Rank test of location optimal for hyperbolic secant distribution

There are at least two reasons for a symmetric, unimodal, diffuse tailed hyperbolic secant distribution to be interesting in real-life applications. It displays one of the common types of non normality in natural data and is closely related to the logistic and Cauchy distributions that often arise in practice. To test the difference in location between two hyperbolic secant distributions, we develop a simple linear rank test with trigonometric scores. We investigate the small-sample and asymptotic properties of the test statistic and provide tables of the exact null distribution for small sample sizes. We compare the test to the Wilcoxon two-sample test and show that, although the asymptotic powers of the tests are comparable, the present test has certain practical advantages over the Wilcoxon test.

Comparative phylogeographic summary statistics for testing simultaneous vicariance

Testing for simultaneous vicariance across comparative phylogeographic data sets is a notoriously difficult problem hindered by mutational variance, the coalescent variance, and variability across pairs of sister taxa in parameters that affect genetic divergence. We simulate vicariance to characterize the behaviour of several commonly used summary statistics across a range of divergence times, and to characterize this behaviour in comparative phylogeographic datasets having multiple taxon-pairs. We found Tajima's D to be relatively uncorrelated with other summary statistics across divergence times, and using simple hypothesis testing of simultaneous vicariance given variable population sizes, we counter-intuitively found that the variance across taxon pairs in Nei and Li's net nucleotide divergence (pi(net)), a common measure of population divergence, is often inferior to using the variance in Tajima's D across taxon pairs as a test statistic to distinguish ancient simultaneous vicariance from variable vicariance histories. The opposite and more intuitive pattern is found for testing more recent simultaneous vicariance, and overall we found that depending on the timing of vicariance, one of these two test statistics can achieve high statistical power for rejecting simultaneous vicariance, given a reasonable number of intron loci (> 5 loci, 400 bp) and a range of conditions. These results suggest that components of these two composite summary statistics should be used in future simulation-based methods which can simultaneously use a pool of summary statistics to test comparative the phylogeographic hypotheses we consider here.

Future long-horizon performance measurement conditional on past survival

This paper examines the measurement of long-horizon abnormal performance when stock selection is conditional on an extended period of past survival. Filtering on survival results in a sample driven towards more-established, frequently traded stocks and this has implications for the choice of benchmark used in performance measurement (especially in the presence of the well-documented size effect). A simulation study is conducted to document the properties of commonly employed performance measures conditional on past survival. The results suggest that the popular index benchmarks used in long-horizon event studies are severely biased and yield test statistics that are badly misspecified. In contrast, a matched-stock benchmark based on size and industry performs consistently well. Also, an eligible-stock index designed to mitigate the influence of the size effect proves effective.

Test-retest reliability of four physical activity measures used in population surveys

Accurate monitoring of prevalence and trends in population levels of physical activity (PA) is a fundamental public health need. Test-retest reliability (repeatability) was assessed in population samples for four self-report PA measures: the Active Australia survey (AA, N=356), the short International Physical Activity Questionnaire (IPAQ, N=104), the physical activity items in the Behavioral Risk Factor Surveillance System (BRFSS, N=127) and in the Australian National Health Survey (NHS, N=122). Percent agreement and Kappa statistics were used to assess reliability of classification of activity status as 'active', 'insufficiently active' or 'sedentary'. Intraclass correlations (ICCs) were used to assess agreement on minutes of activity reported for each item of each survey and for total minutes. Percent agreement scores for activity status were very good on all four instruments, ranging from 60% for the NHS to 79% for the IPAQ. Corresponding Kappa statistics ranged from 0.40 (NHS) to 0.52 (AA). For individual items, ICCs were highest for walking (0.45 to 0.78) and vigorous activity (0.22 to 0.64) and lowest for the moderate questions (0.16 to 0.44). All four measures provide acceptable levels of test-retest reliability for assessing both activity status and sedentariness, and moderate reliability for assessing total minutes of activity.

A time-domain test for some types of nonlinearity

The bispectrum and third-order moment can be viewed as equivalent tools for testing for the presence of nonlinearity in stationary time series. This is because the bispectrum is the Fourier transform of the third-order moment. An advantage of the bispectrum is that its estimator comprises terms that are asymptotically independent at distinct bifrequencies under the null hypothesis of linearity. An advantage of the third-order moment is that its values in any subset of joint lags can be used in the test, whereas when using the bispectrum the entire (or truncated) third-order moment is required to construct the Fourier transform. In this paper, we propose a test for nonlinearity based upon the estimated third-order moment. We use the phase scrambling bootstrap method to give a nonparametric estimate of the variance of our test statistic under the null hypothesis. Using a simulation study, we demonstrate that the test obtains its target significance level, with large power, when compared to an existing standard parametric test that uses the bispectrum. Further we show how the proposed test can be used to identify the source of nonlinearity due to interactions at specific frequencies. We also investigate implications for heuristic diagnosis of nonstationarity.

Test-retest reliability and practice effects of a rapid screen of mild traumatic brain injury

Test-retest reliabilities and practice affects of measures from the Rapid Screen of Concussion (RSC), in addition to the Digit Symbol Substitution Test (Digit Symbol), were examined. Twenty five male participants were tested three times; each testing session scheduled a week apart. The test-retest reliability estimates for most measures were reasonably good, ranging from .79 to .97. An exception was the delayed word recall test, which has had a reliability estimate of .66 for the first retest, and .59 for the second retest. Practice effects were evident from Times 1 to 2 on the sentence comprehension and delayed recall subtests of the RSC, Digit Symbol and a composite score. There was also a practice effect of the same magnitude found from Time 2 to Time 3 on Digit Symbol, delayed recall and the composite score. Statistics on measures for both the first and second retest intervals, with associated practice affects, are presented to enable the calculation of reliable change indices (RCI). The RCI may be used to assess any improvement in cognitive functioning after mild Traumatic Brain Injury.

A Score Test for Zero-Inflation in Correlated Count Data

To account for the preponderance of zero counts and simultaneous correlation of observations, a class of zero-inflated Poisson mixed regression models is applicable for accommodating the within-cluster dependence. In this paper, a score test for zero-inflation is developed for assessing correlated count data with excess zeros. The sampling distribution and the power of the test statistic are evaluated by simulation studies. The results show that the test statistic performs satisfactorily under a wide range of conditions. The test procedure is further illustrated using a data set on recurrent urinary tract infections. Copyright (c) 2005 John Wiley & Sons, Ltd.