupational and religious mobility per se.