Some Tests for k£2 Upper Outliers in an Exponential Sample

The sequential procedure for testing up to k upper outliers proposed by Kimber (1982) for one-parameter exponential distribution is modified to a two-parameter exponential distribution. Further null distributions of some test statistics for an upper outlier-pair in a complete or censored sample from a two-parameter exponential distribution are given. Percentage points of the statistic T₁ are tabulated.     

Artificial Tactile Sense Technique for Predicting Beef Tenderness Based on FS Pressure Sensor

We present a rapid system for predicting beef tenderness by mimicking the human tactile sense. The detection system includesa FS pressure sensor, a power supply conversion circuit, a signal amplifier and a box in which the sample is mounted. Asample of raw Longissimus dorsi (LD) muscle is placed in the measuring box; then a rod connected to the pressure sensor ispressed into the beef sample to a given depth; the reaction force of the beef sample is measured and used to predict the tenderness.Sensory evaluation and Warner-Bratzler Shear Force (WBSF) evaluation of samples from the same LD muscle are usedfor comparison. The new detection system agrees with established procedure 95% of the time, and the time to test a sample isless than 5 minutes.     

Sample Size Calculation for Intraclass Correlation in the Presence of Random Loss of Sampled Patients

When a trial involves an invasive laboratory test procedure or requires patients to make a commitment to follow a restrictive test schedule, we can often lose a great proportion of our sampled patients due to refusal of participation into our study. Therefore, incorporating the possible loss of patients into sample size calculation is certainly important in the planning stage of a study. In this paper, we have generalized the sample size calculation procedure for intraclass correlation by accounting for the random loss of patients in the beginning of a trial. We have demonstrated that the simple ad hoc procedure, that raises the estimated sample size in the absence of loss of patients by the factor 1/p_o, where p_o is the retention probability for a randomly selected patient, is adequate when p_o is large (=0.80). When p_o is small (i.e., a high refusal rate), however, use of this simple ad hoc procedure tends to underestimate the required sample size. Furthermore, we have found that if the individual retention probability varied substantially among patients, then the magnitude of the above underestimation could even be critical and therefore, the application of the simple direct adjustment procedure in this situation should be avoided.     

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.     

Testing Equivalence Simultaneously for Location and Dispersion of two Normally Distributed Populations

In clinical trials with an active control usually therapeutical equivalence of a new treatment is investigated by looking at a location parameter of the distributions of the primary efficacy variable. But even if the location parameters are close to each other existing differences in variability may be connected with different risks for under or over treatment in an individual patient. Assuming normally distributed responses a multiple test procedure applying two shifted one-sided t-tests for the mean and accordingly two one-sided F-tests for the variances is proposed. Equivalence in location and variability is established if all four tests lead to a rejection at the (one-sided) level α. A conservative procedure “correcting” the t-tests for heteroscedasticity is derived. The choice of a design in terms of the global level α, the global power, the relevant deviations in the population means and variances, as well as the sample size is outlined. Numerical calculations of the actual level and power for the proposed designs show, that for balanced sample sizes the classical uncorrected one-sided t-tests can be used safely without exaggerating the global type I error probability. Finally an example is given.     

A New Statistical Goodness-of-Fit Test Based on Graphical Representation

A statistical goodness-of-fit test, based on representing the sample observations by linked vectors, is developed. The direction and the length of the linked vectors are defined as functions of the expected values of the order statistics and sample order statistics, respectively. The underlying method can be used to test distributional assumptions for any location-scale family. A test statistic Q_n is introduced and some of its properties are studied. It is shown that the proposed test can be generalized to test if two or more independent samples come from the same distribution. The test procedure provides a graphical method of identifying the true distribution when the null hypothesis is rejected.     

Multi-Sample Slippage Test for Ordered Observations

A multi-sample slippage test based on ordered observations has been given. The test statistic is based on the sum of ranks of the sample. The probability distribution of the test statistic has been worked out for small sample and it turns out to be chi-square distribution for large sample. The analytical procedure has been explained by a numerical example.     

The Nonparametric Behrens‐Fisher Problem: Asymptotic Theory and a Small‐Sample Approximation

A generalization of the Behrens‐Fisher problem for two samples is examined in a nonparametric model. It is not assumed that the underlying distribution functions are continuous so that data with arbitrary ties can be handled. A rank test is considered where the asymptotic variance is estimated consistently by using the ranks over all observations as well as the ranks within each sample. The consistency of the estimator is derived in the appendix. For small samples (n₁, n₂ ≥ 10), a simple approximation by a central t‐distribution is suggested where the degrees of freedom are taken from the Satterthwaite‐Smith‐Welch approximation in the parametric Behrens‐Fisher problem. It is demonstrated by means of a simulation study that the Wilcoxon‐Mann‐Whitney‐test may be conservative or liberal depending on the ratio of the sample sizes and the variances of the underlying distribution functions. For the suggested approximation, however, it turns out that the nominal level is maintained rather accurately. The suggested nonparametric procedure is applied to a data set from a clinical trial. Moreover, a confidence interval for the nonparametric treatment effect is given.     

Double reduction estimation and equilibrium tests in natural autopolyploid populations

Many bioinformatics pipelines include tests for equilibrium. Tests for diploids are well studied and widely available, but extending these approaches to autopolyploids is hampered by the presence of double reduction, the comigration of sister chromatid segments into the same gamete during meiosis. Though a hindrance for equilibrium tests, double reduction rates are quantities of interest in their own right, as they provide insights about the meiotic behavior of autopolyploid organisms. Here, we develop procedures to (i) test for equilibrium while accounting for double reduction, and (ii) estimate the double reduction rate given equilibrium. To do so, we take two approaches: a likelihood approach, and a novel U-statistic minimization approach that we show generalizes the classical equilibrium χ² test in diploids. For small sample sizes and uncertain genotypes, we further develop a bootstrap procedure based on our U-statistic to test for equilibrium. We validate our methods on both simulated and real data.     

A Comparison of Tests for Marginal Homogeneity in Square Contingency Tables

Several asymptotic tests were proposed for testing the null hypothesis of marginal homogeneity in square contingency tables with r categories. A simulation study was performed for comparing the power of four finite conservative conditional test procedures and of two asymptotic tests for twelve different contingency schemes for small sample sizes. While an asymptotic test proposed by STUART (1955) showed a rather satisfactory behaviour for moderate sample sizes, an asymptotic test proposed by BHAPKAR (1966) was quite anticonservative. With no a priori information the performance of (r - 1) simultaneous conditional binomial tests with a Bonferroni adjustment proved to be a quite efficient procedure. With assumptions about where to expect the deviations from the null hypothesis, other procedures favouring the larger or smaller conditional sample sizes, respectively, can have a great efficiency. The procedures are illustrated by means of a numerical example from clinical psychology.     

Outgroup sampling in phylogenetics: Severity of test and successive outgroup expansion

Outgroup sampling is a fundamental step in the design of phylogenetic analyses, independent of optimality criterion, taxonomic group, or source of evidence. Studies have demonstrated the efficient analysis of many thousands of terminals, all of which could be included in any empirical investigation, yet outgroup samples typically include only a small number of terminals. Most discussion of outgroup sampling centers on employing “correct” or “appropriate” outgroup terminals to increase “accuracy” or “reliability” by preventing “errors” such as long branch attraction and “incorrect” ingroup rooting. As an alternative, I develop a theory of outgroup sampling grounded in the logic of scientific discovery, whereby the objective is to test nested hypotheses of ingroup topology and character‐state transformation as severely as possible by incorporating outgroup terminals in unconstrained, simultaneous analysis, using background knowledge to select the terminals that have the greatest chance of refuting those hypotheses. This framework provides a logical basis for selecting outgroup taxa but does not provide grounds for limiting the outgroup sample, given that, ceteris paribus, testability and explanatory power increase with the inclusion of additional terminals. Therefore, I propose the ancillary procedure of successively expanding the outgroup sample until ingroup hypotheses become stable (insensitive) to increased sampling, with each expansion guided by the scientific objectives of outgroup sampling. This is a heuristic procedure that does not prevent more outgroup terminals from being sampled or guarantee that ingroup hypotheses will remain insensitive to further outgroup expansion, and it has no bearing on the objective support of a given hypothesis. Nevertheless, it provides an objective, empirical basis for limiting outgroup sampling in a given research cycle. I illustrate this procedure by examining the effect of successive outgroup expansion on the relationships among the poison frog genera Adelphobates, Dendrobates, and Oophaga.     

Blinded sample size recalculation in multiple composite population designs with normal data and baseline adjustments

The increasing interest in subpopulation analysis has led to the development of various new trial designs and analysis methods in the fields of personalized medicine and targeted therapies. In this paper, subpopulations are defined in terms of an accumulation of disjoint population subsets and will therefore be called composite populations. The proposed trial design is applicable to any set of composite populations, considering normally distributed endpoints and random baseline covariates. Treatment effects for composite populations are tested by combining p-values, calculated on the subset levels, using the inverse normal combination function to generate test statistics for those composite populations while the closed testing procedure accounts for multiple testing. Critical boundaries for intersection hypothesis tests are derived using multivariate normal distributions, reflecting the joint distribution of composite population test statistics given no treatment effect exists. For sample size calculation and sample size, recalculation multivariate normal distributions are derived which describe the joint distribution of composite population test statistics under an assumed alternative hypothesis. Simulations demonstrate the absence of any practical relevant inflation of the type I error rate. The target power after sample size recalculation is typically met or close to being met.     

A Simple Testing Procedure “Control versus k Treatments” for One-sided Ordered Alternatives,with Application in Toxicology

A simple testing procedure “control versus k treatments” for one-sided ordered alternatives for univariate, continuous variables is given. With a simulation study both the first kind risk a and the power behaviour under several distributions, expected value profiles, sample sizes and a levels are shown.     

Tests for profile analysis of paired curves based on friedman ranking methods

Two nonparametric tests are proposed for the comparison of a paired sample of response curves with T congruent time points. The first procedure rank transforms each curve and tests the homogeneity of the resulting pair of averaged rank vectors. The second procedure rank transforms each pair of curves and tests the homogeneity of the related pair of averaged rank vectors. The first test detects only pure interactions; the second test checks if any difference exists between the rank curves. Both tests are presented in finite and asymptotic as well as in combined (by T singular tests) and multivariate form.     

Nonparametric All‐Pairs Multiple Comparisons

Nonparametric all‐pairs multiple comparisons based on pairwise rankings can be performed in the one‐way design with the Steel‐Dwass procedure. To apply this test, Wilcoxon's rank sum statistic is calculated for all pairs of groups; the maximum of the rank sums is the test statistic. We provide exact calculations of the asymptotic critical values (and P‐values, respectively) even for unbalanced designs. We recommend this asymptotic method whenever large sample sizes are present. For small sample sizes we recommend the use of the new statistic according to Baumgartner , Weiss , and Schindler (1998, Biometrics 54 , 1129–1135) instead of Wilcoxon's rank sum for the multiple comparisons. We show that the resultant procedure can be less conservative and, according to simulation results, more powerful than the original Steel‐Dwass procedure. We illustrate the methods with a practical data set.     

On the Behaviour of Fligner-Wolfe-Trend Test “Control versus k Treatments” with Application in Toxicology

The behaviour of Fligner-Wolfe-trend test “control versus k treatments” was characterized by simulation. Sample size estimation took place via non-central t-distribution. Some results on asymptotic efficiency were shown and compared with simulation results for small sample sizes. A test version for umbrella alternatives was given and characterized by simulation.     

Selection of Judges for Sensory Evaluation

A test based on ordered observations for selection of consistent judges for sensory evaluation has been given. The test–statistic depends on the sum of ranks of different products under consideration. The probability distribution of the test-statistic has been worked out for small sample and it turns out to be chi-square distribution for large sample. The analytical procedure has been explained by a numerical example of a taste-testing experiment.     

Powers of Multiple-Testing Procedures for Identification of Genes Significantly Differentially Expressed in Microarray Experiments

Because of the high operation costs involved in microarray experiments, the determination of the number of replicates required to detect a gene significantly differentially expressed in a given multiple-testing procedure is of considerable significance. Calculation of power/replicate numbers required in multiple-testing procedures provides design guidance for microarray experiments. Based on this model and by choice of a multiple-testing procedure, expression noises based on permutation resampling can be considerably minimized. The method for mixture distribution model is suitable to various microarray data types obtained from single noise sources, or from multiple noise sources. By using the biological replicate number required in microarray experiments for a given power or by determining the power required to detect a gene significantly differentially expressed, given the sample size, or the best multiple-testing method can be chosen. As an example, a single-distribution model of t-statistic was fitted to an observed microarray dataset of 3 000 genes responsive to stroke in rat, and then used to calculate powers of four popular multiple-testing procedures to detect a gene of an expression change D. The results show that the B-procedure had the lowest power to detect a gene of small change among the multiple-testing procedures, whereas the BH-procedure had the highest power. However, all multiple-testing procedures had the same power to identify a gene having the largest change. Similar to a single test, the power of the BH-procedure to detect a small change does not vary as the number of genes increases, but powers of the other three multiple-testing procedures decline as the number of genes increases.     

Exact Simultaneous Comparisons with Control in an r × c Contingency Table

Let categorical data coming from a control group and (r - 1) treated groups be given in an r × c contingency table. A simultaneous test procedure of the (r - 1) hypotheses that the probabilities of all c categories do not differ between the i-th treated group and the control is derived. For small tables and small cell frequencies it is exactly performed by generation of all tables having the given marginal sums. If 2 categories or 2 groups only are given the asymptotic distribution of the test statistic is known; otherwise its distribution may be simulated if the computational expenditure of performing an exact test is too large. By means of a Monte Carlo study it is shown that this method meets its level more reliably and that it has a better power than others.     

A Modified Method for Extraction and Identification of Abscisic Acid and Gibberellin-like Substances from the Olive (Olea europaea)

A procedure for extracting and identifying plant hormones, particularly abscisic acid (ABA) and the gibberellins (GA) was developed through modification of methods described in the literature. The procedure is particularly useful for studying more than one hormone simultaneously in a given sample, and when the supply of plant material is limited. The procedure was used to isolate ABA and GA-like substances from olive tissue (i.e., leaves, buds and inflorescences). Gibberellin-like substances were identified by their action on α-amylase release from embryoless barley half-seeds. Characterization of an acidic inhibitor extracted from olive inflorescences by thin-layer chromatography, fluorescence under ultraviolet light, gas chromatography, and physiological effects on wheat coleoptile sections indicate that this inhibitor, or at least a component of it, is very similar if not identical with at least one isomeric form of synthetic abscisic acid.