Tables and Applications of the Bonferroni t-Statistics: A Revision of Dunn's Simultaneous t-Tests

Tables for Bonferroni-adjusted significance levels of Student's t are provided for r = 3(1)30(5)50 etc. and alphas of 0.05, 0.01 and 0.001. The tables are suggested for various applications, for example in replacing analysis of variance of k samples by r simultaneous t tests. Use of the tables is shown by numerical examples. The adjustment of alpha for improving the efficiency of testing is made by WILKINSON for orthogonal comparisons and by HOLM for nonorthogonal comparisons.     

Probleme der Erweiterung der Prüfverteilungen des Maximum-Modulus-Testes und des DUNNETT-Testes

SCHULZ (1976) gave formulas for the approximate computation of the percentage points needed for the comparison of sample means by the Maximum-Modulus-Test resp. by the DUNNETT-Test. Our investigation shows that these formulas are also practicable if the number of the mean differences k is greater than 20. The maximum difference between the exact values and the approximate values of the percentage points amounts to 0,05 in the case of the Maximum-Modulus-Test with k >20 and degrees of freedom v > k for a level of error a = 0,05 resp. a = 0,01. In the case of the DUNNETT-Test this maximum difference amounts to 0,02 for 20 < k < 50 and a = 0,05. Besides it can be here supposed that the approximate percentage points are also practicable for both k >50, a = 0,05 and k >20, a = 0,01.     

A Simple Construction Procedure for Eesolvable Incomplete Block Designs for any Number of Treatments

A simple, straightforward procedure, which requires no special tables or generators, is presented for constructing resolvable incomplete block designs for v=pk, v=p²k, …, treatments, for k≥p, in incomplete blocks of size k. Also, it is shown, how to obtain incomplete block designs for any v in blocks of size k and k+1. The procedure allows construction of balanced incomplete block designs for p = k a prime number. For p = n not a prime number, incomplete block designs can be obtained by the procedure, but are not balanced. However, for p_s being the smallest prime factor of n, p_s + 1 for v = n², p_s²+ p_s + 1 for v = n³, …, arrangements can be obtained for which the occurrence of any treatment pair in the blocks is either zero or one. This is called a zero-one concurrence design. Procedures are described for obtaining additional zero-one concurrence arrangements. It is shown that the efficiency of these designs is maximum. Both intra-block and inter-block analyses are described.     

A Monte Carlo Study to Evaluate the Performance of Selected Tests of Homogeneity in Sparse Contingency Tables

We address the problem of tests of homogeneity in two-way contingency tables in case-control studies when the case category is subdivided into k subcategories. In this situation, we have two cells with large frequencies and 2 X k cells with frequencies that become small as k increases. We propose two ad hoc statistics in which a statistic for the sparse cells is combined with a statistic for the cells with large frequencies. We will study these tests along with the Pearson test (using a chi-square approximation) in a Monte Carlo simulation study. Two sets of null hypothesis models and two sets of alternative hypothesis models are considered. The best test for the models considered is the usual Pearson test (using an approximate chi-square distribution) although the ad hoc models are more powerful under one alternative model considered.     

Age,growth and reproduction in creole perch (Percichthys trucha) in the Negro River,Argentinean Patagonia

Age, growth and reproductive characteristics of creole perch, Percichthys trucha, were investigated in the Negro River, southern Argentina from samples collected seasonally, December 1994–December 1995. Age was estimated via scale and whole otolith reading methods. Total length (n = 413) ranged from 103 to 432 mm, and weight from 12 to 1042 g. Significant differences between the length‐weight relationships of males and females were detected (P < 0.05). Isometric growth was observed in juveniles and males, whereas total population and females exhibited positive allometric growth. The marking pattern in scales and otoliths followed an annual rhythm, with the formation of only one annulus in scales and only one hyaline band in otoliths during autumn‐winter. The oldest males were 5 years old whereas maximum age in females was 12 years from scales and 15 years from otoliths. Because scales were found to underestimate age in individuals older than 4 years, otoliths were considered to be the best structures for creole perch age determination. Gompertz growth parameters based on otolith data were L∞: 428.0 mm, k = 0.46 and t₀ = 0.43 for total population (r = 0.90), L∞: 410.7 mm, k = 0.42 and t₀ = 0.46 for males (r = 0.91), and L∞: 434.1 mm, and k = 0.49 and t₀ = 0.43 for females (r = 0.91). Lengths at first maturity (TL₅₀) were 260 and 241 mm in males and females, respectively, both of which corresponded to ages between 1 and 2 years. Macroscopic gonad inspection and the high percentage of juveniles captured during summer indicated that spawning begins at the end of spring.     

A rapid assay for the binding of actinomycin to DNA.

The theory of countercurrent distribution (CCD) was reviewed and extended. The separation function for the fundamental distribution of CCD was presented in the form n = t²(αk₁+β)²/αk₁(β?1)² where n is the number of transfers, t the abscissa of the standard normal distribution, α = v_m/v₈ the phase ratio, β = k₁/k₂≥ 1 the separation factor, and k₁ the partition coefficient of the more radidly moving component; n was found to be minimal on the condition αk₁ = β. The separation function for the single withdrawal of CCD was obtained in the form N = u + 1 = t²{(αk₁ + 1)^1/2 + [β(αk₁ + β)]^1/2}²/(β ? 1)²+ 1, where N is the number of partition units. From this equation it appears that N is minimal when αk₁ = 0. Compared with the former separation functions presented in the literature, these separation functions have the advantage of giving directly the relationships among the phase ratio, the absolute partition coefficient, the separation factor, the resolution degree, and the number of transfers or partition units required. In addition, the dependencies of the elution volumes and the widths of the elution curves on α, β, and the partition coefficients were considered mathematically by means of differential calculus. The elution volumes were found to have minima at certain αk₁ values. The standard deviations, on the contrary, did not have minima in respect to αk₁. The theory presented can be used for selecting proper operating conditions while separating chemical compounds.     

The Discrete Distribution Used for the Log-rank Test Can Be Inaccurate

When the number of tumors is small, a significance level for the Cox-Mantel (log-rank) test Z is often computed using a discrete approximation to the permutation distribution. For j = 0,…, J let N_j(t) be the number of animals in group j alive and tumor-free at the start of time t. Make a 2 × (1+J) table for each time t of the number of animals R_j(t) with newly palpated tumor out of the total N_j(t) at risk. There are a total of say K tables, one for each distinct time t with observed death or newly palpated tumor. The usual discrete approximation to the permutation distribution of Z is defined by taking tables to be independent with fixed margins N_j(t) and ΣR_j(t) for all t. However, the N_j(t) are random variables for the actual permutation distribution of Z, resulting in dependence among the tables. Calculations for the exact permutation distribution are explained, and examples are given where the exact significance level differs substantially from the usual discrete approximation. The discrepancy arisis primarily because permutations with different Z-scores under the exact distribution can be equal for the discrete approximation, inflating the approximate P-value.     

Cumulative Damage Survival Models for the Randomized Complete Block Design

A continuous time discrete state cumulative damage process {X(t), t ≥ 0} is considered, based on a non‐homogeneous Poisson hit‐count process and discrete distribution of damage per hit, which can be negative binomial, Neyman type A, Polya‐Aeppli or Lagrangian Poisson. Intensity functions considered for the Poisson process comprise a flexible three‐parameter family. The survival function is S(t) = P(X(t) ≤ L) where L is fixed. Individual variation is accounted for within the construction for the initial damage distribution {P(X(0) = x) | x = 0, 1, …,}. This distribution has an essential cut‐off before x = L and the distribution of L – X(0) may be considered a tolerance distribution. A multivariate extension appropriate for the randomized complete block design is developed by constructing dependence in the initial damage distributions. Our multivariate model is applied (via maximum likelihood) to litter‐matched tumorigenesis data for rats. The litter effect accounts for 5.9 percent of the variance of the individual effect. Cumulative damage hazard functions are compared to nonparametric hazard functions and to hazard functions obtained from the PVF‐Weibull frailty model. The cumulative damage model has greater dimensionality for interpretation compared to other models, owing principally to the intensity function part of the model.     

Inhibition of extracellular lipase from Streptomyces rimosus with 3,4-dichloroisocoumarin

Kinetic characterization of lipase inhibition was performed by activity measurement and mass spectrometry (MS), for the first time with serine-protease inhibitor 3,4-dichloroisocoumarin (DCI). Inhibition of Streptomyces rimosus extracellular lipase (SrLip), a member of the SGNH superfamily, by means of DCI follows the mechanism of two-step irreversible inhibition. The dissociation constant of the noncovalent E?I complex and first-order rate constant for inactivation were determined by incubation (K_i* = 26.6?±?2.8 µM, k₂ = 12.2?±?0.6 min–1) or progress curve (K_i* = 6.5?±?1.5 µM, k₂ = 0.11?±?0.01 min–1) method. Half-times of reactivation for lipase inhibited with 10-fold molar excess of DCI were determined by activity measurement (t_1/2 = 11.3?±?0.2?h), matrix-assisted laser desorption/ionization (MALDI, t_1/2 = 13.5?±?0.4?h), and electro-spray ionization (ESI, t_1/2 = 12.2?±?0.5?h) MS. The active SrLip concentration was determined by incubating the enzyme with near equimolar concentrations of DCI, followed by activity and MS measurement.     

Measurement of Cerebral Glucose Utilization Using Washout After Carotid Injection in the Rat

Abstract: The carotid injection technique, used previously to quantitate the kinetics of blood-brain barrier transport of metabolic substrates, may be modified to analyze the rate of cerebral glucose utilization. A 0.2-ml solution of [¹⁴C]glucose (G_F) and [³H]methylglucose (M), an internal reference, is rapidly injected into the carotid artery, followed by microwave fixation of brain at various times up to 4 min after injection. The brain radioactivity is separated into a fraction containing neutral hexoses (G_F and M) and a fraction containing metabolites of glucose. The G_F/M ratio is related to the rate constant (k₃) of brain glucose utilization by the simple, linear equation: In(G_F/M) = In(G_F°/M°) –k₃t, where G_F°/M°= the brain uptake index of glucose, relative to methylglucose, at 5-15 s after injection, and t= the time after carotid injection, e.g., 1–4 min. It is assumed that (a) the rate of influx due to recirculation of label is minimal during the 4-min circulation period; and (b) the rate constants of glucose efflux (k₂) and methylglucose efflux (k₂*) are identical. Independent estimates of k₂ and k₂* showed these parameters to be identical: k₂= 0.14 + 0.08 min-I; k₂*= 0.14 ± 0.02 min-I. A logarithmic plot of G_F/M ratios versus time was linear (r = 0.99), and was described by the slope k₂= 0.21 ± 0.02 min^?1. Assuming glucose is uniformly distributed in brain, then the glycolytic rate = k₃× brain glucose = (0.21 min^?1) (2.6 μmol g^?1) = 0.55 μmol min^?1 g^?1 for the cortex of the barbiturate-anesthetized rat. These studies provide the basis for a simple method of measurement of regional brain glycolysis that does not require either the use of correction factors, e.g., the lumped constant, or the use of differentially labeled glucose.     

Multiple liquid-liquid partition: II. Theory of Martin-Synge distribution (MSD)

The theory of Martin-Synge distribution (MSD) was refined, with special attention being focused upon the derivation of the separation functions. The separation function for the fundamental distribution of MSD was obtained in the form v = t²(αk₁ + 1)(αk₁ + β)[(αk₁ + 1)^1/2 + (αk₁ + β)^1/2]²/αk₁(β ? 1)², where ν is the number of aliquots v_m driven through the apparatus, t the abscissa of the standard normal distribution, α = v_m/v₈ the phase ratio, β = k₁/k₂≥ 1 the separation factor, and k₁ the partition coefficient of the more rapidly moving component; ν was shown to have minima at given αk₁ values. The separation function of the single withdrawal of MSD was presented in the form N = u + 1 = t²(2αk₁ + β + 1)²/(β ? 1)²+ 1, where N is the number of partition units; N is minimal when αk₁ = 0. The elution volumes and standard deviations of the two compounds to be separated were mathematically analyzed in a manner similar to that previously presented when dealing with the theory of counter-current distribution (CCD). As in CCD, the elution volumes in MSD were found to have minima at given αk₁ values. However, the standard deviations of the elution curves also have minima in respect to αk₁ in MSD, which is a different situation as compared to CCD. The selection of optimal operating conditions was found to be more critical in MSD than in CCD.     

Age estimates derived from hard parts of swordfish Xiphias gladius from the north-western Mediterranean Sea

Accurate age estimates for fish are critical for properly understanding stock dynamics and health; this is particularly true for larger billfishes. Here we determined the most accurate aging estimation methods for swordfish (Xiphias gladius). We compared age estimates obtained from fin-ray sections, otolith sections, whole otoliths, and vertebrae collected from 87 swordfish off the east coast of Corsica. Age estimates from otolith sections were most consistently estimated across different readers (lowest average percentage error), followed by fin-ray sections, third vertebrae, and whole otoliths. When the age estimates from the otolith sections were compared with the other three age sclerochronological methods, we found the average percentage error to be lowest between the otolith section and fin-ray methods. However, age estimates from fin rays proved most useful for estimating swordfish younger than 6 years, as the fin ray-based age diverged from that of the otolith sections as the swordfish aged. Combining fin ray and otolith section techniques, we estimated the growth parameters of 1–12-year-old females (L_∞ = 259.412, k = 0.113, t₀ = −2.499) and 1–7-year-old males (L_∞ = 175.543, k = 0.202, t₀ = −2.239). We found that females grew significantly faster than males after 3 years and remained larger thereafter. Our calculated growth rates for this region of the north-western Mediterranean Sea were lower than those of the Atlantic, Pacific, and eastern Mediterranean Sea swordfish populations, and similar to growth rates recorded for the western Mediterranean Sea populations. Our study provides critical knowledge on biological-related parameters to serve as a guide for preserving the swordfish population in the Mediterranean Sea.     

ALGORITHM FOR APPLICATION OF FOURIER ANALYSIS FOR BIORHYTHMIC BASELINES OF PHARMACODYNAMIC INDIRECT RESPONSE MODELS

The change of an indirect pharmacological response R(t) can be described by a periodic time-dependent production rate k_in (t) and a first-order loss constant k_out. If k_in(t) follows some biological rhythm (e.g., circadian), then the response R(t) also displays a periodic behavior. A new approach for describing the input function in indirect response models with biorhythmic baselines of physiologic substances is introduced. The present approach uses the baseline (placebo) response R_b(t) to recover the equation for k_in(t). Fourier analysis provides an approximate equation for R_b(t) that consists of terms (usually two or three) of the Fourier series (harmonics) that contribute most to the overall sum. The model differential equation is solved backward for k_in(t), yielding the equation involving R_b(t). A computer program was developed to perform the square L²-norm approximation technique. Fourier analysis was also performed based on nonlinear regression. Cortisol suppression after inhalation of fluticasone propionate (FP) was modeled based on the inhibition of the secretion rate k_in(t) using ADAPT II. The pharmacodynamic parameters k_out and IC₅₀ were estimated from the model equation with k_in(t) derived by the new approach. The proposed method of describing the input function needs no assumption about the behavior of k_in(t), is as efficient as methods used previously, and is more flexible in describing the baseline data than the nonlinear regression method. (Chronobiology International, 17(1), 77–93, 2000)     

Convergence to Normality of the Asymptotic Quasi‐Score Function on a Linear Model

The asymptotic quasi‐likelihood method is considered for the model y_t = f_t(θ) + M_t, t = 0,1, …,T where f_tθ) is a linear predictable process of the parameter of interest θ, M_t is a martingale difference, and the nature of E(M_t² | ℱ_t–1) is unknown. This paper is concerned with the limiting distribution of the asymptotic quasi‐score function of such a model. Confidence intervals and hypothesis testing of θ is derived from the limiting distribution. Comparison is made between the estimates obtained through this method and those obtained through the least squares method.     

Properties and Application of the Location-Test V (n,k)

The present paper is concerned with the properties of a test statistic V(n, k) to test location differences in the one-sample case with known hypothetical distribution G(x). The test is similar to the WILCOXON two-sample statistic after replacement of the second sample by quantiles of the hypothetical distribution. A comparison with the exact distribution of V(n, k) shows that an approximation by means of the normal distribution provides good results even for small sample sizes. The V-test is unbiased against one-tailed alternatives and it is consistent with a restriction which is hardly relevant in practical applications. With regard to the application we are interested especially in the power and robustness against extreme observations for small sample size n. It is shown that in a normal distribution with known standard deviation V(n, k) is more powerful than STUDENT's t for small n and more robust in the sense considered here. The test statistic is based on grouping of the observations into classes of equal expected frequency. A generalization to arbitrary classes provides an essential extension of applicability such as to discrete distributions and to situations where only relative frequencies of G(x) in fixed classes are known.     

On-line parameter and state estimation of continuous cultivation by extended Kalman filter

Summary The on-line estimation of biomass concentration and of three variable parameters of the non-linear model of continuous cultivation by an extended Kalman filter is demonstrated. Yeast growth in aerobic conditions on an ethanol substrate is represented by an unstructured non-linear stochastic t-variant dynamic model. The filter algorithm uses easily accessible data concerning the input substrate concentration, its concentration in the fermentor and dilution rate, and estimates the biomass concentration, maximum specific growth rate, saturation constant and substrate yield coefficient. The microorganismCandida utilis, strain Vratimov, was cultivated on the ethanol substrate. The filter results obtained with the real data from one cultivation experiment are presented. The practical possibility of using this method for on-line estimation of biomass concentration, which is difficult to measure, is discussed.Nomenclature D dilution rate (h^-1) - DO₂ dissolved oxygen concentration (%) - E identity matrix - F Jacobi matrix of the deterministic part of the system equations g - g continuousn-vector non-linear real function - h m-vector non-linear real function - K Kalman filter gain matrix - K _S saturation constant (kgm^-3) - K_S expectation of the saturation constant estimate - M Jacobi matrix of the deterministic part of the measurement equations h - P(t₀) co-variance matrix of the initial values of the state - P(t_k/t_k) c-variance matrix of the error in (t _k|t _k) - P(t_k+1/t_k) co-variance matrix of the error in (t _k+1|t _k - Q co-variance matrix of the state noise - R co-variance matrix of the output noise - S substrate concentration (kgm^-3) - S _i input substrate concentration - t time - t _k discrete time instant with indexk=0, 1, 2,... - u(t) input vector - v(t_k) measurement (output) noise sequence - w(t) n-vector white Gaussian random process - x(t₀) initial state of the system - (t₀) expectation of the initial state values - x(t) n-dimensional state vector - x(t_k) state vector at the time instantt _k - (t_k|t_k) expectation of the state estimate at timet _k when measurements are known to the timet _k - (t_k+1|t_k) expectation of the state prediction - X biomass concentration (kgm^-3) - expectation of the biomass concentration estimate - y(t_k) m-dimensional output vector at the time instantt _k - Y _XIS substrate yield coefficient - _X|S expectation of the substrate yield coefficient estimate - specific growth rate (h^-1) - _M maximum specific growth rate (h^-1) - expectation of the maximum specific growth rate estimate - state transition matrix     

Giant pandas are losing their edge: Population trend and distribution dynamic drivers of the giant panda

Comprehending the population trend and understanding the distribution range dynamics of species are necessary for global species protection. Recognizing what causes dynamic distribution change is crucial for identifying species' environmental preferences and formulating protection policies. Here, we studied the rear-edge population of the flagship species, giant pandas (Ailuropoda melanoleuca), to (1) assess their population trend using their distribution patterns, (2) evaluate their distribution dynamics change from the second (1988) to the third (2001) survey (2–3 Interval) and third to the fourth (2013) survey (3–4 Interval) using a machine learning algorithm (eXtremely Gradient Boosting), and (3) decode model results to identify driver factors in the first known use of SHapley Additive exPlanations. Our results showed that the population trends in Liangshan Mountains were worst in the second survey (k = 1.050), improved by the third survey (k = 0.97), but deteriorated by the fourth survey (k = 0.996), which indicates a worrying population future. We found that precipitation had the most significant influence on distribution dynamics among several potential environmental factors, showing a negative correlation between precipitation and giant panda expansion. We recommend that further research is needed to understand the microenvironment and animal distribution dynamics. We provide a fresh perspective on the dynamics of giant panda distribution, highlighting novel focal points for ecological research on this species. Our study offers theoretical underpinnings that could inform the formulation of more effective conservation policies. Also, we emphasize the uniqueness and importance of the Liangshan Mountains giant pandas as the rear-edge population, which is at a high risk of population extinction.     

The preparation and kinetic properties of multiple forms of chicken brain acetylcholinesterase

A method for preparing various forms of acetylcholinesterase (A ChE) from chicken brain has been developed and they have been characterized in terms of kinetic parameters such as K_m, rate constant (k), turnover number (k_p), specificity constant (k_sp), V_max and half-life (t_1/2). The solubility experiments show that, there are two major forms of A ChE i.e. water-soluble and membrane-bound A ChE (MBA ChE). The MBA ChE shows several subforms, and on the basis of percentage activity only three MBA ChE forms have been selected for complete characterization by various kinetic parameters. It was found that these three forms of MBA ChE demonstrate significant differences in their kinetic properties.     

The Estimation of a Multivariate Fitness Function from Several Samples Taken from a Population

The situation is considered where the multivariate distribution of certain variables X₁, X₂, …, X_p is changing with time in a population because natural selection related to the X's is taking place. It is assumed that random samples taken from the population at times t₁, t₂, …, t_s are available and it is desirable to estimate the fitness function w_t(x₁, x₂,…,x_p) which shows how the number of individuals with X_i = x_i, i = 1, 2, …, p at time t is related to the number of individuals with the same X values at time zero. Tests for population changes are discussed and indices of the selection on the population dispersion and the population mean are proposed. The situation with a multivariate normal distribution is considered as a special case. A maximum likelihood method that can be applied with any form of population distribution is proposed for estimating w_t. The methods discussed in the paper are illustrated with data on four dimensions of male Egyptian skulls covering a time span from about 4500 B.C. to about 300 A.D. In this case there seems to have been very little selection on the population dispersion but considerable selection on means.     

Rate constants of acetylcholine receptor internalization and degradation in mouse muscles

The rate constants for internalization and subsequent extrusion of acetylcholine receptors (AChRs) during degradation in adult innervated and denervated mouse diaphragm muscles were determined using proteinase K (PK) digestion. This procedure separated ¹²⁵I-α-bungarotoxin (Bgt)-labeled AChRs into PK-sensitive and PK-resistant compartments. The time course of the residual radioactivity in these two compartments suggested that they represented surface membrane and internalized compartments, respectively. The data were compatible with a mathematical model based on the assumption that during degradation of AChRs a surface compartment, A, fed an internal compartment, B, with an internalization rate constant (k_i), and that B is drained from the cell with an extrusion rate constant (k_o). Using the mathematical model, we were able to determine that k_i and k_o were, respectively, 0.068 (t_1/2 ∼ 10.2 days) and 0.69–0.55 (t_1/2 ∼ 1.0– 1.25 days) for innervated muscle and were, respectively, 0.69 (t_1/2 ∼ 1.0 day) and 6.93 (t_1/2 ∼ 0.1day) for denervated muscle. Thus, the rate for internalization was about 8–10 times slower than that for extrusion from the cell for both the slowly degrading innervated (Rs) AChRs and for the rapidly degrading denervated (Rr) AChRs. This inequality betweeen k_i and k_o therefore allows the combined quantity of A(t) + B(t) , usually measured in AChR degradation studies, to approximate a single exponential. J. Cell. Physiol. 181:107–112, 1999. © 1999 Wiley-Liss, Inc.