A New Nonparametric Approach to the Comparison of K Independent Samples of Response Curves

Two simultaneous distribution free test procedures to test the homogeneity of K samples of response curves measured at T points of time each are proposed which react upon the shape of the response curve. One procedure is based on the comparison of K T-tupels of FRIEDMAN-rank sums, the other on the comparison of K T × T-incidence tables, which first were introduced by KANNEMANN (1976). The application of the two procedures is illustrated by a numerical example. In the discussion the tests are compared with each other and with concurring tests.     

A New Nonparametric Approach to the Comparison of K Independent Samples of Response Curves II: A K Sample Generalization of the FRIEDMAN Test

A K sample generalization of the FRIEDMAN test (1937) is introduced which can be used as a nonparametric procedure for testing the homogeneity of the profiles of K independent samples of response curves measured at T identical points of time. While a similar procedure in LEHMACHER & WALL (1978), section 3, is based on T combined tests, each of them at level a/T, here a finite and asymptotic test is presented which is based on a single test statistic. The application of the new multivariate test is illustrated by the same numerical example as in LEHMACHER & WALL (1978). The properties of this test are discussed and compared with the combined test mentioned above.     

Estimation of Fixed and Random Effects in the Functional Nonlinear Errors-in-Variable Model

Consider an experiment where a nonlinear continuous functional relationship exists between y and X. Assume that this relationship has been measured at n replicated points of X from each of t treatments or populations. Assume further that the X are fixed unknown vectors and that the location parameter v is either a fixed unknown vector or a vector of random variables. In the first case various linear hypotheses are to be tested about v, such as tests for main effects and interaction; in the second case, the mean and variance of the random variable v are to be estimated. A two-step procedure based on asymptotic theory is presented to test hypotheses or develop estimates for the fixed effects or random effects functional errors-in-variable model. An example of a one-way random effects model is given.     

Comparing Two Samples of Response Curves by Nonparamètric Tests of Predicted Order

Starting from MOSTELLER'S (1955) one-sample test of predicted order, some two-sample versions are proposed for comparing nonparametrically a treatment group (m response curves) with a control group (n response curves) as to a predicted shape represented by a specified rank order. The tests are applied to two groups of learning curves.     

Multiple Comparisons of Polynomial Distributions

Asymptotically correct 90 and 95 percentage points are given for multiple comparisons with control and for all pair comparisons of several independent samples of equal size from polynomial distributions. Test statistics are the maxima of the X²-statistics for single comparisons. For only two categories the asymptotic distributions of these test statistics result from DUNNETT'S many-one tests and TUKEY'S range test (cf. MILLER, 1981). The percentage points for comparisons with control are computed from the limit distribution of the test statistic under the overall hypothesis H₀. To some extent the applicability of these bounds is investigated by simulation. The bounds can also be used to improve Holm's sequentially rejective Bonferroni test procedure (cf. HOLM, 1979). The percentage points for all pair comparisons are obtained by large simulations. Especially for 3×3-tables the limit distribution of the test statistic under H₀ is derived also for samples of unequal size. Also these bounds can improve the corresponding Bonferroni-Holm procedure. Finally from SKIDÁK's probability inequality for normal random vectors (cf. SKIDÁK, 1967) a similar inequality is derived for dependent X²-variables applicable to simultaneous X²-tests.     

Empirical evaluation of two-sample statistical tests for differences of stepping phase during insect walking

In order to determine which statistical tests can validly be applied to data that describe a temporal relationship between two or more repetitive movements by an animal, we evaluated empirically seven two-sample tests that seemed potentially useful: Student's t test, the Watson Williams test for means, the variance-ratio F test, the Watson Williams test for the concentration parameter k, the Wallraff test, the Mann Whitney test and the Watson U² test. Evaluations were carried out on the timing (phases) of bursts of muscular activity in one leg relative to those in another during free walking in cockroaches. Each statistical test was evaluated by dividing randomly a single parent set of data into two subsets, each subset containing about half the original data set. This division was repeated 400 times, thus generating 400 different pairs of subsets. Each statistical test was used separately on the pairs of subsets to test the null hypothesis that the two samples of each pair came from the same population;; this procedure generated 400 statistics for each test, one for each pair of subsets. An estimate of the reliability of each statistical test was obtained by comparing the number of times the test actually indicated a significant difference between subsets to the number of times it might be expected to do so out (20 out of 400 when tested at the 5% level of significance). This procedure was repeated on ten different sets of data. The outcome of the evaluation suggested that, from an empirical point of view, Student's t, the Mann Whitney, the Wallraff and the Watson U² tests may be useful in assessing differences among the data we analyzed. The variance-ratio F test and the Watson Williams test for the concentration parameter k were clearly not usable. The Watson Williams test for means might be useful in some circumstances. Performing an arcsine transformation of the data did not significantly alter these results. Possible causes of the inapplicability of some of these tests to phase data are discussed.     

The Matched Pairs Problem with Exponential Variates

Two classes of tests for the hypothesis of bivariate symmetry are studied. For paired exponential survival times (t_1j, t_2j), the classes of tests are those based on t_1j-t_2j and those based on log t_1j–log t_2j. For each class the sign, signed ranks, t and likelihood ratio tests are compared via Pitman's criterion of asymptotic relative efficiency (ARE). For tests based on t_1j — t_2j, it is found that: (1) the efficacy of the paired t depends on the coefficient of variation (CV) of the pair means, (2) the signed rank test has the same ARE to the sign test as for the usual location problem. For tests based on log t_1j — log t_2j, the ARE comparisons reduce to the well-known results for the one-sample location problem for samples from a logistic density. Hence, the signed rank test is asymptotically efficient. Furthermore, analyses based on log t_1j — log t_2j are not complicated by the underlying pairing mechanism.     

Distribution-free R sample tests for the hypothesis of parallelism of response profiles

In this paper two nonparametric tests are given for testing the nullhypothesis of parallelity of response curves in r samples. The first procedure is done by a permutation test, whose practical applicability is ensured by a FORTRAN-subroutine available from the author. As the computational work and time grows rapidly with sample sizes, a Monte-Carlo-solution is optionally given by the same procedure. Alternatively an asymptotically distribution-free test based on quadratic forms is constructed for large sample situations.     

Warm and cold receptors of two sensilla on the foreleg tarsi of the tropical bont tickAmblyomma variegatum

Summary A pair of antagonistic thermal receptors has been identified in each of two long, tapering, poreless setae located distally on the foreleg tarsi of the tropicalbont tick,Amblyomma variegatum (Fig. 1). One, the cold receptor, responds to a rapiddrop in temperature (T) with a sudden rise in impulse frequency (F). The other, a warm receptor, responds to a rapidrise inT with a sudden rise inF (Figs. 2, 4). These two units are unusual for sharing their seta with two other units which are mechanosensitive. The four are distinguishable on the basis of spike amplitude and form (Fig. 3). Hence the thermal sensitivity displayed is hardly attributable to the pair of cells with tubular bodies but rather to the two extending up into the seta (for structure, see Hess and Vlimant 1982, 1983 a).As based on the first 100 ms of the response, differential sensitivity to rapidT change is –16.1± 10.4 (imp/s)/°C for cold units, 17.6 ± 9.5 (imp/s)/°C for warm (Table 1). As progressively larger segments of the spike train are employed to determineF, differential sensitivity of the warm unit drops off much more quickly than that of the cold (Table 2, Figs. 5, 6). In the cold unit resolving power (the difference in rapid temperature change discriminable with 90% probability by a pair of responses of a single unit at average sensitivity) continues to increase as the segment of the spike train determiningF is lengthened (from 0.58 °C for 100 ms segments to 0.41 °C for 1,100 ms segments). Resolving power of the warm unit, on the other hand, tends to decrease as longer segments are employed (from 0.52 °C for the first 100 ms to 0.80 °C for the first 1,100 ms). These relationships provoke the question of whether the spike trains may be evaluated in the CNS in different fashions.Abbreviations b slope of characteristic curve - F impulse frequency in impulses per second (imp/s) - n number of individuals examined - Pw partial pressure of water vapor in Torr - r correlation coefficient - s SD of responses from characteristic curve - SD standard deviation - T temperature in °C - T difference inT Refers to difference between initial and end temperature in abruptT changes     

Robust Hotelling-Type T2 Statistics

To test an assumed mean vector, and to test the equality of two mean vectors, robust statistics are developed which have exactly the same form as the Hotelling T² statistics. These statistics are shown to have remarkable type I error robustness and power.     

Computation of densities,bulk moduli and glass transition temperatures of vinylic polymers from atomistic simulation

The aim of molecular modeling is to mimic reality by considering approximations appropriate to the scale at which the simulation is carried out. At the atomic level, forcefields that represent average atomic interactions are used. However, the phase space has to be adequately explored in order to compare successfully computed and experimental properties. The procedure exposed in this article considers an initial selection of relevant configurations on which a simulated annealing process is applied using the first generation forcefield OPLS, followed by a uniform hydrostatic compression using the second generation forcefield COMPASS©. The resulting data are fitted by an equation of state, from which density and bulk modulus are determined. The glass transition is then simulated and T _gs are computed. Our approach is tested using a series of vinylic polymers, which differ from each other by small variations in atomic interaction combinations. The excellent agreement with experimental data shows the validity of the procedure exposed. Moreover, a clear linear relationship between simulated and experimental T _gs is revealed.     

On the Use of the Shapiro‐Wilk Test in Two‐Stage Adaptive Inference for Paired Data from Moderate to Very Heavy Tailed Distributions

Paired data arises in a wide variety of applications where often the underlying distribution of the paired differences is unknown. When the differences are normally distributed, the t‐test is optimum. On the other hand, if the differences are not normal, the t‐test can have substantially less power than the appropriate optimum test, which depends on the unknown distribution. In textbooks, when the normality of the differences is questionable, typically the non‐parametric Wilcoxon signed rank test is suggested. An adaptive procedure that uses the Shapiro‐Wilk test of normality to decide whether to use the t‐test or the Wilcoxon signed rank test has been employed in several studies. Faced with data from heavy tails, the U.S. Environmental Protection Agency (EPA) introduced another approach: it applies both the sign and t‐tests to the paired differences, the alternative hypothesis is accepted if either test is significant. This paper investigates the statistical properties of a currently used adaptive test, the EPA's method and suggests an alternative technique. The new procedure is easy to use and generally has higher empirical power, especially when the differences are heavy‐tailed, than currently used methods.     

A new perspective on size hierarchies in nature: patterns, causes, and consequences

Many plant and animal aggregations have size hierarchies within which a variety of sizes of individuals, from large to small, can be found. Size hierarchies are thought to indicate the existence of competition amongst individuals within the aggregation, but determining their exact cause is difficult. The key to understanding size hierarchies lies in first quantifying the pattern of size and growth of individuals. We conducted a quantitative investigation of pattern in the size hierarchy of the clown anemonefish Amphiprion percula, in Madang Lagoon, Papua New Guinea. Here, groups of A. percula occupy sea anemones (Heteractis magnifica) that provide protection from predators. Within each anemone there is a single group composed of a breeding pair and zero to four non-breeders. Within each group there is a single size hierarchy; the female is largest (rank 1), the male is second largest (rank 2), and the non-breeders get progressively smaller (ranks 3–6). We demonstrate that individuals adjacent in rank are separated by body size ratios whose distribution is significantly different from the distribution expected under a null model—the growth of individuals is regulated such that each dominant ends up being about 1.26 times the size of its immediate subordinate. We show that it is decisions about growth at the individual level that generate the size hierarchy at the group level, and thereby determine maximum group size and population size. This study provides a new perspective on the pattern, causes and consequences of size hierarchies.     

Do the maximum sizes,ages and patterns of growth of three reef‐dwelling labrid species at two latitudes differ in a manner conforming to the metabolic theory of ecology?

The size and age data and patterns of growth of three abundant, reef‐dwelling and protogynous labrid species (Coris auricularis, Notolabrus parilus and Ophthalmolepis lineolata) in waters off Perth at c. 32° S and in the warmer waters of the Jurien Bay Marine Park (JBMP) at c. 30° S on the lower west coast of Australia are compared. Using data for the top 10% of values and a randomization procedure, the maximum total length (L_T) and mass of each species and the maximum age of the first two species were estimated to be significantly greater off Perth than in the JBMP (all P < 0·001) and the maximum ages of O. lineolata in the two localities did not differ significantly (P > 0·05). These latitudinal trends, thus, typically conform to those frequently exhibited by fish species and the predictions of the metabolic theory of ecology (MTE). While, in terms of mass, the instantaneous growth rates of each species were similar at both latitudes during early life, they were greater at the higher latitude throughout the remainder and thus much of life, which is broadly consistent with the MTE. When expressed in terms of L_T, however, instantaneous growth rates did not exhibit consistent latitudinal trends across all three species. The above trends with mass, together with those for reproductive variables, demonstrate that a greater amount of energy is directed into somatic growth and gonadal development by each of these species at the higher latitude. The consistency of the direction of the latitudinal trends for maximum body size and age and pattern of growth across all three species implies that each species is responding in a similar manner to differences between the environmental characteristics, such as temperature, at those two latitudes. The individual maximum L_T, mass and age and pattern of growth of O. lineolata at a higher and thus cooler latitude on the eastern Australian coast are consistent with the latitudinal trends exhibited by those characteristics for this species in the two western Australian localities. The implications of using mass rather than length as the indicator variable when comparing the maximum sizes of the three species and the trends exhibited by the instantaneous growth rates of those species at different latitudes are explored. Although growth curves fitted to both the L_T and masses at age for the males of each species lay above those for their females, this would not have influenced the conclusions drawn from common curves for both sexes.     

Graphical Methods for Analysing Combination Effects in Dose-Response Experiments

An organbath experiment with bovine tracheal muscle strips with cumulative increases in concentrations of a substance A in the absence and presence of a fixed concentration of a second substance B is considered as an example for demonstrating graphical methods to analyse drug combination effects. The response of each strip is individually described and estimated by a nonlinear dose response curve. From the curves of the combined action theoretical curves of substance A are derived, which were expected if the combination effect was simple similar or independent, respectively. The first graphical method consists in comparing the derived curves for substance A with the curves for substance A directly fitted. It is cheeked by eye if the group of derived curves can clearly be distinguished from the group of directly fitted curves. The second graphical method differs from the first method in so far, as not the curves are visualized but the parameter vectors corresponding to them. In contrast to widely used analytical methods the proposed graphical methods allow to treat individual instead of averaged dose response relationships. The methods can help to decide if the combination effect may be considered as independent, simple similar or none of both.     

Implication of correlations among some common stability statistics — a Monte Carlo simulations

Stability analysis of multilocation trials is often based on a mixed two-way model. Two stability measures in frequent use are the environmental variance (S _i ² )and the ecovalence (W _i). Under the two-way model the rank orders of the expected values of these two statistics are identical for a given set of genotypes. By contrast, empirical rank correlations among these measures are consistently low. This suggests that the two-way mixed model may not be appropriate for describing real data. To check this hypothesis, a Monte Carlo simulation was conducted. It revealed that the low empirical rank correlation amongS _i ² and W _i is most likely due to sampling errors. It is concluded that the observed low rank correlation does not invalidate the two-way model. The paper also discusses tests for homogeneity of S _i ² as well as implications of the two-way model for the classification of stability statistics.     

A New Testing Approach for Comparing the Overall Homogeneity of Survival Curves

The assessment of overall homogeneity of time‐to‐event curves is a key element in survival analysis. The currently commonly used methods, e.g., log‐rank and Wilcoxon tests, may have a significant loss of statistical testing power under certain circumstances. In this paper a new statistical testing approach is developed to compare the overall homogeneity of survival curves. The proposed new method has greater power than the commonly used tests to detect overall differences between crossing survival curves. The small‐sample performance of the new test is investigated under a variety of situations by means of Monte Carlo simulations. Furthermore, the applicability of the proposed testing approach is illustrated by a real data example from a kidney dialysis trial. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison of Parameters from Rhythmometric Models with Multiple Components on Hybrid Data

Population multiple components is a statistical tool useful for the analysis of time-dependent hybrid data. With a small number of parameters, it is possible to model and to predict the periodic behavior of a population. In this article, we propose two methods to compare among populations rhythmometric parameters obtained by multiple component analysis. The first is a parametric method based in the usual statistical techniques for comparison of mean vectors in multivariate normal populations. The method, through MANOVA analysis, allows comparison of the MESOR and amplitude-acrophase pair of each component among two or more populations. The second is a nonparametric method, based in bootstrap techniques, to compare parameters from two populations. This test allows one to compare the MESOR, the amplitude, and the acrophase of each fitted component, as well as the global amplitude, orthophase, and bathyphase estimated when all fitted components are harmonics of a fundamental period. The idea is to calculate a confidence interval for the difference of the parameters of interest. If this interval does not contain zero, it can be concluded that the parameters from the two models are different with high probability. An estimation of p-value for the corresponding test can also be calculated. Both methods are illustrated with an example, based on clinical data. The nonparametric test can also be applied to paired data, a special situation of great interest in practice. By the use of similar bootstrap techniques, we illustrate how to construct confidence intervals for any rhythmometric parameter estimated from population multiple components models, including the orthophase, bathyphase, and global amplitude. These tests for comparison of parameters among populations are a needed tool when modeling the nonsinusoidal rhythmic behavior of hybrid data by population multiple component analysis.     

A Generalization of the GMANOVA-Model

It is shown that in some experimental designs the MANOVA- and the GMANOVA-model are too restrictive either to yield all hypothesis tests of interest or to reflect all known features of the design. An extension of these models is derived by relating the response vectors with the unknown model parameters by linear equations which may be completely different for each of the p components of the response vector and for each of the n independent vectors. For situations, in which a Wishart-distributed estimator for the underlying common covariance matrix is attainable, a test for any s-dimensional linear hypothesis on the model parameters is derived.     

Expression Vectors for the Rapid Purification of Recombinant Proteins in <Emphasis Type="Italic">Bacillus subtilis</Emphasis>

We describe the construction of six novel plasmid-based IPTG-inducible expression vectors for Bacillus subtilis and related species. While one vector allows intracellular production of recombinant proteins, the second provides a strong secretion signal. The third vector allows addition of the c-Myc epitope tag, and the remaining three vectors provide the purification tags His and Strep. The versatility of all six vectors was demonstrated by the insertion of several reporter genes and by their regulated overexpression. Recombinant proteins with a His- or Strep-tag could be purified to near homogeneity in a single step.