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Introduction: Older adults with Alzheimer's disease (AD) experience drastic changes in their physical and mental abilities. AD patients became heavily dependent on their caregivers for everyday functions, which have significant implications not only for them but also for their caregivers. So, many AD caregivers experienced an increased level of depression and anxiety symptoms, lower perceived control, and higher burden compared to non-AD caregivers. Therefore, psychological first aid (PFA) and educational interventions are designed to enable those caregivers to meet the daily requirements of their patient care and to cope with its challenges. Aim: Determine the effect of psychological first aid program on stress level and psychological well-being among caregivers of older adults with Alzheimer's disease. Design: One group pre-test post-test was followed. Subjects: A convenience sample of one hundred (100) caregivers of older adults with AD. Setting: All online groups concerned with the care of Alzheimer's disease patients on Facebook. Tools: Socio-demographic and clinical data of older adults with Alzheimer's disease and their caregivers' questionnaire, Alzheimer's disease knowledge scale, Kingston caregiver stress scale, and authentic identity measures (AIM) scale of psychological well-being Results: The psychological first aid program has highly statistically significant effect on the AD caregivers' knowledge, stress level and psychological well-being as (t=-30.707, P = 0.000, t = 8.500, P = 0.000 & t= -4.763, P = 0.000 respectively). Conclusion: Psychological first aid program is considered an effective intervention in decreasing the AD caregivers' stress and increasing their psychological wellbeing and knowledge regarding delivering care for AD patients. [ABSTRACT FROM AUTHOR]

Information for evaluating the statistical significance of stepwise regression models developed with a forward selection procedure is presented. Cumulative distributions of the adjusted coefficient of determination (R²) under the null hypothesis of no relationship between the dependent variable and m potential independent variables are derived from a Monté Carlo simulation study. The study design included sample sizes of 25, 50, and 100, available independent variables of 10, 20, and 40, and three criteria for including variables in the regression model. The results reveal that the biases involved in testing statistical significance by two well-known rules are very large, thus demonstrating the desirability of using the Monté Carlo cumulative R² distributions developed by the authors. Although the results were derived under the assumption of uncorrelated predictors, the authors show that the results continue to be useful for the correlated predictor case. [ABSTRACT FROM AUTHOR]

In a classic significance test, based on a random sample with size n, a P value will be calculated at size n aiming to reject the null hypothesis. The sample size n, however, can retrospectively be divided into partial samples (1, 2, 3, ... , n-2, n-1, n) and a test of significance can be calculated for each partial sample. As a result, several partial samples will provide significant P values whereas others will not show significant P values. In this paper, we propose a significance test that takes into account the additional information from the P values of the n - 1 partial samples of a random sample. We show that the n-1 P values can greatly modify the results of a classic significance test. [ABSTRACT FROM AUTHOR]

The use of religious/spiritual resources may increase when dealing with the stress of a cancer diagnosis. However, there has been very little research conducted into changes in religious/spiritual beliefs and practices as a result of a cancer diagnosis outside the USA. The aim of this study was to examine the impact of a breast cancer diagnosis on patients' religious/spiritual beliefs and practices in the UK where religious practice is different. The study used two methods. One compared the religious/spiritual beliefs and practices of 202 patients newly diagnosed with breast cancer with those of a control group of healthy women ( n = 110). The other examined patients' perceived change in religious/spiritual beliefs and practices at the time of surgery with those in the year prior to surgery. The aspects of religiousness/spirituality assessed were: levels of religiosity/spirituality, strength of faith, belief in God as well as private and public practices. Patient's perceived their belief in God, strength of faith and private religious/spiritual practices to have significantly increased shortly after surgery compared with the year prior to surgery. However, there were no significant differences in religious/spiritual beliefs and practices between patients and healthy participants. Change scores demonstrated both a reduction and an increase in religious/spiritual beliefs and practices. Although belief in God, strength of faith and private religious/spiritual practices were perceived by patients to be significantly higher after their cancer diagnosis, no significant differences in religious/spiritual beliefs and practices were found between the cancer group at the time of surgery and the control group. Different methodologies appear to produce different results and may explain contradictions in past US studies. Limitations of this study are discussed and suggestions for future research are made. [ABSTRACT FROM AUTHOR]

Power method polynomial transformations are commonly used for simulating continuous nonnormal distributions with specified moments. However, conventional moment-based estimators can (a) be substantially biased, (b) have high variance, or (c) be influenced by outliers. In view of these concerns, a characterization of power method transformations by L-moments is introduced. Specifically, systems of equations are derived for determining coefficients for specified L-moment ratios, which are associated with standard normal and standard logistic-based polynomials of order five and three. Boundaries for L-moment ratios are also derived, and closed-formed formulae are provided for determining if a power method distribution has a valid probability density function. It is demonstrated that L-moment estimators are nearly unbiased and have relatively small variance in the context of the powermethod. Examples of fitting powermethod distributions to theoretical and empirical distributions based on the method of L-moments are also provided. [ABSTRACT FROM AUTHOR]

We proposed a statistical method to construct simultaneous confidence intervals on all linear combinations of means without assuming equal variance where the classical Scheffé's simultaneous confidence intervals no longer preserve the familywise error rate (FWER). The proposed method is useful when the number of comparisons on linear combinations of means is extremely large. The FWERs for proposed simultaneous confidence intervals under various configurations of mean variances are assessed through simulations and are found to preserve the predefined nominal level very well. An example of pairwise comparisons on heteroscedastic means is given to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

Objectives: This study examined selected effects of the proper use of nonparametric inferential statistical methods for analysis of nonnormally distributed data, as exemplified by emergency department length of stay (ED LOS). The hypothesis was that parametric methods have been used inappropriately for evaluation of ED LOS in most recent studies in leading emergency medicine (EM) journals. To illustrate why such a methodologic flaw should be avoided, a demonstration, using data from the National Hospital Ambulatory Medical Care Survey (NHAMCS), is presented. The demonstration shows how inappropriate analysis of ED LOS increases the probability of type II errors. Methods: Five major EM journals were reviewed, January 1, 2004, through December 31, 2007, and all studies with ED LOS as one of the reported outcomes were reviewed. The authors determined whether ED LOS was analyzed correctly by ascertaining whether nonparametric tests were used when indicated. An illustrative analysis of ED LOS was constructed using 2006 NHAMCS data, to demonstrate how inferential testing for statistical significance can deliver differing conclusions, depending on whether nonparametric methods are used when indicated. Results: Forty-nine articles were identified that studied ED LOS; 80% did not perform a test of normality on the ED LOS data. Data were not normally distributed in all 10 of the studies that did perform such tests. Overall, 43% failed to use appropriate nonparametric methods. Analysis of NHAMCS data confirmed that failure to use nonparametric bivariate tests results in type II statistical error and in multivariate models with less explanatory power (a smaller R 2 value). Conclusions: ED LOS, a key ED operational metric, is frequently analyzed incorrectly in the EM literature. Applying parametric statistical tests to such nonnormally distributed data reduces power and increases the probability of a type II error, which is the failure to find true associations. Appropriate use of nonparametric statistics should be a core component of statistical literacy because such use increases the validity of ED research and quality improvement projects. ACADEMIC EMERGENCY MEDICINE 2010; 17:1113-1121 © 2010 by the Society for Academic Emergency Medicine [ABSTRACT FROM AUTHOR]

Introduction: Angiogenesis, growth of new blood vessels from pre-existing vessels, is a crucial physiological process for tissue regeneration. This state is also seen in pathological processes such as malignancies and endometriosis. Vascular endothelial growth factor (VEGF) is a major mediator of angiogenesis and vascular permeability which is known to play an important role in the development of endometriosis. The aim of this study was to investigate the relationship between +405 G>C VEGF polymorphism and endometriosis in an Iranian population.. Materials and Methods: The study population was comprised of 105 women with and 150 women without laparoscopic evidence of endometriosis. Genomic DNA from blood cells was extracted using salting out method. Genotype and allele frequency of +405 G>C polymorphism was compared between women with endometriosis and the controls using PCR-RFLP. Statistical analysis was performed using SPSS 13.0 software. Chi-squared test and odds ratio plus 95% confidence interval were deter- mined. A p-value less than 0.05 was considered statistically significant. Results: While the +405 VEGF genotype frequencies in the case group were 41.3% G/G, 46.2% C/G and %12.5 C/C, they were 32% GG, %53.3GC and 14.7% CC in the control group. The distribution ofthree genotypes and allele frequencies of +405 G>C VEGF polymorphism between the case and control groups did not demonstrate any significant difference. Conclusion: In contrast to previous studies, no significant correlation was found between +405 G>C VEGF polymorphism and endometriosis. Since this was the first study in an Iranian population, further investigation with bigger sample sizes may be indicated to be able to generalize the findings. [ABSTRACT FROM AUTHOR]

The extremal index parameter θ characterizes the degree of local dependence in the extremes of a stationary time series and has important applications in a number of areas, such as hydrology, telecommunications, finance, and environmental studies. In this study, a novel estimator for θ based on the asymptotic scaling of block-maxima and resampling is introduced. It is shown to be consistent and asymptotically normal for a large class of rn-dependent time series. Further, a procedure for the automatic selection of its tuning parameter is developed and different types of confidence intervals that prove useful in practice proposed. The performance of the estimator is examined through simulations, which show its highly competitive behavior. Finally, the estimator is applied to three real datasets of daily crude oil prices, daily returns of the S&P 500 stock index, and high-frequency, intraday traded volumes of a stock. These applications demonstrate additional diagnostic features of statistical plots based on the new estimator. Supplementary materials including an appendix with complete proofs, the crude oil dataset, and an R-script implementing the estimators are available online. [ABSTRACT FROM AUTHOR]

Statistical experiments, more commonly referred to as Monte Carlo or simulation studies, are used to study the behavior of statistical methods and measures under controlled situations. Whereas recent computing and methodological advances have permitted increased efficiency in the simulation process, known as variance reduction, such experiments remain limited by their finite nature and hence are subject to uncertainty; when a simulation is run more than once, different results are obtained. However, virtually no emphasis has been placed on reporting the uncertainty, referred to here as Monte Carlo error, associated with simulation results in the published literature, or on justifying the number of replications used. These deserve broader consideration. Here we present a series of simple and practical methods for estimating Monte Carlo error as well as determining the number of replications required to achieve a desired level of accuracy. The issues and methods are demonstrated with two simple examples, one evaluating operating characteristics of the maximum likelihood estimator for the parameters in logistic regression and the other in the context of using the bootstrap to obtain 95% confidence intervals. The results suggest that in many settings, Monte Carlo error may be more substantial than traditionally thought. [ABSTRACT FROM AUTHOR]

The use of equivalence testing in scientific research is increasing beyond its traditional role in the drug approval process. Largely due to its ease of use and recommendations from the U.S. Food and Drug Administration guidance, the most common statistical method for testing equivalence is the two one- sided tests (TOST) procedure. Like classical point-null hypothesis testing, TOST is subject to multiplicity concerns as more comparisons are made. Here we give a condition that bounds the familywise error rate (FWER) using TOST and leads to a simple solution for controlling the FWER. Specifically, we demonstrate that if all pairwise comparisons of k independent groups are being evaluated for equivalence, then simply scaling the nominal type I error rate down by (k - 1) is sufficient to maintain the FWER at the desired value or less. The resulting rule is much less conservative than the equally simple Bonferroni correction. An example of equivalence testing in a non- drug development setting is given. [ABSTRACT FROM AUTHOR]

This article reviews literature on confidence intervals for p, assuming (Bernoulli) single, double, and multistage sampling. Methods used to produce approximate single-sampling confidence intervals extend to double sampling as well. A new Wilson approximate confidence interval procedure for double sampling is compared with existing procedures in terms of general interval properties, such as interval invariance, and performance (in terms of actual coverage probability and expected length) for double-sampling plans from the literature. [ABSTRACT FROM AUTHOR]

Confidence interval presents a range of possible values within which, with some certainty, we can find the statistical measure of the population. As such, it is an objective estimate of (in)precision and sample size of certain research. Therefore, we can consider confidence interval also as a measure of the sample and research quality. Confidence interval is defined by its margins of error. Depending on the confidence level that we choose, the interval margins of error and respective range also change. The most used confidence intervals in the biomedical literature are the 90%, 95%, 99% and not so often 99.9% one. The narrower the margins of an interval are, the higher is the estimate accuracy. The 95% confidence interval is traditionally the most used interval in the literature and this relates to the generally accepted level of statistical significance P < 0.05. There is a rule for same sized samples: the smaller the confidence level is, the higher is the estimate accuracy. Only the studies with a large sample will give a very small confidence interval, which points to high estimate accuracy with a high confidence level. A confidence interval can be attributed to almost every statistical measure. Although there are some other ways of calculating it, the confidence interval is generally and most frequently calculated using standard error. The P value and the confidence interval are two complementary statistical indicators. They describe the same thing, but in two different ways. The P value describes probability that the observed phenomenon (difference) occurred by chance, whereas the confidence interval provides margins of error within which it is possible to expect the value of that phenomenon. In the last twenty years, increasing number of journals require reporting of the confidence intervals for each of their key results. Reporting of this confidence interval provides additional information about the sample and the results. It is, moreover, very useful and irreplaceable supplement to a classical hypothesis testing and to the generally accepted P value. It should become a standard of all scientific journals to report key results with respective confidence intervals because it enables better understanding to the interested reader. [ABSTRACT FROM AUTHOR]

In this study, we analyzed the validity of the conventional 80% power. The minimal sample size and power needed to guarantee non-overlapping (1 - a)% confidence intervals for population means were calculated. Several simulations indicate that the minimal power for two means (m= 2) to have non-overlapping CIs is .80, for (1 - α) set to 95%. The minimal power becomes .86 for 99% CIs and .75 for 90% CIs. When multiple means are considered, the required minimal power increases considerably. This increase is even higher when the population means do not increase monotonically. Therefore, the often adopted criterion of a minimal power equal to .80 is not always adequate. Hence, to guarantee that the limits of the CIs do not overlap, most situations require a direct calculation of the minimum number of observations that should enter in a study. [ABSTRACT FROM AUTHOR]

Comparison of two samples can sometimes be conducted on the basis of analysis of receiver operating characteristic (ROC) curves. A variety of methods of point estimation and confidence intervals for ROC curves have been proposed and well studied. We develop smoothed empirical likelihood-based confidence intervals for ROC curves when the samples are censored and generated from semiparametric models. The resulting empirical log-likelihood function is shown to be asymptotically chi-squared. Simulation studies illustrate that the proposed empirical likelihood confidence interval is advantageous over the normal approximation-based confidence interval. A real data set is analysed using the proposed method. [ABSTRACT FROM AUTHOR]

The two-stage design is popular in epidemiology studies and clinical trials due to its cost effectiveness. Typically, the first stage sample contains cheaper and possibly biased information, while the second stage validation sample consists of a subset of subjects with accurate and complete information. In this paper, we study estimation of a survival function with right-censored survival data from a two-stage design. A non-parametric estimator is derived by combining data from both stages. We also study its large sample properties and derive pointwise and simultaneous confidence intervals for the survival function. The proposed estimator effectively reduces the variance and finite-sample bias of the Kaplan–Meier estimator solely based on the second stage validation sample. Finally, we apply our method to a real data set from a medical device postmarketing surveillance study. [ABSTRACT FROM AUTHOR]

Much research has been devoted to modelling strategies for longitudinal data with missingness, recently especially within the missingness not at random context. In this paper, the relatively unexplored but practically highly relevant domain of non-monotone missingness with multivariate ordinal responses is broached. For this, a dedicated version of the multivariate Dale model is formulated. Furthermore, we also assess the sensitivity of these models to their assumptions, by using the technique of global influence. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to provide theoretical justification for some existing methods for constructing confidence intervals for the sum of coefficients in autoregressive models. We show that the methods of Stock (1991), Andrews (1993), and Hansen (1999) provide asymptotically valid confidence intervals, whereas the subsampling method of Romano and Wolf (2001) does not. In addition, we generalize the three valid methods to a larger class of statistics. We also clarify the difference between uniform and pointwise asymptotic approximations, and show that a pointwise convergence of coverage probabilities for all values of the parameter does not guarantee the validity of the confidence set. [ABSTRACT FROM AUTHOR]

The article focuses on correcting a significance test for clustering. Neglecting the effect of clustering and analyzing the data as if each treatment group were a simple random sample are common mistakes in the analysis of cluster randomized trials. These mistakes may in turn lead to an overstatement of the accuracy of results and anticonservative suppositions regarding precision and statistical importance of treatment effects. The article offers a correction to the t statistic that would be calculated if clustering were incorrectly ignored. The correction made is a multiplicative factor that depends on the total sample size, cluster size and intraclass correlation ρ.

In this article, we provide a method of estimation for the treatment effect in the adaptive design for censored survival data with or without adjusting for risk factors other than the treatment indicator. Within the semiparametric Cox proportional hazards model, we propose a bias-adjusted parameter estimator for the treatment coefficient and its asymptotic confidence interval at the end of the trial. The method for obtaining an asymptotic confidence interval and point estimator is based on a general distribution property of the final test statistic from the weighted linear rank statistics at the interims with or without considering the nuisance covariates. The computation of the estimates is straightforward. Extensive simulation studies show that the asymptotic confidence intervals have reasonable nominal probability of coverage, and the proposed point estimators are nearly unbiased with practical sample sizes. [ABSTRACT FROM AUTHOR]

The article intends to examine the accuracy of various approximate methods in the context of the two-independent and the two-dependent samples design. It includes information on various closed-form approximations to the exact confidence interval bounds. It is informed that while examining the accuracy of two-independent samples design, participants are randomly assigned to an experimental or a control group by researchers. Moreover, it is reported that researchers conducted Monte Carlo simulations in order to determine the accuracy of the various approximations under a wide variety of conditions.

The article focuses on a research about the estimation of population proportions through the process of population-sample regression and establishes the regression coefficient with specific focus on only one sample. The established regression coefficient is the unbiased estimator of the squared correlation and using it as a shrinkage coefficient results to credibility intervals that are narrower than that of conventional confidence intervals. Researchers used 285 subjects that were made to select one of two optional responses and results reflected that the credibility interval was 33% narrower than that of the conventional confidence interval.

We give a large-sample analysis of the minimal coverage probability of the usual confidence intervals for regression parameters when the underlying model is chosen by a "conservative" (or "overconsistent") model selection procedure. We derive an upper bound for the large-sample limit minimal coverage probability of such intervals that applies to a large class of model selection procedures including the Akaike information criterion as well as various pretesting procedures. This upper bound can be used as a safeguard to identify situations where the actual coverage probability can be far below the nominal level. We illustrate that the (asymptotic) upper bound can be statistically meaningful even in rather small samples. [ABSTRACT FROM AUTHOR]

In this article we study a general class of goodness-of-fit tests for a parametric conditional mean of a linear or nonlinear time series model. Among the properties of the proposed tests are that they are suitable when the conditioning set is infinite-dimensional; that they are consistent against a broad class of alternatives, including Pitman's local alternatives converging at the parametric rate ≪~l/2, with n the sample size; and that they do not need to choose a lag order depending on the sample size or to smooth the data. It turns out that the asymptotic null distributions of the tests depend on the data generating process, so a new bootstrap procedure is proposed and theoretically justified. The proposed bootstrap tests are robust to higher-order dependence, particularly to conditional heteroscedasticity of unknown form. A simulation study compares the finite-sample performance of the proposed and competing tests and shows that our tests can play a valuable role in time series modeling. Finally, an application to an economic price series highlights the merits of our approach. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of estimating high-density regions from univariate or multivariate data samples. We estimate minimum volume sets, whose probability is specified in advance, known in the literature as density contour clusters. This problem is strongly related to One-Class Support Vector Machines (OCSVM). We propose a new method to solve this problem, the One-Class Neighbor Machine (OCNM) and we show its properties. In particular, the OCNM solution asymptotically converges to the exact minimum volume set prespecified. Finally, numerical results illustrating the advantage of the new method are shown. [ABSTRACT FROM AUTHOR]

An oft-cited advantage of empirical likelihood is that the confidence intervals that are produced by this nonparametric technique are not necessarily symmetric. Rather, they reflect the nature of the underlying data and hence give a more representative way of reaching inferences about the functional of interest. However, this advantage can easily become a disadvantage if the resultant intervals are unduly influenced by one of the data points. This article proposes simple methods for evaluating the effect of single points on empirical likelihood confidence intervals. In addition to suggesting diagnostics for detecting important observations, we examine the use of bootstrap and of jackknife influence functions to assess the extremity of suspect points. [ABSTRACT FROM AUTHOR]

Most standard statistical methods treat numerical data as if they were real (infinite-number-of-decimal-places) observations. The issue of quantization or digital resolution can render such methods inappropriate and misleading. This article discusses some of the difficulties of interpretation and corresponding difficulties of inference arising in even very simple measurement contexts, once the presence of quantization is admitted. It then argues (using the simple case of confidence interval estimation based on a quantized random sample from a normal distribution as a vehicle) for the use of statistical methods based on "rounded data likelihood functions" as an effective way of handling the matter. [ABSTRACT FROM AUTHOR]

We consider the problem of setting a confidence interval or bound for a linear combination of variance components related to a multivariate normal distribution, which includes important applications such as comparing variance components and testing the bioequivalence between two drug products. The lack of an exact confidence interval for a general linear combination of variance components spurred the development of a modified large-sample (MLS) method that was shown to be superior to many other approximation methods. But existing MLS method requires the use of independent estimators of variance components. Using a chi-squared representation of a quadratic form of a multivariate normal vector, we extend the MLS method to situations in which estimators of variance components are dependent. Using Edgeworth and Cornish-Fisher expansions, we explicitly derive the second-order asymptotic coverage error of the MLS confidence bound. Our results show that the MLS confidence bound is not second-order accurate in general, but is much better than the confidence bound based on normal approximation and is nearly second-order accurate in some special cases. Our results also show how to construct an MLS confidence bound that is second-order accurate. As an application, we discuss the use of the MLS method in assessing population bioequivalence, with some simulation results and an example. [ABSTRACT FROM AUTHOR]

This article extends recent results [Scand. J. Statist. 28 (2001) 699] about exact non-parametric inferences based on order statistics with progressive type-II censoring. The extension lies in that non-parametric inferences are now covered where the dependence between involved order statistics cannot be circumvented. These inferences include: (a) tolerance intervals containing at least a specified proportion of the parent distribution, (b) prediction intervals containing at least a specified number of observations in a future sample, and (c) outer and/or inner confidence intervals for a quantile interval of the parent distribution. The inferences are valid for any parent distribution with continuous distribution function. The key result shows how the probability of an event involving k dependent order statistics that are observable/uncensored with progressive type-II censoring can be represented as a mixture with known weights of corresponding probabilities involving k dependent ordinary order statistics. Further applications/developments concerning exact Kolmogorov-type confidence regions are indicated. [ABSTRACT FROM AUTHOR]

This article focuses on hypothesis testing from p values to Bayes factors. Testing hypotheses involves deciding on the plausibility of two or more hypothetical statistical models based on some data. It may be that there are two hypothesis on equal footing. In 1908, W. S. Gossett derived the distribution of the Student t statistic and used it to test null hypotheses about one mean and the difference of two means. His approach is used widely today. First, choose test statistic. Next, calculate its p value, which is the probability, assuming that the null hypothesis is true, that one would obtain a value of the test statistic as or more extreme than that obtained from the data. Finally, interpret this value as the probability that the null hypothesis is true. Of course, the p value is not the probability that the null hypothesis is true, but small values do cause one to doubt the null hypothesis. The general techniques have been applied in so many innovative ways. In Bayesian hypothesis testing, some common complaints included that the p value is not the probability that the null hypothesis is true. Another is that the p value is not very useful when sample sizes are large. The Bayesian approach to hypothesis testing answers complaints at a cost of requiring a prior distribution on the parameter.

In this paper, a goodness-of-fit test for the latent class model is presented. The test uses only the limited information in the second-order marginal distributions from a set of k dichotomous variables, and it is intended for use when k is large and the sample size, n, is moderate or small. In that situation, a 2[sup k] contingency table formed by the full cross-classification of k variables will be sparse in the sense that a high proportion of cell frequencies will be equal to zero or 1, and the chi-square approximation for traditional goodness-of-fit statistics such as the likelihood ratio will not be valid. The second-order marginal frequencies, which correspond to the bivariate distributions, are rarely sparse even when the joint frequencies have a high proportion of zero cells. Results from Monte Carlo experiments are presented that compare the rates of Type I and Type II errors for the proposed test to the rates for traditional goodness-of-fit tests. Results show that under commonly encountered conditions, a test of fit based on the limited information in the second-order marginals has a Type II error rate that is no higher than the error rate found for full-information test statistics, and that the test statistic given in this paper does not suffer from ill effects of sparseness in the joint frequencies. [ABSTRACT FROM AUTHOR]

Statistical power is a topic of importance to any researcher using statistical inference testing. Studies with low levels of statistical power usually result in inconclusive findings, even though the researcher may have expended much time and effort gathering the data for analysis. A survey of the statistical power of articles employing statistical inference testing published in leading MIS journals shows that their statistical power is, on average, substantially below accepted norms. The consequence of this low power is that MIS researchers typically have a 40 percent chance of not detecting the phenomenon under study, even though it, in fact, may exist. Fortunately, there are several techniques, beyond expanding the sample size (which often may be impossible), that researchers can use to improve the power of their studies. Some are as easy as using a different but more powerful statistical test, while others require developing more elaborate sampling plans or a more careful construction of the research design. Attention to the statistical power of a study is one key ingredient in assuring the success of the study. This article should serve as a useful guide for MIS researchers in the planning, execution, and interpretation of inferential statistical analyses. [ABSTRACT FROM AUTHOR]

Cet article s'applique à ľanalyse de données de dénombrement résultant de phénomènes de jumelage. Les paires formées par le jumelage ďé1éments 'semblables' sont cependant exclues. Plusieurs modèles sont proposés et analysés. On s'attache surtout à développer des méthodes aptes à déceler les paires qui se manifestent plus (ou moins) souvent que ne le voudrait le hasard. [ABSTRACT FROM AUTHOR]

A new theory is developed for nonparametric analyses of r × k contingency tables, where the columns correspond to k ordered categories. The work is motivated by concern that conventional nonparametric theory yields inferences concerning the given categories, but results are often interpreted as if for a continuum. Asymptotic distributions are derived under random cut-points models for the Mann-Whitney (-Wilcoxon) U statistic. A model is recommended under which the exact moments of U are simple functions of k and the two sample sizes. For two more general models, the asymptotic variance is given for k ≤ 12 and k = 20, 30. Tables of empirical critical values show that the recommended model yields P values very close to P values under the general models. [ABSTRACT FROM AUTHOR]

We present a procedure for finding simultaneous confidence intervals for the expectations μ = (μj, )jn=1 of a set of independent random variables, identically distributed up to their location parameters, that yields intervals less likely to contain zero than the standard simultaneous confidence intervals for many μ ≠ 0. The procedure is defined implicitly by inverting a nonequivariant hypothesis test with a hyperrectangular acceptance region whose orientation depends on the unsigned ranks of the components of μ, then projecting the convex hull of the resulting confidence region onto the coordinate axes. The projection to obtain simultaneous confidence intervals implicitly involves solving n! sets of linear inequalities In n variables, but the optima are attained among a set of at most n2 such sets and can be found by a simple algorithm. The procedure also works when the statistics are exchangeable but not independent and can be extended to cases where the inference is based on statistics for μ that are independent but not necessarily identically distributed, provided that there are known functions of μ that are location parameters for the statistics. In the general case, however, it appears that all n! sets of linear inequalities must be examined to find the confidence intervals. [ABSTRACT FROM AUTHOR]

Exact simultaneous one-sided confidence intervals for contrasts in normal means are discussed. The set C of contrast vectors considered is of one of two forms: Either it is a cone whose coordinates are monotone for a partial ordering defined on the coordinate index set {1,. . . , m} or it is the polar of such a cone. It is shown that the intervals obtained are inverted from test statistics that may be used for testing the null hypothesis that the mean vector μ lies in the dual (or negative polar) cone of Κ, against the alternative that μ is not in the dual of Κ. Corresponding conservative two-sided intervals are also discussed. The structure of such cones is considered and results concerning dual norms for such cones are obtained. Illustrations for simple ordering, simple-tree, and umbrella orderings are discussed. [ABSTRACT FROM AUTHOR]

In a nonrandom sample or a nonrandomized comparison of treated and control groups, methods are developed for displaying the sensitivity of confidence intervals for population quantiles to the magnitude of the departure from random selection. Quantiles of a single distribution and for a shift in two distributions are both discussed. These confidence intervals are based on a new inequality for the distribution of the number of successes in a nonrandom sample or nonrandomized comparison. The inequality has additional applications. In particular, it greatly accelerates the computations in a sensitivity analysis for the Mantel-Haenszel statistic in a 2 × 2 × S contingency table. Examples include a nonrandom collection of blood samples from a town with comparatively high levels of radon gas, an observational study of chromosome damage from mercury, and a study of the drug allopurinol as a cause of skin rash. The proof of the inequality makes use of Savage's lattice for ranks and Holley's inequality, which gives sufficient conditions for stochastic ordering in a lattice. [ABSTRACT FROM AUTHOR]

In this article we consider statistical inference for the autoregressive parameter of a first-order autoregressive sequence with positive innovations via an extreme value estimator ø. We show that a bootstrap procedure correctly estimates the sampling distribution of an asymptotically pivotal quantity (whose distribution depends only on the exponent of regular variation of the innovation distribution) based on ø, provided that the ratio of the bootstrap sample size m and the original sample size n converges to zero. This result enables us to construct a totally nonparametric confidence interval for the autoregressive parameter. We also consider bootstrapping a normalized version of ø with an application toward bias correction. To obtain the bootstrap validity results, we develop a continuous convergence result for certain associated point processes. We also present results of simulation studies and a numerical example. [ABSTRACT FROM AUTHOR]

We begin with a decision-theoretic investigation into confidence sets that minimize expected volume at a given parameter value. Such sets are constructed by inverting a family of uniformly most powerful tests, and hence they also enjoy the optimality property of being uniformly most accurate. In addition, these sets possess Bayesian optimal volume properties and represent the first case (to our knowledge) of a frequentist 1 -- α confidence set that possesses a Bayesian optimality property. The hypothesis testing problem that generates these sets is similar to that encountered in bioequivalence testing. Our sets are optimal for testing bioequivalence in certain settings; in the case of the normal distribution, the optimal set is a curve known as the limaçon of Pascal. We illustrate the use of these curves with a biopharmaceutical example. [ABSTRACT FROM AUTHOR]

This article introduces a resampling procedure called the stationary bootstrap as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on weakly dependent stationary observations Previously, a technique based on resampling blocks of consecutive observations was introduced to construct confidence intervals for a parameter of the in-dimensional joint distribution of in consecutive observations where in is fixed This procedure has been generalized by constructing a "blocks of blocks" resampling scheme that yields asymptotically valid procedures even for a multivariate parameter of the whole (i.e., infinite-dimensional) joint distribution of the stationary sequence of observations These methods share the construction of resampling blocks of observations to form a pseudo-time series, so that the statistic of interest may be recalculated based on the resampled data set But in the context of applying the method to stationary data, it is natural to require the resampled pseudo-time series to be stationary (conditional on the original data) as well Although the aforementioned procedures lack this property, the stationary procedure developed here is indeed stationary and possesses other desirable properties The stationary procedure is based on resampling blocks of random length. where the length of each block its a geometric distribution In this article, fundamental consistency and weak convergence properties of the stationary resampling scheme are developed. [ABSTRACT FROM AUTHOR]

Ranked-set samples have been shown to lead to improved methods of estimation in parametric settings under specific distributional forms when actual measurement of the sample observations is difficult but ranking them is relatively easy. The earliest work with ranked-set data concentrated on estimating a population mean or variance. More recently, a ranked-set sample estimator of a cumulative distribution function was developed and used to obtain a simultaneous confidence interval for the function. In this article, we take the next logical step and use this ranked-set empirical distribution function to construct distribution-free competitors to the standard Mann-Whitney-Wilcoxon estimation and testing procedures. The appropriate null distribution tables for the associated test are presented for the case of perfect ranking. Asymptotic relative efficiency comparisons between the simple random sample Mann-Whitney-Wilcoxon procedures and their ranked-set analogues are discussed, and the results of a small-sample Monte Carlo simulation study of the same arc presented. [ABSTRACT FROM AUTHOR]

A commonly occurring statistical inference problem in practice is that of making simultaneous comparisons among three or more treatment means mu[sub l] (1 is less than or equal to i is less than or equal to k) for certain experimental designs. One way to do this, the T method proposed by Tukey (1953), constructs simultaneous confidence intervals for all pairwise differences of the treatment means mu[sub 1] - mu[sub 1] (1 is less than or equal to l, j is less than or equal to k, i is not equal to j). The joint confidence level of these confidence intervals, however, depends in a very complicated fashion on the covariance structure of the treatment mean estimates mu[sub ,] and, therefore, for designs where the covariance structure is not "simple," the joint confidence level is not readily apparent. In general, this is the case for any unbalanced design or for designs in which the treatment mean estimates mu[sub l] have unequal correlations. Tukey conjectured in 1953 that whatever the correlation structure of the treatment mean estimates mu[sub ] the T method would always provide a conservative set of confidence intervals, that is, that the actual joint confidence level of the confidence intervals would always be at least as great as the nominal joint confidence level 1 - alpha. In this article a discussion is undertaken of the evidence that the T method in general provides a conservative set of simultaneous confidence intervals. It is shown that the coverage probability of the simultaneous confidence intervals depends on the covariance structure only through the k(k - 1)/2 variances of the pairwise differences of the treatment mean estimates. A set of sufficient, but not necessary, conditions on these variances is given, which ensures that the T-method confidence intervals are conservative. In addition, the application of the T method to various common experimental designs that produce correlated treatment... [ABSTRACT FROM AUTHOR]

This article discusses importance sampling as an alternative to conventional Monte Carlo sampling for estimating exact significance levels in a broad class of two-sample tests, including all of the linear rank tests (with or without censoring), homogeneity tests based on the chi-squared, hypergeometric, and likelihood ratio statistics, the Mantel-Haenszel trend test, and Zelen's test for a common odds ratio in several 2 x 2 contingency tables. Inference is based on randomly selecting 2 x k contingency tables from a reference set of all such tables with fixed marginals. Through a network algorithm, the tables are selected in proportion to their importance for reducing the variance of the estimated Monte Carlo p-value. Spectacular gains, up to four orders of magnitude, are achieved relative to conventional Monte Carlo sampling. The technique is illustrated on four real data sets. [ABSTRACT FROM AUTHOR]

The Mantel-Haenszel (MH) test (Mantel and Haenszel 1959) is a widely used method for analyzing sets of two-by-two tables that compare the outcome of two treatments in several strata (Bailar and Anthony 1977). The procedure tests the null hypothesis of no partial association between treatment and outcome in any of the strata, or tables, against the alternative that the partial association, as measured by the common odds ratio, differs from 1. Birch (1964) showed that for a fixed number of tables, both the MH test and an earlier version due to Cochran (1954) are asymptotically identical to the uniformly most powerful unbiased test of this hypothesis. This article is concerned with calculating the power of the MH test as a prelude to embarking upon a study. We consider versions of the test with and without corrections for continuity. The spirit behind the approximations is that, although the odds ratio is the appropriate parameter for computing asymptotic power under local alternatives, in practice studies are designed for nonlocal alternatives. Our approach is based on evaluating a weighted difference of proportions of success in each table, rather than a weighted average of log-odds ratios, and is valid even if the odds ratios differ from table to table. The adequacy of our approximations to power is evaluated for planning three types of studies: the comparative binomial (CB), the double dichotomy (DD), and the survey (SY). In the CB trial, the proportion lambda[sub l] of patients in the ith strata, as well as the proportion rho[sub l] of patients in the ith strata who are assigned to the first treatment, are constants (I = 1, 2, ..., N). For the DD only the rho[sub l]'s are constant, whereas for the SY both vectors are random variables. We first approximate power under the condition that for each stratum NE(lambda[sub l]) is large. This approximation cannot distinguish between corrected and uncorrected statistics nor among the different sampling schemes. In some [ABSTRACT FROM AUTHOR]

In the two-sample problem under random censorship we consider the uncensored observations and the censored ones as two separate groups. For each group a suitable rank statistic is obtained, and these two are then combined to a final one. This idea, which was first employed in Akritas (1983), is shown here to produce tests that (a) closely resemble the ordinary rank tests for the uncensored case and do not require the calculation of the Kaplan-Meier estimator, (b) are comparatively easy to apply and to understand, and (c) allow results on asymptotic normality to follow simply from standard results for the uncensored case. It is shown that the loss due to using two separate rankings rather than one complete ranking is asymptotically negligible. The optimal score function for each of the two separate rank statistics is seen to depend on the censoring distribution. Whereas in Akritas (1983) no assumption on the form of the censoring distribution was made (unrestricted adaptation), here we pursue restricted adaptation that results in simple score functions. In particular, motivated by the model of Koziol and Green (1976), we assume that the censoring distribution is a suitable function of the survival distribution. An example related to the Wilcoxon test is used for illustration. The effect of restricted adaptation on the efficiency of the test is examined by both exact efficiency calculations and simulation results. [ABSTRACT FROM AUTHOR]

Suppose that y[sub 1] ..... y[sub k] are normal random variables with ordered means u[sub 1] less than or equal to u[sub 2] less than or equal to ... less than or equal to u[sub k].. A confidence bound is found for each u[sub i] that takes advantage of the ordering. The upper and lower bounds are the maximum and minimum values of x such that the hypotheses that x < u[sub i] and u, < x are accepted by their respective likelihood ratio tests. These bounds are often more precise than the usual bounds and can be used to determine the safety of a toxin and to bound the virtual safe dose in a low-dose extrapolation. Simultaneous intervals for u[sub 1],..., u[sub k] are also derived. [ABSTRACT FROM AUTHOR]

Although a number of approximations to the distribution (under uniformity) of the scan statistic are known, they are, when the sample size is large, either difficult to compute or numerically unstable. A simple upper bound for the upper tail of the distribution, based on a result of Hunter (1976), is derived. It is found that for large sample sizes and a reasonably wide range of window widths, this bound gives a numerically stable approximation that is sufficiently accurate for hypothesis testing purposes. [ABSTRACT FROM AUTHOR]

The problem of constructing optimal confidence bands for a simple linear regression over the whole real line is considered. Optimality is defined as minimization of the average width of the bands weighted by a normalized function. This weight function is presented as an indicator of experimental interest in the varying width of the band. A comparison between the commonly seen hyperbolic bands and segmented-line bands is presented. [ABSTRACT FROM AUTHOR]

For small domains, we have a choice between design-consistent estimators that make the strongest possible use of auxiliary information and model-dependent design-biased alternatives such as the synthetic estimator. In this article, a design-consistent method is developed that borrows strength in the same way that the design-biased synthetic estimator does. The latter has a design-based mean squared error (MSE) advantage in small samples under the supposition that domains resemble each other. Under deviations from that model, however, and with moderate to large samples, the design-consistent method gives a smaller MSE. It also has the advantage that design-based variance estimators and design-based confidence intervals can be easily obtained. This article emphasizes that the choice of estimation method depends on a complex interaction of factors that include sample size, sampling fraction, domain size, and departures from the model. [ABSTRACT FROM AUTHOR]

In observational studies, the distribution of treatment assignments is unknown, and therefore randomization tests are not generally applicable. However, permutation tests that condition on sample information about the treatment assignment mechanism can be applicable in observational studies, provided treatment assignment is strongly ignorable. These tests use the conditional distribution of the treatment assignments given a sufficient statistic for the unknown parameter of the propensity score. Several tests that are commonly used in observational studies are particular instances of this general procedure. Moreover, conditional permutation tests and covariance adjustment are closely related, in the sense that the conditional permutation distribution of the covariance adjusted difference leads to the same inferences as the conditional permutation distribution of the unadjusted difference of sample means. A backtrack algorithm is developed to permit efficient calculation of the exact conditional significance level, and two approximations are discussed. A clinical study of treatments for lung cancer is used to illustrate the technique. Conditional permutation tests extend previous large sample results on the propensity score by providing a basis for exact tests and confidence intervals in small observational studies when treatment assignment is strongly ignorable. [ABSTRACT FROM AUTHOR]