bluuebunny/crossref_metadata_2025 huggingface dataset:
A Decomposition for the Inclined Point‐Symmetry Model in a Square Contingency Table
Authors: Tomizawa S.
Published: May 2007

In a square contingency table the inclined point‐symmetry model which is an extension of the point‐symmetry model is proposed and a decomposition for its model is shown. Moreover a test theory for the decomposed models and an example are given.
Testing the Homogeneity of Relative Risk in Case‐Control Studies with Multiple Matching
Authors: Le Chap T.
Published: May 2007

This paper purposes a simple chi‐square test for the homogeneity of relative risk in case‐control studies with multiple matching.
Four Kinds of Symmetry Models and their Decompositions in a Square Contingency Table with Ordered Categories
Authors: Tomizawa S.
Published: May 2007

In a square contingency table four kinds of symmetry models are proposed and their decompositions are given. Two models of them are extensions of the local point‐symmetry model and the reverse local point‐symmetry model by TOMIZAWA (1985), and the other two models are concerned with the inclined point‐symmetry model by TOMIZAWA (1986) and the conditional symmetry model by MCCULLAGH (1978). An example is given.
P‐values For Discrete Test Statistics
Authors: Franck W. E.
Published: May 2007

This paper considered the relative merits of the P‐value and the mid‐P‐value. It is shown that inference based on the mid‐P‐value is in a certain sense on firmer ground. In particular the expected mid‐P‐value does not change under an irrelevant breakup in the test statistic.
A Modified Exact Test for 2 × 2 Contingency Tables
Authors: Haber M.
Published: May 2007

A modified exact test is proposed for 2×2 contingency tables. This test, which is based on a less conservative definition of the concept of significance (STONE, 1969) is compared with a modified form of Pearson's X2 test and with Tocher's randomized exact (UMPU) test. The sizes of the new test lie near the nominal 0.05 levels while those of the X2 test usually exceed the nominal level, sometimes by a factor of 2 or more. The power of the modified test is usually close to that of the UMPU test.
A Note on a Continuity Correction for Testing in Three‐Dimensional Configural Frequency Analysis
Authors: Küchenhoff H.
Published: May 2007

A continuity correction is proposed for the test statistics of HABERMAN (1978) and LEHMACHER (1981) for identifying overfrequented (or underfrequented) cells in the three‐dimensional Configural Frequency Analysis (CFA). Its quality is shown by comparison with the test based on the exact distribution of the cell frequencies.
Model‐Based Statistical Procedures for the Analysis of in Vitro Mutagenesis Assays
Authors: Kaldor John
Published: May 2007

A number of short‐term screening assays for potential chemical carcinogens and mutagens involve the measurement of mutation rates inin vitrocell populations. In this paper, statistical procedures are proposed for the analysis of results from these assays. The procedures, which are based on previously developed stochastic models of cell growth and mutation, include hypothesis tests for the comparison of mutation rates in treated and control cultures, and estimation and hypothesis tests for the parameters of a linear mutagenesis dose‐response. Computer simulation is used to validate the methods, and they are illustrated by an analysis of data obtained under the mouse lymphoma mutagenesis protocol.
General Derivation of Intraclass Correlation Coefficients
Authors: Schemper M.
Published: May 2007

A general intraclass correlation coefficient is derived similarly to the general correlation coefficient given by KENDALL (1962). This coefficient II embraces as specific cases three intraclass correlations, related to Pearson's r, Kendall's tau and Spearman's rs, that were dealt with by FISHER (1921), WHITFIELD (1949), SHIRAHATA (1981) and SCHEMPER (1984). Formal relationships are presented and the qualification of the three coefficients for specific applications is discussed.
A Comparison Between Several Goodness of Fit Tests for Cox's Model
Authors: Nagelkerke N. J. D. , Oosting J. , Hart A. A. M.
Published: May 2007

A comparison is made between two approaches to testing goodness of fit of Cox's regression model for survival data. The first approach is based on the inclusion of time dependent covariates, whereas the second one is based on the autocovariance of successive contributions to the derivative of the loglikelihood. It appears that the second test is most appropriate for testing in situations where the structure of the departure from proportional hazards is not known a priori. An approximate expression for the relative efficiency of the two test procedures is presented.
A Power Law Model for Survival Data Using GLIM
Authors: Wu Shu‐Chen Ho , Fung Karen Yuen
Published: May 2007

This paper proposes a regression model for the Weibull survival distribution of which the scale parameter is a power function of covariates. The estimation of parameters for partially censored data is pursued by using a statistical package called GLIM. Two sets of carcinogenic data are used to illustrate this procedure.
Yule‐Coefficients for Second‐ and Higher‐Order Associations
Authors: Lienert G. A. , von Eye A.
Published: May 2007

The well‐known Q coefficient of association defined by YULE (1900) for two attributes is generalized from first‐order association Q to second‐order association Q for three attributes and to higher‐order Q's for more than three attributes (or binary variables). Q analysis of t binary variables is shown to be a suitable means for describing simple (quasi‐parametric) or complex (multi‐nonparametric) relationships in a t‐dimensional contingency cube. A biometrical example is given using clinical data.
Some Methods for Summarizing Survivorship Data in Nonstandard Situations
Authors: Gore A. P. , Paranjape Sharayu , Rajarshi M. B. , Gadgil Madhav
Published: May 2007

One difficulty in summarising biological survivorship data is that the hazard rates are often neither constant nor increasing with time or decreasing with time in the entire life span. The promising Weibull model does not work here. The paper demonstrates how bath tub shaped quadratic models may be used in such a case. Further, sometimes due to a paucity of data actual lifetimes are not as certainable. It is shown how a concept from queuing theory namely first in first out (FIFO) can be profitably used here. Another nonstandard situation considered is one in which lifespan of the individual entity is too long compared to duration of the experiment. This situation is dealt with, by using ancilliary information. In each case the methodology is illustrated with numerical examples.
Tables and Procedures for the Determination of Power and Sample Sizes in Univariate and Multivariate Analyses of Variance and Regression
Authors: Hager W. , Möller H.
Published: May 2007

The available power tables for use in experimental design only serve for limited practical purposes, since they are restricted to very few levels of significance such as .01, .05, and .10. With these values, however, usually no correction for cumulating error probabilities, for example, by the Dunn‐Bonferroni method, can be achieved, because (very) low values of a and sometimes even of α are necessary. Therefore, power tables are presented that encompass a wide range of different values for a (.0005 to .40), for power (.50 to .9995), and for 45 different values of the degrees of freedom for the numerator of the F ratio (u = 1 to 150). Four of the 16 tables are printed. Their use is demonstrated for some paradigmatic problems in univariate and multivariate analyses of variance and regression.
A Likelihood Ratio Test of the Equality of Paired Survival Data with Censoring
Authors: Knapp R. G. , Gross A. J. , Cantor A. B.
Published: May 2007

A test is developed to determine whether the mean survival times are equal when dealing with paired survival data.

We assume the data follow a bivariate exponential distribution for which the variables are conditionally independent. The unconditional distribution is derived in which the distribution of the nuissance variable is general.

A method based on the likelihood ratio is derived to obtain the test. The data are allowed to have both left and right censoring.
Randomization Tests for Censored Survival Distributions
Authors: Edgington E. S. , Gore A. P.
Published: May 2007

This paper discusses the application of randomization tests to censored survival distributions. The three types of censoring considered are those designated by MILLER (1981) as Type 1 (fixed time termination), Type 2 (termination of experiment at r‐th failure), and random censoring. Examples utilize the Gehan scoring procedure. Randomization tests for which computer programs already exist can be applied to a variety of experimental designs, regardless of the presence of censored observations.
Correlation and Linear Regression if the Random Variables are Subject to Errors or Fluctuations
Authors: Horn M. , Guiard V.
Published: May 2007

For the model x=a+e, y=b+d estimators of Pearson's coefficient of correlation and of the line of regression between a and b are presented. The problem of prediction is dealt with.
The Performance of Goodness of Fit Tests for Logistic Regression with Discrete Covariates
Authors: Korn L. R. , Hosmer D. W. , Lemeshow S.
Published: May 2007

This paper considers the distribution of previously proposed goodness of fit tests when some or all of the covariates are dichotomous variables. The simulations show that of the statistics suggested for testing fit only one appears suitable for use with discrete covariates. This statistic uses conditional maximum likelihood estimates and groups the estimated probabilities into groups of equal size or into groups based on the patterns of the covariates when these are few in number.
Closed Form Estimators of Latent Cell Frequencies
Authors: Bonett D. G. , Woodward J. A. , Bentler P. M.
Published: May 2007

One‐stage and two‐stage closed form estimators of latent cell frequencies in multidimensional contingency tables are derived from the weighted least squares criterion. The first stage estimator is asymptotically equivalent to the conditional maximum likelihood estimator and does not necessarily have minimum asymptotic variance. The second stage estimator does have minimum asymptotic variance relative to any other existing estimator. The closed form estimators are defined for any number of latent cells in contingency tables of any order under exact general linear constraints on the logarithms of the nonlatent and latent cell frequencies.
The Statistical Properties of Genetic Absolute Distance
Authors: Katz M. , Goux J.‐M.
Published: May 2007

The statistical properties of one estimator of absolute genetic distance (1/2) K∑i=1 |pxi‐yr|, tween two populations X and Y, are presented. It is shown that using this distance in small samples can be misleading particularly when populations are close to each other.
Some Properties of Plackett and Hewlett's Model for the Joint Action of Drugs
Authors: Unkelbach H. D. , Wolf Th.
Published: May 2007

The model of PLACKETT and HEWLETT (1963) for the joint action of mixtures of drugs in the case of quantal response is discussed in terms of isobols. The model is shown to be able to fit quite different types of joint actions.
Equidirection: A Measure of Similarity Among Time Series
Authors: Yassouridis A. , Hansert E.
Published: May 2007

In the present paper we investigate the concept of equidirection, i.e. similarity in the direction of variation, or parallelism in the broader sense, among m (m ≧ 2) times series, especially under the assumption that the time series are realizations of processes with independent increments. However, the processes need not be stationary. Furthermore, the probabilities for the direction of variation may be unstable, in which case only upper and lower bounds are known. A measure based on the concept of equidirection was developed that enables identification of clusters of similar time series and analysis of relationships among variables.
Linear Predictivity: An Alternative for MANOVA and Multivariate Multiple Regression
Authors: Lefkovitch L. P.
Published: May 2007

The maximal linear predictable combination of a set of dependent variables is defined as that linear combination maximizing the multiple correlation coefficient with the predictor set. It allows the relative importance of a number of factors to be evaluated for the joint response, rather than for the response of each dependent variable in turn. The procedure is illustrated by an example.

AMS subject classification: major 62J10, 62H20; minor 62H25.
Small Sample Comparison of Some Tests for Equality of Two Proportions
Authors: Ahluwalia R. , Rohatgi V. K.
Published: May 2007

Powers of some tests of equality of two proportions are compared for small samples and approximate level .05. Numerical results indicate that the asymptotic results hold also for small and moderate sample sizes.
Harmonic Mean Approach to Regression Analysis Under Heteroscedasticity and Nonnormality
Authors: Tabatabai M. A. , Tan W. Y.
Published: May 2007

In this paper, by combining the harmonic mean approach with the Welch and the James procedure (see WELCH 1951, JAMES, 1951), we develop some robust procedures for testing parallelism in several straight lines under heteroscedasticity and nonnormality. Through Monte Carlo simulations it is shown that these new tests are quite robust with respect to departure from normality. For small sample sizes, however, the TAN‐TABATABAI (1984) Fβ and F*β tests appear to be more powerful than the new tests, although when sample sizes are not small, there are hardly any differences between the Tan‐Tabatabai Fβ and F*β tests and the new tests.
The Relative Power of Two Asymptotic Multivariate Tests for Homogeneity in a Contingency Table
Authors: Onukogu Ike B.
Published: May 2007

In a three way contingency table two multivariate tests for homogeneity have been proposed by the author (1983) a the “catanova” test, which is a trace “metric” test and b the “multinova” test which is determinant based. Both tests are asymptotically distributed as chi‐square.

In this paper, the power values of the tests are compared and conditions are given for preference of each test.
On Combining Estimates of Relative Risk Using the Negative Binomial Mode
Authors: Bennett B. M.
Published: May 2007

The negative binomial distribution (N.B.) was previously proposed (BENNETT, 1981) in the estimation of and tests of significance for the relative risk (ψ) in prospective studies in epidemiology. This paper discusses the application of the N.B. model in combining estimates of ψ from a series of prospective studies and in statistical tests of the equality of these estimates.
The Point Evaluation Method for Approximating Function Means, Variances and Covariances
Authors: Manly B. F. J.
Published: May 2007

A perennial problem in statistics is the determination of biases, variances and covariances for functions of random variables X1, X2, …, Xn which themselves have a known distribution. A common approach is through equations based upon Taylor series approximations but a “point evaluation” method may sometimes be a useful alternative. This involves approximating the multivariate distribution of the X variables by the 2n points given by X1=μ1±1, X2 = μ2 ±2, …, Xn = = μn μn, where μi is the mean and σi the standard deviation of Xi, with appropriate point weights. An advantage over the Taylor series approach is that function derivatives do not have to be explicitely calculated. The point evaluation method is particularly useful in cases where the X variables are uncorrelated. Then the evaluation of the 2n points can be replaced by the evaluation of 2n points. The point evaluation method is illustrated with powers of a normally distributed variable, and with estimation of gene frequencies from ABO blood group frequencies.
A General Statistical Model for Multifactorial Inheritance of Discontinuous Traits
Authors: Bonet D. G. , Smalley Susan I. , Woodward J. A.
Published: May 2007

A general statistical model for the analysis of ordered discrete phenotypes given a multifactorial mode of inheritance is outlined. This model can be applied to give (i) components of variance and covariance for various genetic and environmental effects that are eatimable from the genetic sampling design, (ii) a factor analysis structure, and (iii) regression estimates for description of the relationship among the genetic and environmental factors.
Parent/offspring Relations for a Fitness Related Character
Authors: Skovgaard I. M.
Published: May 2007

Some parent/offspring relations of a quantitative character are discussed, in particular in relation to the mean change from one generation to the next. It is shown that the prediction of this “progress” as the heritability multiplied by the selection differential takes only the slope of the parent/offspring relation into account and holds if, and only if, the population mean is a fixpoint of the mid‐parent/offspring regression in the case of a character that is unrelated to sex. In particular, two examples show that this may not be the case if the character is related to fitness by pleiotropic effects of single genes.
Using Elementary or Non‐Elementary Models in Contingency Table Analysis. Application to Medical Problems
Authors: Enke H.
Published: May 2007

Information available should always be considered in any statistical analysis. But it is also true that the good presentation and interpretability of the results should be aimed at. In this paper the research situation (kind of variables and theoretical relations between them) and good presentation and interpretability of graphical models are linked together.
An Evaluation of Different Methods in Epidemiologic Studies of Radiation Risks
Authors: Schindel F.
Published: May 2007

The probability of detecting possible late effects of ionizing radiation in human populations depends on the size of exposure in the study population and on the epidemiologic evaluation method used. This is not only due to the mathematical or statistical properties of the method, but also to the choice of the control population, which may be either external (usually large) or internal (usually not so large). Moreover, the use of a large external control population often results in an increasing influence of selection factors expressing themselves e.g. through the ‘healthy worker’ effect. In this paper three different methods usually employed in follow‐up studies are reviewed: the calculation of Standardized Mortality Ratios (SMR), a contingency table analysis based on Person‐Years (PY) and the comparison of Cumulative Mean Doses (CMD) within different subcohorts. The methods are illustrated with a simple radiation risk model; nevertheless, most of the conclusions apply to non‐radiation risk studies as well. The CMD‐method is shown to be heavily selection sensitive.
Iso‐ and Anisoasymmetry Testing in Pre‐post Rating Designs
Authors: Heilmann W.‐R. , Lienert G. A.
Published: May 2007

It is suggested to test against anisoasymmetry rather than against marginal homogeneity if (1) a pre‐post treatment matched pairs contingency table is ordinally scaled by clinical ratings and if (2) the alternative to marginal homogeneity is a shift in location from pre‐ to post treatment ratings. Testing against anisoasymmetry may detect treatment effects which are not manifest in marginal inhomogeneities.
Investigations on Some Attributes of the Likelihood Function for MPN Determination
Authors: Diener W.
Published: May 2007

The paper investigates the likelihood function to determine the MPN (Most Probable Number as a measure of concentration in the virology), dependent on several parameters. Taking only ‘probable’ result schemes into the MPN‐tables they would become much shorter. There are suggested two conditions for the selection of the result schemes, given and compared by some tables together with a mathematical foundation of the number of the selected schemes. Some tables and a theorem about success probabilities of the result schemes point out their changes under different conditions (number of tubes, number of dilutions, dilution ratio), and make it possible to estimate success probabilities of result schemes not selected by the more restricted condition.
Estimation of Individual Growth Curves by Empirically Weighted Least Squares
Authors: Louv W. C.
Published: May 2007

The simultaneous estimation of individual growth curves and a mean growth curve is accomplished by weighted least squares. A polynomial curve is fitted for each individual and the polynomial parameters are linear functions of parameters corresponding to covariates. A simple, computationally efficient variance‐covariance estimator is derived. The resultant estimate is used in the weighted least squares estimation. The results are compared to empirical Bayes estimation.
The Effects of Misspecification of a Regression Model
Authors: Nagelkerke N. J. D. , Hart A. A. M. , Oosting J.
Published: May 2007

The consequences of the misspecification of a regression model are considered. For small effects of covariates a proportional consistency theorem is derived. The consistent estimation of the covariance matrix of the estimates is discussed.
On the Detection of Unusual Points in Regression
Authors: Paul S. R.
Published: May 2007

Some procedures, based on studentized residuals and the diagonal elements of the ‘hat’ matrix, for the detection of unusual points in regression are discussed. These procedures are quite simple but effective to uncover unusual structure of the data. Some examples are given.
On Testing a Trend in Means in Oneway Layout
Authors: Le Chap T.
Published: May 2007

A test for a trend in means in oneway layout is discussed with particular emphasis on sample size determination. The proposed method amounts to formulating a linear contrast among sample means and testing it for significance. The resulting test statistic is reduced to a test by Barlow et al. (1972) When sample sizes are equal and to the Armitage‐Kendall correlation test for a trend in proportions when the response variable is dichotomous. The problem of sample size determination is discussed and illustrated with numerical examples.
Log‐linear Models in a Study of Gall Bladder Disease
Authors: Janardan K. G. , Pandarinath S.
Published: May 2007

Biliary drainage and X‐rays have been used singly and together in the diagnosis of gall bladder disease. Data from two sets of patients were statistically analyzed using log‐linear analysis of contingency tables. The results of the study show that “biliary drainage” is dependent of “X‐ray” and “Pathology”; abnormal X‐ray is associated with abnormal pathology. Thus, biliary drainage is not of such value as to base surgery on it alone. However, X‐rays are of significant value in the diagnosis of the gall bladder disease and to decide whether a surgery is needed or not.
Maximum Likelihood Estimation of Genetic Parameters in Cell Populations
Authors: Tan W. Y. , Tou Conrad
Published: May 2007

In this paper we consider a cell population such as bacteria consisting of two types of cells, mutant and nonmutant. Under the mutation and homogeneous pure birth processes, this paper derives a maximum likelihood estimation procedure for estimating mutation rate and birth rate. The method is applied to Newcombe's data; further some Monte Carlo studies are generated. The numerical results indicate that the method is quite efficient for estimating genetic parameters in cell populations.
Probability of Inadmissible Estimates of Heritability from Regression and Half‐sib Analyses
Authors: Prabhakaran V. T. , Jain J. P.
Published: May 2007

Formulae are derived for the probability of obtaining inadmissible estimates of heritability (h2) in half‐sib and intra‐sire regression analyses, under the additive‐dominance‐epistasis model of gene action. Results for several combinations of sire/dam number, h2 and the proportion of additive x additive epistasis are given for the balanced situation.
Test Procedures in Configural Frequency Analysis (CFA) Controlling the Local and Multiple Level
Authors: Perli H.‐G. , Hommel G. , Lehmacher W.
Published: May 2007

The test statistics used until now in the CFA have been developed under the assumption of the overall hypothesis of total independence. Therefore, the multiple test procedures based on these statistics are really only different tests of the overall hypothesis. If one likes to test a special cell hypothesis, one should only assume that this hypothesis is true and not the whole overall hypothesis. Such cell tests can then be used as elements of a multiple test procedure.

In this paper it is shown that the usual test procedures can be very anticonservative (except of the two‐dimensional, and, for some procedures, the three‐dimensional case), and corrected test procedures are developed. Furthermore, for the construction of multiple tests controlling the multiple level, modifications of Holm's (1979) procedure are proposed which lead to sharper results than his general procedure and can also be performed very easily.
Rank Analysis of Block Designs Having Different Cell Frequencies
Authors: Rai S. C.
Published: May 2007

A distribution–free test is considered for testing the treatment effects in block designs with different cell frequencies. A test statistic which is a function of treatment ranks has been proposed which is distributed as chi‐square for large samples. The null distribution of the test statistic has been obtained. The entire procedure has been explained by a numerical example.
A Linear Model with Plot Effects
Authors: Gill D. S. , Janardan K. G.
Published: May 2007

It is a common practice to analyze the data from agricultural experiments using randomized block design where each block has homogeneous experimental units (plots). However, many times, during the period of study, due to unavoidable circumstances such as natural calamities, say floods, for example, plots are no longer homogeneous. Thus, it is desirable to consider the plot effects also in the model. An appropriate model and an example of the analysis of data with plot effects is provided here.
Analysis of Proportions in One‐ or Two‐Way Tables with Spoiled Data
Authors: Bennett B. M.
Published: May 2007

This paper discusses the analysis of data on proportions in contingency tables. The X2 ‘index of dispersion test’ (e.g. Fisher, 1954) is developed in these situations and compared with the use of the ‘logit’ transformation. An example using Osborn's (1979) data is given, illustrating the estimation of one or more missing observations.
Some Tests for k£2 Upper Outliers in an Exponential Sample
Authors: Likeš J.
Published: May 2007

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.
Relative Efficiencies of a Class of Goodness of Fit Tests for Randomly Censored Data
Authors: Koziol J. A.
Published: May 2007

We investigate the relative performances of a class of goodness of fit procedures for randomly censored data. For purposes of planning experiments, we quantify the loss of information induced by censorship. We evaluate efficiencies against particular alternatives of interest in survival studies, as the amount of censorship increases. We caution against attributing various power and efficiency properties of the goodness of fit criteria that are obtained under no censorship to situations where the censorship is far from negligible.
Prediction of the Standardized Risk Ratio via Proportional Mortality Analysis
Authors: Marsh G. M. , Winwood J. P. , Rao B. R.
Published: May 2007

The relationship between the commonly used indiréctly standardized comparative mortality indices, the standardized mortality ratio (SMR) and the standardized proportional mortality ratio (SPMR) is well known; whereas, the relationship between their less commonly used directly adjusted counterparts, the standardized risk ratio (SRR) and the recently proposed externally standardized proportional mortality ratio (SePMR) has been heretofore not developed. This paper fills this void by demonstrating the algebraic and statistical relationship between the SRR and the SePMR and showing how, under some modest assumptions, valid inferences about the SRR can be based on analysis of SePMR's. More specifically, an asymptotic prediction interval has been developed for the SePMRi which, with high probability, contains the ratio RSRRi = SRRi/SRR. The utility of the SePMRi is supported empirically using data from a recent retrospective cohort study of mineral fiber workers.
Multivariate Probability in Terms of Marginal Probability and Correlation Coefficient
Authors: Seneta E.
Published: May 2007

This paper is motivated by a practical problem relating to student performance in a number of subjects of equal standing. Its mathematical formulation is to find an approximation to a multivariate probability of the form Pr {X1⩾a, X2⩾a, …, XN⩾a} for arbitrary a and N, in terms of p = Pr {X1⩾a} and q = Corr (Xi, Xj), i≠j, where Xi, i = 1, …, N are exchangeable random variables with mean 0 and variance unity.
Measures of Imbalance for Unbalanced Models
Authors: Khuri A. I.
Published: May 2007

In this paper we present a procedure to measure the degree of imbalance of an unbalanced data set. The procedure is based on choosing an appropriate loglinear model for the subclass frequencies of the data. A measure of imbalance is then introduced as some function of the chi‐squared statistic used in the goodness‐of‐fit test for the loglinear model. The proposed procedure can also be used to measure departures from certain types of balance, such as proportionality of subclass frequencies, partial balance, and last‐stage uniformity.
A Theoretical Model for Estimating Linkage in F2 Populations with Distorted Single Gene Segregation
Authors: Heun M. , Gregorius H.‐R.
Published: May 2007

A model is presented which allows estimation of linkage from dihybrid F2 populations with distorted single gene segregation by applying the maximum‐likelihood method.

For different selection processes operating on one locus at either the gametic or the zygotic level, it can be demonstrated that, if the deficit is previously taken into account, testing for free recombination can be carried out without prior knowledge of the causes of this deficit. In the presence of linkage, the expected frequencies of two phenotypic classes depend on whether gametic or zygotic selection is operating. The remaining two classes can be utilized for the estimation of linkage as their frequency ratio is independent of these selection types.

The application of this procedure to situations with coupling, incomplete penetrance, gametic and zygotic selection is discussed.
A Note on Heritability of a Dichotomous Trait
Authors: Im S.
Published: May 2007

In a random effects model for a dichotomous trait, we prove that the heritability of the dichotomous trait given in Dempster & Lerner (1950) is strictly smaller than the intraclass correlation. A numerical comparison is given.
Tests for Trends in Incidence Rate Ratios
Authors: Nurminen M.
Published: May 2007

Breslow (1984) described an efficient score test for trend in incidence density rate ratios for cohort studies under a conditional Poisson or binomial model employing maximum likelihood estimation of the rate parameters. In this communication, an alternative derivation of this statistic that is based on an unconditional approach is provided, along with an examination of associated goodness‐of‐fit tests and methods of confidence interval estimation. The procedures are illustrated by a cohort study of ischemic heart disease mortality following industrial exposure to carbon disulfide.
Test Based on Independent, but Non‐identically Distributed Random Variables
Authors: Hüsler Jürg
Published: May 2007

The binomial test is applied for the problem of testing a hypothesis based on a sample of independent, but non‐identically distributed random variables. The used basic idea is that each random variable indicates the presence of the hypothesis. Hence each random variable is transformed such that the binomial test can be used as a simple procedure.
Semi‐Markov Model and Its Application
Authors: Jain R. K.
Published: May 2007

In this paper, a numerical procedure based on the theory of semi‐Markov process is presented to study the prognosis of the cancer of cervix. Data is used to illustrate the predictive ability of the model.
Multi‐Sample Slippage Test for Ordered Observations
Authors: Rai S. C.
Published: May 2007

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.
Simultaneous Selection of Extreme Populations: A Subset Selection Approach
Authors: Mishra Satya N. , Dudewicz Edward J.
Published: May 2007

The problem of selecting a “best” (largest mean, or smallest mean) population from a collection of k independent populations was formulated and solved by Bechhofer (1954). Gupta (1965) solved another important problem, that of selecting a subset of populations containing the “best” population from the original collection of populations. Since then many variations of the problem have been considered. Tong (1969) and Lewis (1980) have investigated the problem of selecting extreme populations (populations with a largest, and populations with a smallest, mean) with respect to one and two standard populations, respectively. In this paper we study the selection of extreme populations in absence of any standard population. We formulate subset‐selection procedures when variances are known and equal, and also in the most general case when they are unknown and unequal. Nonexistence of a single‐stage procedure is noted for this latter case (even if variances are equal). A two‐stage procedure and some of its associated properties are discussed. Tables needed for application are provided, as is a worked example.
On a Model for Estimating the Parameter of the Human Reproductive Process
Authors: Biswas S. , Sehgal V. K.
Published: May 2007

Attempt has been made in this paper to estimate certain parameters (data pertaining to which are either not available or easily reportable) of the human reproductive process as the period of postpartum ammenorrhoea (P.P.A.), number of foetal wastages in between live births etc., using a truncated negative binomial probability model. In view of the hypothesis that the probability of foetal wastages varies from mother to mother, the truncated negative binomial distribution has been compounded by weighing with the best prior Beta distribution of the parameter. Estimation has been made by successive approximation using the method of moments.
A Method of Fuzzy‐Theory‐Based Computer‐Aided Exploratory Data Analysis
Authors: Bandemer H. , Roth K.
Published: May 2007

When evaluating functional relationships from given data in an exploratory state of investigation, we only want to get an imagination of a possibly existing trend. Usually, methods of local or empirical regression are chosen to meet this purpose. In the paper we suggest an alternative using the possibilities of modern picture processing methods and computers. The data were transformed into a grey‐tone picture representing a fuzzy observation set, the maximum trace of which yieldsthedesired first impression of the trend and may serve as the starting point for further detailed evaluation of the functional relationship. The method is illustrated by a real‐data numerical example.
Dual Designs and Their Application in Genetical Experiments
Authors: Puri P. D. , Nigam A. K. , Kageyama S.
Published: May 2007

The dual of incomplete block designs has been studied with th́eir applications in genetical experiments. Partial diallel crosses (PDC) of type I have been constructed using balanced incomplete block (BIB) designs, partially balanced incomplete block (PBIB) designs and their dual designs. Simplified analysis of PDC has been presented using the dual property of these designs. List of optimal PDC having simple analysis has been given.
Confidence Limits on Heritability Under Non‐normal Variations
Authors: Singhal R. A.
Published: May 2007

Moment approximation for the non‐normal sampling distribution of the ratio of mean squares in the balanced one‐way Model II is found close to that of the Snedecor's F‐distribution. The confidence limits for heritability of paternal half‐sib correlations, derived employing F‐distribution, are, in general, remarkably narrow for platykurtic and wide for leptokurtic sire effects than the normal limits. The effect of kurtosis of environmental deviations on these limits is of no consequence whereas the effect of skewness is invisible.
Statistical Analysis of Factorial Diallel Design over Environments
Authors: Wolf J.
Published: May 2007

Starting from the experimental situation that in each of a environments all mp combinations between m maternal and p paternal genotypes are raised in b replications (blocks), a linear model is formulated for a quantitative character. On the basis of this model formulae for the analysis of variance are given. The expectations of mean squares as well as the estimations of effects (general and specific combining ability and their interaction terms with environments) and their variances are given for different combinations of fixed and random factors.
Alternative Models for Correlating Toxic Effects
Authors: Verducci J. S.
Published: May 2007

Two very different types of correlation are examined. First, the problem of correlating two different toxic potentials, such as mutagenesis and carcinogenesis, over a class of chemicals is discussed and shown to be quite difficult unless strong assumptions are made about the dose‐response curves for each effect. The second type of correlation is that of joint occurrences of symptoms over a population of subjects. A latent class model whose parameters are linear functions of dosage is proposed based on a two‐stage theory of carcinogenesis. This model surpasses various alternative models in predicting multiple site tumors resulting from exposure to the solvent 1,3‐butadiene.
Nonparametric Comparison of Longitudinal Response Patterns from Paired Samples Using Configural Frequency Analysis
Authors: Von Eye Alexander , Lienert Gustav A.
Published: May 2007

Nonparametric methods of Configural Frequency Analysis (CFA) for comparing longitudinal response patterns are discussed. Characteristics of diagonally symmetric frequency distributions are mapped with hypotheses on the locus of treatment effects. Test statistics for the analysis of local dependencies are discussed. In particular, applications to paired samples are considered. A biomedical example is given from research on the effects of spasmolytic drugs. Local CFA‐testing is compared with global testing. Alternative strategies of testing and the respective underlying assumptions are discussed.
Selection of Judges for Sensory Evaluation
Authors: Rai S. C.
Published: May 2007

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.
Classical Analysis of Variance Methods and Nonparametric Counterparts
Authors: Van Der Laan Paul , Verdooren L. Rob
Published: May 2007

The present investigation is concerned with the use of classical and nonparametric techniques in the analysis of experiments. Occasionally biometricians are confronted with results arising from an experiment with data which do not necessarily satisfy the assumption of Normality, the basis of the classical analysis of variance methods. Sometimes the biometrician handles such a situation by transformation of the observations and applying the classical techniques. Although this attack may lead to a satisfactory analysis, the results may be questionable in a number of cases. In analyzing continuous data without the Normality assumption nonparametric methods provide realistic alternatives. In this paper a number of problems will be discussed with and without the Normality assumption resulting in the well‐known classical analysis and its nonparametric counterparts. Most of the nonparametric procedures to be discussed are based on ranks.
Analysis of Square Contingency Tables with Ordered Categories by a New Method of Applying the 1‐Weight Modified Marginal Homogeneity Models
Authors: Tomizawa Sadao
Published: May 2007

For square contingency tables with ordered categories, this note proposes a new method of applying Tomizawa's (1987) 1‐weight modified marginal homogeneity models and applies to the 4×4 tables on unaided vision analysed by Tomizawa (1987) and by Stuart (1955). A possible explanation which is derived from fitting those models is first obtained using this new method.
Some Results on Error Rates for Quadratic Discrimination with Known Population Parameters
Authors: Young Dean M. , Turner Danny W. , Marco Virgil R.
Published: May 2007

Let population Πi, i = 1,2, be characterized by a multivariate normal density function, N(μi,∑i), i = 1, 2, respectively. This paper provides conditions under which simple conditional error rates may be computed for the quadratic discriminant function with known population parameters. Also, a simple bound on the overall error rate is derived. Examples are given which demonstrate the proposed methods.
Application of Logistic Regression and Logistic Discrimination in Medical Decision Making
Authors: Dietz E.
Published: May 2007

The logit linear model has been shown to be very useful for investigations in many fields of biology and medicine. One kind of application of this model is that of logistic discriminant analysis. To conquer some theoretical disadvantages of logistic discriminant analysis and Fisher's linear discriminant analysis too, it has been recommended to augment their model equations with appropriate interaction terms. The present paper discusses experiences with epidemiologic data going this way.
A Generalization of the GMANOVA‐Model
Authors: Hecker H.
Published: May 2007

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.
Testing Hypotheses on the Mean Vector Under an Intraclass Correlation Structure
Authors: Bhoj Dinesh S.
Published: May 2007

A statistic is proposed for testing hypotheses on the mean vector of a p‐variate normal distribution when the variance covariance matrix has an intraclass correlation structure. The powers of the test are computed and compared with those obtained from the statistics of Cox and Han (1982) and Clement et al. (1981). The power comparisons support the use of the proposed test.
A Note on Non‐Parametric Tests for the Change‐Point Problem
Authors: Koziol James A.
Published: May 2007

Two general classes of non‐parametric tests for the change‐point problem are introduced. In‐variance principles lead to accessible asymptotic distribution theory.
Statistical Methods for Using Nonlinear Models to Compare Silage Treatments
Authors: Hinds M. A. , Milliken G. A.
Published: May 2007

Statistical methods are described which can be used to compare treatments where the response is described by a nonlinear model. The nonlinear analysis of covariance is described for a one‐way treatment structure and a two‐way treatment structure. Methods for constructing confidence bands about a model and about the difference of two models are described. Examples involving the dynamics of silage fermentation are used to demonstrate the methods.
On a Mixed‐Type Randomized Rule for Selecting Superior Binomial Models
Authors: Huang Wen‐Tao , Saleh A. K. Md. Ehsanes
Published: May 2007

We propose a new class of selection rules for selecting superior models from finite Binomial models. This new class of rules extends the classes of classical rules and shows its superiority to the classical selection rules by some Monte Carlo results. This new class of rules is easier and more flexible to apply than these known classical rules.
A Rapid and Efficient Estimation Procedure for the Negative Binomial Distribution
Authors: Kemp A. W. , Kemp C. D.
Published: May 2007

This paper presents a new noniterative procedure for estimating the parameters of a negative binomial distribution. The procedure uses the first moment equation and an equation based on the weighted sample mean, with weights ωx∝ αz. The selection of a value for α is examined. A simulation study has been carried out and also the method has been applied to the 35 data sets analysed by Martin and Katti (1965, Biometrics) in order to compare it with the method of moments and with the method of maximum likelihood (ML). We conclude that the new procedure has greater relative efficiency than the method of moments; it gives estimates which are consistently close to ML and are easy to calculate.
Non‐Parametric Methods for the 2‐Period‐Cross‐Over Design Under Weak Model Assumptions
Authors: Brunner E. , Neumann N.
Published: May 2007

A nonparametric analysis for the two period cross‐over design has first been suggested by Koch (1972) and has been discussed by Hills and Armitage (1979). As known rank tests on sums or differences of the data are applied in this procedure, the results on the one hand are not invariant under monotonous transformations and on the other hand the procedure is only correct for models with additive effects. Therefore, in the present article generalized effects will first be defined in the 2‐period cross‐over design without the assumption of a linear model and then rank test will be presented which test tese effects without the need of sums or differences of the data. In the appendix the equivalence of the hypothesis for the generalized effects to the known hypotheses for the effects in the linear model will be shown. The application of the procedures will be demonstrated by means of an example in literature.