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.

Experimental support for the make-up hypothesis in nestling tawny owls (Strix aluco)

Body condition can affect coloration of traits used in sexual selection and parent-offspring communication by inducing rapid internal changes in pigment concentration or aggregation, thickness of collagen arrays, or blood flux. The recent "makeup hypothesis" proposes an alternative honesty-reinforcing mechanism, with behaviorally mediated deposition of substances on body surfaces ("cosmetics") generating covariation between body condition and coloration. In birds, the uropygial gland wax is actively spread on feathers using the bill and changes in its deposition rate may cause rapid changes in bill and plumage coloration. Using tawny owl nestlings, we tested 3 predictions of the makeup hypothesis, namely that 1) quantity of preen wax deposited accounts for variation in bill coloration, 2) an immune stimulation (induced by injection of a lipopolysaccharide [LPS]) impairs uropygial gland wax production, and 3) different intensities of immune stimulations (strong vs. weak stimulations induced by injections of either LPS or phytohemagglutinin [PHA], respectively) and high versus low food availabilities result in different bill colorations. We found that 1) preen wax reduced bill brightness, 2) a challenge with LPS impaired uropygial gland development, and 3) nestlings challenged with LPS had a brighter bill than PHA-injected nestlings, whereas diet manipulation had no significant effect. Altogether, these results suggest that a strong immune challenge may decrease preen wax deposition rate on the bill of nestling birds, at least by impairing gland wax production, which causes a change in bill coloration. Our study therefore highlights that cosmetic colors might signal short-term variation in immunological status.

The V-region disease hypothesis: evidence from autoimmune encephalomyelitis.

Experimental allergic encephalomyelitis has been shown to have an immunological basis. In fact, the disease can be induced by T cells specific for myelin basic protein, a molecule found in abundance in the central nervous system. In this article, Ellen Heber-Katz and Hans Acha-Orbea discuss the T-cell receptor (TCR) repertoire of the encephalitogenic T-cell response, and show that a limited V gene pool, in fact a single V beta and two V alpha families, are being used by the PL/J and B10.PL mice and by every rat strain examined, even though the antigenic determinants and the major histocompatibility complex (MHC) molecules are different in all cases. This extraordinary finding suggests that the TCR is involved in encephalitogenicity in a way that not only involves the recognition of antigen in association with MHC, but also as an effector molecule that results in encephalitis. If this is true, it implies that TCRs, in general, play more than one role in mammalian physiology.

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.

Comparing and validating hypothesis test procedures: Graphical and numerical tools

When the behaviour of a specific hypothesis test statistic is studied by aMonte Carlo experiment, the usual way to describe its quality is by givingthe empirical level of the test. As an alternative to this procedure, we usethe empirical distribution of the obtained \emph{p-}values and exploit itsinformation both graphically and numerically.

The squeeze cell hypothesis for the activation of jasmonate synthesis in response to wounding

Jasmonates are lipid mediators that control defence gene expression in response to wounding and other environmental stresses. These small molecules can accumulate at distances up to several cm from sites of damage and this is likely to involve cell-to-cell jasmonate transport. Also, and independently of jasmonate synthesis, transport and perception, different long-distance wound signals that stimulate distal jasmonate synthesis are propagated at apparent speeds of several cmmin(-1) to tissues distal to wounds in a mechanism that involves clade 3 GLUTAMATE RECEPTOR-LIKE (GLR) genes. A search for jasmonate synthesis enzymes that might decode these signals revealed LOX6, a lipoxygenase that is necessary for much of the rapid accumulation of jasmonic acid at sites distal to wounds. Intriguingly, the LOX6 promoter is expressed in a distinct niche of cells that are adjacent to mature xylem vessels, a location that would make these contact cells sensitive to the release of xylem water column tension upon wounding. We propose a model in which rapid axial changes in xylem hydrostatic pressure caused by wounding travel through the vasculature and lead to slower, radially dispersed pressure changes that act in a clade 3 GLR-dependent mechanism to promote distal jasmonate synthesis.

P value and the theory of hypothesis testing: an explanation for new researchers.

In the 1920s, Ronald Fisher developed the theory behind the p value and Jerzy Neyman and Egon Pearson developed the theory of hypothesis testing. These distinct theories have provided researchers important quantitative tools to confirm or refute their hypotheses. The p value is the probability to obtain an effect equal to or more extreme than the one observed presuming the null hypothesis of no effect is true; it gives researchers a measure of the strength of evidence against the null hypothesis. As commonly used, investigators will select a threshold p value below which they will reject the null hypothesis. The theory of hypothesis testing allows researchers to reject a null hypothesis in favor of an alternative hypothesis of some effect. As commonly used, investigators choose Type I error (rejecting the null hypothesis when it is true) and Type II error (accepting the null hypothesis when it is false) levels and determine some critical region. If the test statistic falls into that critical region, the null hypothesis is rejected in favor of the alternative hypothesis. Despite similarities between the two, the p value and the theory of hypothesis testing are different theories that often are misunderstood and confused, leading researchers to improper conclusions. Perhaps the most common misconception is to consider the p value as the probability that the null hypothesis is true rather than the probability of obtaining the difference observed, or one that is more extreme, considering the null is true. Another concern is the risk that an important proportion of statistically significant results are falsely significant. Researchers should have a minimum understanding of these two theories so that they are better able to plan, conduct, interpret, and report scientific experiments.