Testing hypotheses in order

In certain circumstances, one wishes to test one hypothesisonly if certain other hypotheses have been rejected. This orderingof hypotheses simplifies the task of controlling the probabilityof rejecting any true hypothesis. In an example from an observationalstudy, a treated group is shown to be further from both of twocontrol groups than the two control groups are from each other.     

A comparison of exact, mid-P, and score tests for matched case-control studies

A recently developed algorithm for generating the distribution of sufficient statistics for conditional logistic models can be put to a twofold use. First, it provides an avenue for performing inference for matched case-control studies that does not rely on the assumption of a large sample size. Second, joint distributions generated by this algorithm can be used to make comparisons of various inferential procedures that are free from Monte Carlo sampling errors. In this paper, these two features of the algorithm are utilized to compare small-sample properties of the exact, mid-P value, and score tests for a conditional logistic model with two unmatched binary covariates. Both uniparametric and multiparametric tests, performed at a nominal significance level of .05, were studied. It was found that the actual significance levels of the mid-P test tend to be closer to the nominal level when compared with those of the other two tests.     

Trophic egg laying: hypotheses and tests

Trophic egg-laying – wherein mothers provide non-developing eggs for offspring to eat – has attracted much empirical attention to diverse taxa (e.g. amphibians, non-social and eusocial insects, fish, and marine gastropods). However, there has been been only a limited exchange of ideas among studies of different taxa. We advocate a unified approach to the study of trophic eggs within an evolutionary ecological framework. In this paper, we stress the importance of elucidating the adaptive function of trophic eggs through explicit hypothesis testing, and our primary objective is to outline key experiments that can test adaptive and functional hypotheses. Currently, some cases of hypothesized trophic eggs may simply represent offspring consumption of eggs that failed to develop for non-adaptive reasons (e.g. sperm limitation). Furthermore, in many trophic egg-laying species, it is unclear whether trophic eggs have evolved to provision offspring or to reduce cannibalism among offspring. With increased focus on theory and hypothesis testing, the study of trophic eggs can offer important insight into topics such as sibling rivalry, parent–offspring conflict, and parental care.     

Age and reproduction in birds - hypotheses and tests

It is well known that reproductive performance improves with age in birds. Many hypotheses, involving factors such as differential survival, delayed breeding, breeding experience, foraging ability and reproductive effort, have been proposed to explain this pattern. Although these hypotheses are not mutually exclusive, they can be classified in three major groups relating to progressive appearance or disappearance of phenotypes, age-related improvements of competence, and optimization of reproductive effort. However, a closer examination of the literature reveals that only few studies have rigorously tested the hypotheses. Future work should focus on carefully designed tests that critically investigate the hypotheses.     

Testing separate families of segregation hypotheses: bootstrap methods.

Aspects of the statistical modeling and assessment of hypotheses concerning quantitative traits in genetics research are discussed. It is suggested that a traditional approach to such modeling and hypothesis testing, whereby competing models are "nested" in an effort to simplify their probabilistic assessment, can be complimented by an alternative statistical paradigm - the separate-families-of-hypotheses approach to segregation analysis. Two bootstrap-based methods are described that allow testing of any two, possibly non-nested, parametric genetic hypotheses. These procedures utilize a strategy in which the unknown distribution of a likelihood ratio-based test statistic is simulated, thereby allowing the estimation of critical values for the test statistic. Though the focus of this paper concerns quantitative traits, the strategies described can be applied to qualitative traits as well. The conceptual advantages and computational ease of these strategies are discussed, and their significance levels and power are examined through Monte Carlo experimentation. It is concluded that the separate-families-of-hypotheses approach, when carried out with the methods described in this paper, not only possesses some favorable statistical properties but also is well suited for genetic segregation analysis.     

Effects of long-range correlations in DNA on sequence alignment score statistics.

Long-range correlations in genomic base composition are a ubiquitous statistical feature among many eukaryotic genomes. In this article, these correlations are shown to substantially influence the statistics of sequence alignment scores. Using a Gaussian approximation to model the correlated score landscape, we calculate the corrections to the scale parameter lambda of the extreme value distribution of alignment scores. Our approximate analytic results are supported by a detailed numerical study based on a simple algorithm to efficiently generate long-range correlated random sequences. We find both, mean and exponential tail of the score distribution for long-range correlated sequences to be substantially shifted compared to random sequences with independent nucleotides. The significance of measured alignment scores will therefore change upon incorporation of the correlations in the null model. We discuss the magnitude of this effect in a biological context.     

Testing hypotheses regarding the genetics of adaptation

Many of the hypotheses regarding the genetics of adaptation require that one know specific details about the genetic basis of complex traits, such as the number and effects of the loci involved. Developments in molecular biology have made it possible to create relatively dense maps of markers that can potentially be used to map genes underlying specific traits. However, there are a number of reasons to doubt that such mapping will provide the level of resolution necessary to specifically address many evolutionary questions. Moreover, evolutionary change is built upon the substitution of individual mutations, many of which may now be cosegregating in the same allele. In order for this developing area not to become a mirage that traps the efforts of an entire field, the genetic dissection of adaptive traits should be conducted within a strict hypothesis-testing framework and within systems that promise a reasonable chance of identifying the specific genetic changes of interest. Continuing advances in molecular technology may lead the way here, but some form of genetic testing is likely to be forever required.     

Testing hypotheses for maternal effects in Daphnia magna

Maternal effects are widely observed, but their adaptive nature remains difficult to describe and interpret. We investigated adaptive maternal effects in a clone of the crustacean Daphnia magna, experimentally varying both maternal age and maternal food and subsequently varying food available to offspring. We had two main predictions: that offspring in a food environment matched to their mothers should fare better than offspring in unmatched environments, and that offspring of older mothers would fare better in low food environments. We detected numerous maternal effects, for example offspring of poorly fed mothers were large, whereas offspring of older mothers were both large and showed an earlier age at first reproduction. However, these maternal effects did not clearly translate into the predicted differences in reproduction. Thus, our predictions about adaptive maternal effects in response to food variation were not met in this genotype of Daphnia magna.     

Testing goodness-of-fit in logistic case-control studies

We present a goodness-of-fit test for the logistic regressionmodel under case-control sampling. The test statistic is constructedvia a discrepancy between two competing kernel density estimatorsof the underlying conditional distributions given case-controlstatus. The proposed goodness-of-fit test is shown to comparevery favourably with previously proposed tests for case-controlsampling in terms of power. The test statistic can be easilycomputed as a quadratic form in the residuals from a prospectivelogistic regression maximum likelihood fit. In addition, theproposed test is affine invariant and has an alternative representationin terms of empirical characteristic functions.     

Testing hypotheses of adaptive variation in cricket ovipositor lengths

We experimentally tested a series of hypotheses proposed by Masaki (1979, 1986) for the evolution of ovipositor length in crickets. Female crickets use the ovipositor to bury eggs in the soil, where it was hypothesized to protect their eggs from desiccation, cold and other disturbance. However, we found no effect of depth on the overwinter survival of eggs of three species of Nemobiinae. The probability of hatchlings reaching the soil surface was negatively correlated with depth documenting a significant cost to females laying eggs deep in the soil. Hatchling survival may be an important agent of selection on ovipositor length in habitats of different soil moistures. Hatchling survival in the soil was also correlated with body size, which may impose a constraint on egg-size fecundity trade-offs. Females of a bivoltine population of Allonemobius socius lay eggs at shallower depths when reared under summer compared to fall conditions and, therefore, may be able to respond to selection through behavioral plasticity when morphological adaptation is constrained by allometry.     

Testing superiority and non-inferiority hypotheses in active controlled clinical trials

Switching between testing for superiority and non-inferiority has been an important statistical issue in the design and analysis of active controlled clinical trial. In practice, it is often conducted with a two-stage testing procedure. It has been assumed that there is no type I error rate adjustment required when either switching to test for non-inferiority once the data fail to support the superiority claim or switching to test for superiority once the null hypothesis of non-inferiority is rejected with a pre-specified non-inferiority margin in a generalized historical control approach. However, when using a cross-trial comparison approach for non-inferiority testing, controlling the type I error rate sometimes becomes an issue with the conventional two-stage procedure. We propose to adopt a single-stage simultaneous testing concept as proposed by Ng (2003) to test both non-inferiority and superiority hypotheses simultaneously. The proposed procedure is based on Fieller's confidence interval procedure as proposed by Hauschke et al. (1999).