Abstract: Current scientific techniques in genomics and image processing routinely produce hypothesis testing problems with hundreds or thousands of cases to consider simultaneously. This poses new difficulties for the statistician, but also opens new opportunities. In particular, it allows empirical estimation of an appropriate null hypothesis. The empirical null may be considerably more dispersed than the usual theoretical null distribution that would be used for any one case considered separately. An empirical Bayes analysis plan for this situation is developed, using a local version of the false discovery rate to examine the inference issues. Two genomics problems are used as examples to show the importance of correctly choosing the null hypothesis.

Abstract: Bai and Perron (1998), henceforth BP, considered estimating multiple structural changes in a linear model. The results are obtained under a general framework of partial structural changes which allows a subset of the parameters not to change.1 Methods to efficiently compute estimates are discussed in Bai and Perron (2003). BP also addressed the problem of testing for multiple structural changes under very general conditions on the data and the errors: they considered a type test for the null hypothesis of no change vs. a pre-specified number of changes and also vs. an alternative of an arbitrary number of changes (up to some maximum), as well as a procedure that allows one to test the null hypothesis of, say, I changes, vs. the alternative hypothesis of I + 1 changes. The latter is particularly useful in that it allows a specific to general modeling strategy to consistently determine the appropriate number of changes in the data. The tests can be constructed allowing different serial correlation in the errors, different distribution for the data and the errors across segments or imposing a common structure.

Abstract: The interactions between plants of different species, age or size play an important role in the dynamics of an ecosystem and can induce specific structures. These interactions can be studied by analysing the spatial structure of the corresponding bivariate patterns. The intertype L12-function has recently been successfully used in many papers for that purpose. However, when interpreting the results obtained with ecological data, at least two different null hypotheses – independence or random labelling – can be appropriate, depending on the context of the study and the nature of the data. As these two hypotheses correspond to different confidence intervals, an inappropriate choice of the null hypothesis can lead to misinterpretations of biotic interactions when studying ecological data. This problem has rarely been mentioned in the literature. In this paper we clarify the differences between these two null hypotheses, and illustrate the risk of misinterpretation when using an inappropriate null hy...

Abstract: Stationarity or statistical homogeneity is an important prerequisite for subsequent statistical analysis on a given section of a soil profile to be valid. The estimation of important soil statistics such as the variance is likely to be biased if the profile is not properly demarcated into stationary sections. Existing classical statistical tests are inadequate even for simple identification of stationarity in the variance because the spatial variations of soil properties are generally correlated with each other. In this paper, a modified Bartlett statistical test is proposed to provide a more rational basis for rejecting the null hypothesis of stationarity in the correlated case. The accompanying rejection criteria are determined from simulated correlated sample functions and summarized into a convenient form for practical use. A statistical-based soil boundary identification procedure is then developed using the modified Bartlett test statistic. Based on the analysis of a piezocone sounding record, two a...

Abstract: Using one of the key properties of copulas that they remain invariant under an arbitrary monotonic change of variable, we investigate the null hypothesis that the dependence between financial assets can be modelled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks are compatible with the Gaussian copula hypothesis, while this hypothesis can be rejected for the dependence between pairs of commodities (metals). Notwithstanding the apparent qualification of the Gaussian copula hypothesis for most of the currencies and the stocks, a non-Gaussian copula, such as the Student copula, cannot be rejected if it has sufficiently many ‘degrees of freedom’. As a consequence, it may be very dangerous to embrace blindly the Gaussian copula hypothesis, especially when the coefficient of correlation between the pairs of assets is too high, such that the tail dependence neglected by the Gaussian copula can became large, leading to the ignoring of extreme events which may occur...

Abstract: A rapidly growing number of studies deals with the prediction of epileptic seizures. For this purpose, various techniques derived from linear and nonlinear time series analysis have been applied to the electroencephalogram of epilepsy patients. In none of these works, however, the performance of the seizure prediction statistics is tested against a null hypothesis, an otherwise ubiquitous concept in science. In consequence, the evaluation of the reported performance values is problematic. Here, we propose the technique of seizure time surrogates based on a Monte Carlo simulation to remedy this deficit.

Abstract: Ratio analysis is a commonly used analytical tool for verifying the performance of a firm. While ratios are easy to compute, which in part explains their wide appeal, their interpretation is problematic, especially when two or more ratios provide conflicting signals. Indeed, ratio analysis is often criticized on the grounds of subjectivity, that is the analyst must pick and choose ratios in order to assess the overall performance of a firm. In this paper we demonstrate that Data Envelopment Analysis (DEA) can augment the traditional ratio analysis. DEA can provide a consistent and reliable measure of managerial or operational efficiency of a firm. We test the null hypothesis that there is no relationship between DEA and traditional accounting ratios as measures of performance of a firm. Our results reject the null hypothesis indicating that DEA can provide information to analysts that is additional to that provided by traditional ratio analysis. We also apply DEA to the oil and gas industry to demonstrate how financial analysts can employ DEA as a complement to ratio analysis.

Abstract: Because the probability of obtaining an experimental finding given that the null hypothesis is true [p(F\H0)] is not the same as the probability that the null hypothesis is true given a finding [p(H0\F)], calculating the former probability does not justify conclusions about the latter one. As the standard null-hypothesis significance-testing procedure does just that, it is logically invalid (J. Cohen, 1994). Theoretically, Bayes's theorem yields p(H0\F), but in practice, researchers rarely know the correct values for 2 of the variables in the theorem. Nevertheless, by considering a wide range of possible values for the unknown variables, it is possible to calculate a range of theoretical values for p(H0\F) and to draw conclusions about both hypothesis testing and theory evaluation.

Abstract: Economists have recognized the possibility that a time series may change structure from trend-stationarity to difference-stationarity, or vice versa. Taking difference-stationarity as the null hypothesis, we develop tests for this possibility, where neither the location nor direction of any possible change under the alternative hypothesis need be specified.

Abstract: With a sample of 94 Pleistocene cranial capacities between the time period of 1.8 Ma and 50 Ka now known, we consider the evolution of cranial capacity in Homo, with the null hypothesis that the changes over time are a result of one process. We employ a new method that uses a resam- pling approach to address the limitations imposed on the methods of previous studies. To test the null hypothesis, we examine the distribution of changes in adjacent temporal samples and ask whether there are differences between earlier and later samples. Our analyses do not reject the hypothesis of a single process of brain size change, but they are incompatible with an interpretation of punctuated equilibrium during this period. The results of this paper are difficult to reconcile with the case for cladogenesis in the Homo lineage during the Pleistocene.

Abstract: The interactions between plants of different spe- cies, age or size play an important role in the dynamics of an ecosystem and can induce specific structures. These interac- tions can be studied by analysing the spatial structure of the corresponding bivariate patterns. The intertype L12-function has recently been successfully used in many papers for that purpose. However, when interpreting the results obtained with ecological data, at least two different null hypotheses - inde- pendence or random labelling - can be appropriate, depending on the context of the study and the nature of the data. As these two hypotheses correspond to different confidence intervals, an inappropriate choice of the null hypothesis can lead to misinterpretations of biotic interactions when studying eco- logical data. This problem has rarely been mentioned in the literature. In this paper we clarify the differences between these two null hypotheses, and illustrate the risk of misinterpretation when using an inappropriate null hypothesis. We review the main characteristics of these two hypotheses, and analyse the spatial structure of both real data from forest stands and simulated virtual stands of different structures. We demon- strate that the risk of misinterpretation is quite high, and that extreme misinterpretations, i.e. cases leading to opposite con- clusions in terms of spatial interaction, can occur in a signifi- cant number of cases. We therefore propose some guidelines to help ecologists avoid such misinterpretations.

Abstract: We outline the general framework of adaptive combination tests and discuss their relationship to flexible group sequential designs. An important field of applications is sample size reassessment. We discuss reassessment rules based on conditional power arguments using either the observed or the prefixed effect size. These rules tend to lead to large expected sample sizes for small actual effects. However, the application of a maximal bound for the second stage sample size leads to more favourable properties. Additionally, we consider an optimized reassessment rule in terms of expected sample sizes. Since the adaptive design does not use the classical test statistics for some types of sample size reassessments, the adaptive test may reject the null hypothesis while the classical one-sample test does not. We characterize sample size reassessment rules, where such inconsistencies are avoided. Finally, the extension of flexibility to the number of stages is explored. In the first interim analysis a second interim analysis is only planned if the chance to achieve a decision there is high. This leads to savings in the average number of interim analysis performed, without paying a noticeable price in terms of expected sample size.

Abstract: We investigated the way experienced users interpret Null Hypothesis Significance Testing (NHST) outcomes. An empirical study was designed to compare the reactions of two populations of NHST users, psychological researchers and professional applied statisticians, when faced with contradictory situations. The subjects were presented with the results of an experiment designed to test the efficacy of a drug by comparing two groups (treatment/placebo). Four situations were constructed by combining the outcome of the t test (significant vs. nonsignificant) and the observed difference between the two means D (large vs. small). Two of these situations appeared as conflicting (t significant/D small and t nonsignificant/D large). Three fundamental aspects of statistical inference of statistical inference were investigated by means of open questions: drawing inductive conclusions about the magnitude of the true difference from the data in hand, making predictions for future data, and making decisions about stopping ...

Abstract: Null hypothesis significance tests are commonly used to provide a link between empirical evidence and theoretical interpretation. However, this strategy is prone to the "p-value fallacy" in which effects and interactions are classified as either "noise" or "real" based on whether the associated p value is greater or less than .05. This dichotomous classification can lead to dramatic misconstruals of the evidence provided by an experiment. For example, it is quite possible to have similar patterns of means that lead to entirely different patterns of significance, and one can easily find the same patterns of significance that are associated with completely different patterns of means. Describing data in terms of an inventory of significant and nonsignificant effects can thus completely misrepresent the results. An alternative analytical technique is to identify competing interpretations of the data and then use likelihood ratios to assess which interpretation provides the better account. Several different methods of calculating the likelihood ratios are illustrated. It is argued that this approach satisfies a principle of "graded evidence," according to which similar data should provide similar evidence.

Abstract: This article considers the problem of testing the null hypothesis of stochastic stationarity in time series characterized by variance shifts at some (known or unknown) point in the sample. It is shown that existing stationarity tests can be severely biased in the presence of such shifts, either oversized or undersized, with associated spurious power gains or losses, depending on the values of the breakpoint parameter and on the ratio of the prebreak to postbreak variance. Under the assumption of a serially independent Gaussian error term with known break date and known variance ratio, a locally best invariant (LBI) test of the null hypothesis of stationarity in the presence of variance shifts is then derived. Both the test statistic and its asymptotic null distribution depend on the breakpoint parameter and also, in general, on the variance ratio. Modifications of the LBI test statistic are proposed for which the limiting distribution is independent of such nuisance parameters and belongs to the family of...

Abstract: Epidemiologists face issues of sample size every time they design a study. Sample size determi? nation has two distinct aspects. One is the tech? nical aspect of how to calculate the sample size re? quired to meet the desired Type I error rate and the power for any specified state of nature. (By "state of nature," I mean the exact point in the relevant multidimensional parameter space for the statistical test? ing problem, the point that corresponds to the hy? pothesized effect that one seeks to detect. If the specified state of nature is "close" to any state that satisfies the null hypothesis, a relatively large sample size will be required to achieve the desired power, whereas if the specified state of nature is "far" from the null hypothesis, a relatively small sample size will do.) The second and more philosophic aspect of sample size determination is the question of how to specify the state of nature that is most relevant to the study. The paper by Yang et al.1 is noteworthy in that it provides an avenue for thinking about this more philosophic aspect. Their core idea is that, in designing a study to detect a certain phenomenon (in this case, "gene-environment interaction"), the size of the effect under investigation can be usefully examined from multiple points of view. The authors consider two: one based on the relative odds ratio for interaction (Rt), and the other based on a population attributable fraction attributable to interac? tion (PAFj). Both points of view describe the same phenomenon, the same state of nature. Mathematically, to fix one is to determine the other. Even so, for a given state of nature, the relation between the value of Rt and the corresponding value of PAFt is not intuitively obvi? ous. Consequently, it is useful to calculate both. A comparison of their values provides perspective on the size of interaction that one views as reasonable to detect. The authors' core idea can be useful for design issues in

Abstract: One of the key assumptions of the standard linear instrumental variables (IV) model is that the instruments and endogenous variables are correlated. This is the identification assumption, without which the usual IV estimator is neither consistent nor asymptotically normal. If the correlation between the instruments and the endogenous variables is nonzero, but slight, then the conventional Gaussian asymptotic theory for the IV model can nevertheless provide a very poor approximation to the actual sampling distribution of estimators and test statistics. Recognizing the identification assumption on which the IV model relies, it is quite common in the applied literature to test for instrument relevance by a first-stage F-test. The null hypothesis is one of a total lack of identification. A rejection of this hypothesis by no means implies that issues of weak instruments can be ignored (Staiger and Stock, 1997). But a failure to reject this hypothesis is a strong indication of identification difficulties. The firststage F-test is an important and useful diagnostic in the IV model. The generalized method of moments (GMM) model (Hansen, 1982) nests the linear IV model as a special case. Not surprisingly, analogous issues arise in this model. Researchers have found that, in many contexts, the conventional Gaussian asymptotic theory provides a poor approximation to the sampling distribution of GMM estimators and test statistics. There are many possible reasons why this could happen, but they include identification problems. However, I am aware of no test of the identification condition in the nonlinear-inparameters GMM model in the existing literature. This paper proposes such a

Abstract: Statistical power is the probability of accepting the null hypothesis when it is false (type II error). This research note reports the results of a statistical power analysis of international business research published in the Journal of International Business Studies, Management International Review, the Academy of Management Journal, and the Strategic Management Journal from 1990 to 1999. The results show that, although average statistical power is high compared with other disciplines, it is sufficient only for large effect sizes (ESs). Only studies published in the Journal of International Business Studies and the Academy of Management Journal achieve average statistical power levels that are sufficient for both medium and large ESs. Still the observed likelihood of committing type II errors in international business research is very high for small ESs (92%) and high for medium ESs (45%). In addition, statistical power is not explicitly mentioned or used by international business researchers, a weakness that this note is designed to change.

Abstract: Scientists often need to test hypotheses and construct corresponding confidence intervals. In designing a study to test a particular null hypothesis, traditional methods lead to a sample size large enough to provide sufficient statistical power. In contrast, traditional methods based on constructing a confidence interval lead to a sample size likely to control the width of the interval. With either approach, a sample size so large as to waste resources or introduce ethical concerns is undesirable. This work was motivated by the concern that existing sample size methods often make it difficult for scientists to achieve their actual goals. We focus on situations which involve a fixed, unknown scalar parameter representing the true state of nature. The width of the confidence interval is defined as the difference between the (random) upper and lower bounds. An event width is said to occur if the observed confidence interval width is less than a fixed constant chosen a priori. An event validity is said to occur if the parameter of interest is contained between the observed upper and lower confidence interval bounds. An event rejection is said to occur if the confidence interval excludes the null value of the parameter. In our opinion, scientists often implicitly seek to have all three occur: width, validity, and rejection. New results illustrate that neglecting rejection or width (and less so validity) often provides a sample size with a low probability of the simultaneous occurrence of all three events. We recommend considering all three events simultaneously when choosing a criterion for determining a sample size. We provide new theoretical results for any scalar (mean) parameter in a general linear model with Gaussian errors and fixed predictors. Convenient computational forms are included, as well as numerical examples to illustrate our methods.

Abstract: This article builds a nonparametric method for inference from roll-call cohesion scores. Cohesion scores have been a staple of legislative studies since the publication of Rice’s 1924 thesis. Unfortunately, little effort has been dedicated to understanding their statistical properties or relating them to existing models of legislative behavior. I show how a common use of cohesion scores, testing for distinct voting blocs, is severely biased toward Type I error, practically guaranteeing significant findings even when the null hypothesis is correct. I offer a nonparametric method—permutation analysis—that solves the bias problem and provides for simple and intuitive inference. I demonstrate with an examination of roll-call voting data from the Brazilian National Congress.

Abstract: Two groups of sequential testing procedures are proposed to detect an abrupt change in the distribution of a sequence of observations: truncated and open ended. They are based on large sample strong approximations of the efficient score vector under the null hypothesis of no change and under the alternative hypothesis. An estimator of the time of change is proposed and its approximate bias is analyzed. The estimation of the new parameters that describe the changed distribution naturally follows.

Abstract: A growing literature analyzes determinants of insurance prices using time series data on insurer underwriting margins. If the variables analyzed are stationary, conventional regression models may be appropriately used to test hypotheses. Based on pretests for a unit root, several studies have instead used co-integration analysis to analyze the long-run relationship between purportedly nonstationary underwriting margins and macroeconomic variables. We apply a battery of unit root tests to investigate whether underwriting margins are stationary under different assumptions concerning deterministic components in the data generating process (DGP). When linear and/or quadratic trends are included in the assumed DGPs, the tests reject the null hypothesis of a unit root for loss ratios, expense ratios, combined ratios, and economic loss ratios from 1953 through 1998 for many of the individual lines examined and for all lines combined. Consistent with prior work on whether macroeconomic variables have unit roots, a simulation of test power for underwriting margins during the sample period demonstrates that nonrejections of the null hypothesis of a unit root could easily reflect low power. The overall findings suggest that conventional regression methods can be used appropriately to analyze underwriting margins after controlling for deterministic influences and transforming any nonstationary regressors.

Abstract: This paper re-evaluates the time series properties of financial ratios. It presents new empirical analysis which explicitly allows for the possibility that financial ratios can be characterized as non-linear mean-reverting processes. Financial ratios are widely employed as explanatory variables in accounting and finance research with applications ranging from the determinants of auditors' compensation to explaining firms' investment decisions. An implicit assumption in this empirical work is that the ratios are stationary so that the postulated models can be estimated by classical regression methods. However, recent empirical work on the time series properties of corporate financial ratios has reported that the level of the majority of ratios is described by non-stationary, (1), integrated processes and that the ratio differences are parsimoniously described by random walks. We hypothesize that financial ratios may follow a random walk near their target level, but that the more distant a ratio is from target, the more likely the firm is to take remedial action to bring it back towards target. This behavior will result in a significant size distortion of the conventional stationarity tests and lead to frequent non-rejection of the null hypothesis of non-stationarity, a finding which undermines the use of these ratios as reliable conditioning variables for the explanation of firms' decisions.

Abstract: This paper considers inference for the break point in the segmented regression or piece-wise regression model. Standard likelihood theory does not apply because the break point is absent under the null hypothesis. We use results by DAVIES for this type of non-standard set-up [Biometrika 64 (1977), 247-254 and 74 (1987), 33-43] to obtain a test for the null hypothesis of no break point. A confidence interval can be constructed provided replicate data are available. The methods are exemplified using two longitudinal datasets, the one from ecology, the anther from pharmacology.

Abstract: This paper re-evaluates the time series properties of financial ratios. It presents new empirical analysis which explicitly allows for the possibility that financial ratios can be characterized as non-linear mean-reverting processes. Financial ratios are widely employed as explanatory variables in accounting and finance research with applications ranging from the determinants of auditors’ compensation to explaining firms’ investment decisions. An implicit assumption in this empirical work is that the ratios are stationary so that the postulated models can be estimated by classical regression methods. However, recent empirical work on the time series properties of corporate financial ratios has reported that the level of the majority of ratios is described by non-stationary, I(1), integrated processes and that the ratio differences are parsimoniously described by random walks. We hypothesize that financial ratios may follow a random walk near their target level, but that the more distant a ratio is from target, the more likely the firm is to take remedial action to bring it back towards target. This behavior will result in a significant size distortion of the conventional stationarity tests and lead to frequent non-rejection of the null hypothesis of non-stationarity, a finding which undermines the use of these ratios as reliable conditioning variables for the explanation of firms’ decisions.

Abstract: What is negative about negative data? Scientists understand negative data from our training in data analysis and statistics, where we use a positive concept of negative data. Negative data are data that do not enable us to reject our null hypothesis. Such data are often difficult to publish because it is not possible to prove the null hypothesis. Every active research scientist has a large drawer where these data languish. In the area of environmental biosafety, however, some scientists have begun to use “negative data” in a second, normative way. This normative concept of negative data has socio-political connotations, where “negative” data has come to connote results that GMO proponents could use to support, and GMO opponents could use to oppose the development of GMOs. This politicization of GMO biosafety research is worthy of study in its own right, but EBR is prepared to accept any kind of “negative” or “positive” data.

Abstract: This paper proposes a new testing strategy for unemployment hysteresis as the joint restriction of a unit-root in the unemployment rate and no feedback effect of unemployment in the Phillips wage equation. The associated test statistics are derived when this joint restriction is imposed and when a sequential two steps testing strategy is adopted. An empirical application leads to reject the null hypothesis of wage hysteresis for most of our OECD countries. Evidence against hysteresis is reinforced when accounting for wage adjustments in the bivariate approach.

Abstract: Using one of the key property of copulas that they remain invariant under an arbitrary monotonous change of variable, we investigate the null hypothesis that the dependence between financial assets can be modeled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks are compatible with the Gaussian copula hypothesis, while this hypothesis can be rejected for the dependence between pairs of commodities (metals). Notwithstanding the apparent qualification of the Gaussian copula hypothesis for most of the currencies and the stocks, a non-Gaussian copula, such as the Student's copula, cannot be rejected if it has sufficiently many "degrees of freedom". As a consequence, it may be very dangerous to embrace blindly the Gaussian copula hypothesis, specially when the correlation coefficient between the pair of asset is too high as the tail dependence neglected by the Gaussian copula can be as large as 0.6, i.e., three out five extreme events which occur in unison are missed.

Abstract: We propose a new measure of proximity of samples based on confidence limits for the bulk of a population constructed using order statistics. For this measure of proximity, we compute approximate confidence limits corresponding to a given significance level in the cases where the null hypothesis on the equality of hypothetical distribution functions may or may not be true. We compare this measure of proximity with the Kolmogorov–Smirnov and Wilcoxon statistics for samples from various populations. On the basis of the proposed measure of proximity, we construct a statistical test for testing the hypothesis on the equality of hypothetical distribution functions.