The algebraic equality of two asymptotic tests for the hypothesis that a normal distribution has a specified correlation matrix

It is proved the algebraic equality between Jennrich's (1970) asymptotic$X^2$ test for equality of correlation matrices, and a Wald test statisticderived from Neudecker and Wesselman's (1990) expression of theasymptoticvariance matrix of the sample correlation matrix.

Bringing game theory to hypothesis testing: Establishing finite sample bounds on inference

Small sample properties are of fundamental interest when only limited data is avail-able. Exact inference is limited by constraints imposed by speci.c nonrandomizedtests and of course also by lack of more data. These e¤ects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a .ctitious game against nature.We use this method to investigate sequential tests for the di¤erence between twomeans when outcomes are constrained to belong to a given bounded set. Tests ofinequality and of noninferiority are included. We .nd that inference in terms oftype II error based on a balanced sample cannot be improved by sequential sampling or even by observing counter factual evidence providing there is a reasonable gap between the hypotheses.

Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size

This paper analyzes whether standard covariance matrix tests work whendimensionality is large, and in particular larger than sample size. Inthe latter case, the singularity of the sample covariance matrix makeslikelihood ratio tests degenerate, but other tests based on quadraticforms of sample covariance matrix eigenvalues remain well-defined. Westudy the consistency property and limiting distribution of these testsas dimensionality and sample size go to infinity together, with theirratio converging to a finite non-zero limit. We find that the existingtest for sphericity is robust against high dimensionality, but not thetest for equality of the covariance matrix to a given matrix. For thelatter test, we develop a new correction to the existing test statisticthat makes it robust against high dimensionality.

Exact and approximate stepdown methods for multiple hypothesis testing

Consider the problem of testing k hypotheses simultaneously. In this paper,we discuss finite and large sample theory of stepdown methods that providecontrol of the familywise error rate (FWE). In order to improve upon theBonferroni method or Holm's (1979) stepdown method, Westfall and Young(1993) make eective use of resampling to construct stepdown methods thatimplicitly estimate the dependence structure of the test statistics. However,their methods depend on an assumption called subset pivotality. The goalof this paper is to construct general stepdown methods that do not requiresuch an assumption. In order to accomplish this, we take a close look atwhat makes stepdown procedures work, and a key component is a monotonicityrequirement of critical values. By imposing such monotonicity on estimatedcritical values (which is not an assumption on the model but an assumptionon the method), it is demonstrated that the problem of constructing a validmultiple test procedure which controls the FWE can be reduced to the problemof contructing a single test which controls the usual probability of a Type 1error. This reduction allows us to draw upon an enormous resamplingliterature as a general means of test contruction.

The economic effects of the Protestant Reformation: Testing the Weber hypothesis in the German Lands

Many theories, most famously Max Weber s essay on the Protestant ethic, have hypothesizedthat Protestantism should have favored economic development. With their considerablereligious heterogeneity and stability of denominational affiliations until the 19th century, theGerman Lands of the Holy Roman Empire present an ideal testing ground for this hypothesis.Using population figures in a dataset comprising 272 cities in the years 1300 1900, I find no effectsof Protestantism on economic growth. The finding is robust to the inclusion of a varietyof controls, and does not appear to depend on data selection or small sample size. In addition,Protestantism has no effect when interacted with other likely determinants of economic development.I also analyze the endogeneity of religious choice; instrumental variables estimates ofthe effects of Protestantism are similar to the OLS results.

Hypothesis on immigration and welfare

The number of hypothesis trying to explain which are the reasons behind the decision to migrate to work into a developed country are diverse and at the same time, difficult to test due to the multiplicity of factors which affect it. This papers attempts to move forward trying to disentangle which are the socio-economic factors that explain the differences in the figures of immigrants in the OECD countries. We show empirical evidence about the determinants of the migratory flows to 17 OECD countries from 65 countries in the 1980-2000 period. Our results reveal the importance to differentiate the inflows composition by at least income in the origin countries. Thus, regarding inflows from non-high-income countries, the results suggest that there is a pull effect from monetary and not real income, and then, the welfare magnets hypothesis should be rejected. This group reacts more to the migratory policy than the inflows coming from high-income countries, although those policies designed to slow down the inflows have not been able, in the aggregate, to reduce them.

The quasi-judicial role of large retailers: An efficiency hypothesis of their relation with suppliers

The paper explores an efficiency hypothesis regarding the contractual process between large retailers, such as Wal-Mart and Carrefour, and their suppliers. The empirical evidence presented supports the idea that large retailers play a quasi-judicial role, acting as "courts of first instance" in their relationships with suppliers. In this role, large retailers adjust the terms of trade to on-going changes and sanction performance failures, sometimes delaying payments. A potential abuse of their position is limited by the need for re-contracting and preserving their reputations. Suppliers renew their confidence in their retailers on a yearly basis, through writing new contracts. This renovation contradicts the alternative hypothesis that suppliers are expropriated by large retailers as a consequence of specific investments.

Time-scale and other invariants of integrative mechanical behavior in living cells.

In dealing with systems as complex as the cytoskeleton, we need organizing principles or, short of that, an empirical framework into which these systems fit. We report here unexpected invariants of cytoskeletal behavior that comprise such an empirical framework. We measured elastic and frictional moduli of a variety of cell types over a wide range of time scales and using a variety of biological interventions. In all instances elastic stresses dominated at frequencies below 300 Hz, increased only weakly with frequency, and followed a power law; no characteristic time scale was evident. Frictional stresses paralleled the elastic behavior at frequencies below 10 Hz but approached a Newtonian viscous behavior at higher frequencies. Surprisingly, all data could be collapsed onto master curves, the existence of which implies that elastic and frictional stresses share a common underlying mechanism. Taken together, these findings define an unanticipated integrative framework for studying protein interactions within the complex microenvironment of the cell body, and appear to set limits on what can be predicted about integrated mechanical behavior of the matrix based solely on cytoskeletal constituents considered in isolation. Moreover, these observations are consistent with the hypothesis that the cytoskeleton of the living cell behaves as a soft glassy material, wherein cytoskeletal proteins modulate cell mechanical properties mainly by changing an effective temperature of the cytoskeletal matrix. If so, then the effective temperature becomes an easily quantified determinant of the ability of the cytoskeleton to deform, flow, and reorganize.

Anàlisi factorial confirmatòria per a variables categòriques: Aplicació al qüestionari de discapacitat WHODAS-II

Objective: To describe the methodology of Confirmatory Factor Analyis for categorical items and to apply this methodology to evaluate the factor structure and invariance of the WHO-Disability Assessment Schedule (WHODAS-II) questionnaire, developed by the World HealthOrganization.Methods: Data used for the analysis come from the European Study of Mental Disorders(ESEMeD), a cross-sectional interview to a representative sample of the general population of 6 european countries (n=8796). Respondents were administered a modified version of theWHODAS-II, that measures functional disability in the previous 30 days in 6 differentdimensions: Understanding and Communicating; Self-Care, Getting Around, Getting Along withOthers, Life Activities and Participation. The questionnaire includes two types of items: 22severity items (5 points likert) and 8 frequency items (continuous). An Exploratory factoranalysis (EFA) with promax rotation was conducted on a random 50% of the sample. Theremaining half of the sample was used to perform a Confirmatory Factor Analysis (CFA) inorder to compare three different models: (a) the model suggested by the results obtained in theEFA; (b) the theoretical model suggested by the WHO with 6 dimensions; (c) a reduced modelequivalent to model b where 4 of the frequency items are excluded. Moreover, a second orderfactor was also evaluated. Finally, a CFA with covariates was estimated in order to evaluatemeasurement invariance of the items between Mediterranean and non-mediterranean countries.Results: The solution that provided better results in the EFA was that containing 7 factors. Twoof the frequency items presented high factor loadings in the same factor, and one of thempresented factor loadings smaller than 0.3 with all the factors. With regard to the CFA, thereduced model (model c) presented the best goodness of fit results (CFI=0.992,TLI=0.996,RMSEA=0.024). The second order factor structure presented adequate goodness of fit (CFI=0.987,TLI=0.991, RMSEA=0.036). Measurement non-invariance was detected for one of the items of thequestionnaire (FD20 ¿ Embarrassment due to health problems).Conclusions: AFC confirmed the initial hypothesis about the factorial structure of the WHODAS-II in 6factors. The second order factor supports the existence of a global dimension of disability. The use of 4of the frequency items is not recommended in the scoring of the corresponding dimensions.

Lag-one autocorrelation in short series: Estimation and hypothesis testing

In the first part of the study, nine estimators of the first-order autoregressive parameter are reviewed and a new estimator is proposed. The relationships and discrepancies between the estimators are discussed in order to achieve a clear differentiation. In the second part of the study, the precision in the estimation of autocorrelation is studied. The performance of the ten lag-one autocorrelation estimators is compared in terms of Mean Square Error (combining bias and variance) using data series generated by Monte Carlo simulation. The results show that there is not a single optimal estimator for all conditions, suggesting that the estimator ought to be chosen according to sample size and to the information available of the possible direction of the serial dependence. Additionally, the probability of labelling an actually existing autocorrelation as statistically significant is explored using Monte Carlo sampling. The power estimates obtained are quite similar among the tests associated with the different estimators. These estimates evidence the small probability of detecting autocorrelation in series with less than 20 measurement times.

Differences in phasic development rate amongst wheat cultivars independent of responses to photoperiod and vernalization. A viewpoint of the intrinsic earliness hypothesis

Differences amongst wheat cultivars in the rate of reproductive development are largely dependent on differences in their sensitivity to photoperiod and vernalization. However, when these responses are accounted for, by growing vernalized seedlings under long photoperiods, cultivars can still differ markedly in time to ear emergence. Control of rate of development by this ‘third factor’ has been poorly understood and is variously referred to as intrinsic earliness, earliness in the narrow sense, basic vegetative period, earliness per se, and basic development rate. Certain assumptions are made in the concept of intrinsic earliness. They are that differences in intrinsic earliness (i) are independent of the responses of the cultivars to photoperiod and vernalization, (ii) apply only to the length of the vegetative period up to floral initiation (as suggested by several authors), (iii) are maintained under different temperatures, measured either in days or degree days. As a consequence of this, the ranking of cultivars (from intrinsically early to intrinsically late) must be maintained at different temperatures. This paper, by the re-analysis of published data, examines the extent to which these assumptions can be supported. Although it is shown that intrinsic earliness operates independently of photoperiod and vernalization responses, the other assumptions were not supported. The differences amongst genotypes in time to ear emergence, grown under above-optimum vernalization and photoperiod (that is when the response to these factors is saturated), were not exclusively due to parallel differences in the length of the vegetative phase, and the length of the reproductive phase was independent of that of the vegetative phase. Thus, it would be possible to change the relative allocation of time to vegetative and reproductive periods with no change in the full period to ear emergence. The differences in intrinsic earliness between cultivars were modified by the temperature regime under which they were grown, i.e. the difference between cultivars (both considering the full phase to ear emergence or some sub-phases) was not a constant amount of time or thermal time at different temperatures. In addition, in some instances genotypes changed their ranking for ‘intrinsic earliness’ depending on the temperature regime. This was interpreted to mean that while all genotypes are sensitive to temperature they differ amongst themselves in the extent of that sensitivity. Therefore, ‘intrinsic earliness’ should not be considered as a static genotypic characteristic, but the result of the interaction between the genotype and temperature. Intrinsic earliness is therefore likely to be related to temperature sensitivity. Some implications of these conclusions for plant breeding and crop simulation modelling are discussed.

The differentiation hypothesis and the Flynn effect

Many studies have shown that IQs have been increasing over the last half century. These increases have come to be known as «the Flynn effect». The «Flynn effect» represents a difference on ability-level between groups of the same age but different cohort. The ability-level differentiation hypothesis represents a difference on the relevance of cognitive factors between groups of high and low ability. Hence, it should be possible to imitate the ability-level differentiation effect by comparing groups of the same age but different cohort. The indifferentiation hypothesis represents no differences on the relevance of cognitive abilities in all age groups within the same cohort. The aim of the present study is to test the relationships between these phenomena. For this purpose we analyzed the American standardisation samples of the WISC, WISC-R and WISC-III. Results support the link between the Flynn effect and the differentiation hypothesis. Also, reported evidence replicate previous findings supporting the indifferentiation hypothesis. Implications for the assessment of the intelligence are discussed.

Task complexity, the Cognition Hypothesis and second language learning and performance

In this paper we describe a taxonomy of task demands which distinguishes between Task Complexity, Task Condition and Task Difficulty. We then describe three theoretical claims and predictions of the Cognition Hypothesis (Robinson 2001, 2003b, 2005a) concerning the effects of task complexity on: (a) language production; (b) interaction and uptake of information available in the input to tasks; and (c) individual differences-task interactions. Finally we summarize the findings of the empirical studies in this special issue which all address one or more of these predictions and point to some directions for continuing, future research into the effects of task complexity on learning and performance.

The spreading of the introduced seaweed Caulerpa taxifolia (Vahl) C. Agardh in the Mediterranean Sea: testing the boat transportation hypothesis

The Spreading of the Introduced Seaweed Caulerpa taxifolia (Vahl) C. Agardh in the Mediterranean Sea: Testing the Boat Transportation Hypothesis

More evidence concerning the aspect hypothesis: The acquisition of English progressive aspect by Catalan-Spanish instructed learners

A robust finding of studies investigating the Aspect Hypothesis is that learners at early stages of acquisition show a strong preference for using the progressive aspect as associated with activity verbs. As they advance in their acquisition of the second or foreign language, learners move from this prototypical association to associations traditionally considered to be more peripheral (e.g.-ing with accomplishments or achievements). Within this framework, the goal of this paper is to provide further evidence from groups of learners with different proficiency levels with regard to the acquisition of progressive aspect by tutored learners of English who are bilingual Catalan-Spanish. This is done by eliciting data by means of two different task types and by looking at both tokens and types. Our results are consistent with previous research according to which-ing morphology is closely associated with durative lexical aspect, although not necessarily with activity predicates. The study also shows that the type of task has an influence on the frequency and the distribution of learners" progressive forms.