Journal of Data Science

Abstract: In this paper we endeavour to provide a largely non-technical description of the issues surrounding unbalanced factorial ANOVA and review the arguments made for and against the use of Type I, Type II and Type III sums of squares. Though the issue of which is the `best' approach has been debated in the literature for decades, to date confusion remains around how the procedures differ and which is most appropriate. We ultimately recommend use of the Type II sums of squares for analysis of main effects because when no interaction is present it tests meaningful hypotheses and is the most statistically powerful alternative.

Abstract: Despite the availability of software for interactive graphics, current survey processing systems make limited use of this modern tool. Interactive graphics offer insights, which are difficult to obtain with traditional statis tical tools. This paper shows the use of interactive graphics for analysing survey data. Using Labour Force Survey data from Pakistan, we describe how plotting data in different ways and using interactive tools enables analysts to obtain information from the dataset that would normally not be possible using standard statistical methods. It is also shown that interacative graphics can help the analyst to improve data quality by identifying erroneous cases.

Providing a new distribution is always precious for statisticians. A new three parameter distribution called the gamma normal distribution is defined and studied. Various structural properties of the new distribution are derived, including some explicit expressions for the moments, quantile and generating functions, mean deviations, probability weighted moments and two types of entropy. We also investigate the order statistics and their moments. Maximum likelihood techniques are used to fit the new model and to show its potentiality by means of two examples of real data. Based on three criteria, the proposed distribution provides a better fit then the skew-normal distribution.

Although hypothesis testing has been misused and abused, we argue that it remains an important method of inference. Requiring preregistration of the details of the inferences planned for a study is a major step to preventing abuse. But when doing hypothesis testing, in practice the null hypothesis is almost always taken to be a “point null”, that is, a hypothesis that a parameter is equal to a constant. One reason for this is that it makes the required computations easier, but with modern computer power this is no longer a compelling justification. In this note we explore the interval null hypothesis that the parameter lies in a fixed interval. We consider a specific example in detail.

Abstract:In this paper, for evaluating and comparing the heterogeneous balance-variation order pair of any two decision-making trial and evaluation laboratory (DEMATEL) theories, in which one has larger balance and smaller variation, and on the contrary, the other one has smaller balance and larger variation, the first author proposed a useful integrated validity index to evaluate any DEMATEL theory by combining Liu's balanced coefficient and Liu's variation coefficient .Using this new validity index, three kinds of DEMATELs with a same direct relational matrix, including the traditional DEMATEL, shrinkage DEMATEL and balance DEMATEL, are compared, a simple validity experiment is conducted, the results show that the balance DEMATEL has the best performance, the performance of the shrinkage coefficient is better than that of the traditional DEMATEL.

Abstract: Graphs are a great aid in interpreting multidimensional data. Two examples are employed to illustrate this point. In the first the many dissimilarities generated in the Analytic Network Process (ANP) are anal ysed using Individual Differences Scaling (INDSCAL). This is the first time such a procedure has been used in this context. In the second the single set of dissimilarities that arise from the Analytic Hierarchy Process (AHP) are analysed using Multidimensional Scaling (MDS). The novel approach adopted here replaces a complex iterative procedure with a systematic ap proach that may be readily automated.

Abstract: The traditional approach by Fama and Macbeth (1973) to the validity of an asset pricing model suffers from two drawbacks. Firstly, it uses the ordinary least squares (OLS) method, which is sensitive to outliers, to estimate the time-series beta. Secondly, it takes averages of the slope coefficients from cross-sectional regressions which ignore the importance of time-series properties. In this article, robust estimators and a longitudinal approach are applied to avoid the problems of these two kinds. We use data on the electronics industry in Taiwan’s stock market during the period from September 1998 to December 2001 in order to examine whether betas from the Capital Asset Pricing Model (CAPM) are a valid measure of risk and whether industries to which the firms belong explain excess returns. The methods we propose lead to more explanatory power than the traditional OLS results.

Abstract: Response variables that are scored as counts, for example, number of mastitis cases in dairy cattle, often arise in quantitative genetic analysis. When the number of zeros exceeds the amount expected such as under the Poisson density, the zero-inflated Poisson (ZIP) model is more appropriate. In using the ZIP model in animal breeding studies, it is necessary to accommodate genetic and environmental covariances. For that, this study proposes to model the mixture and Poisson parameters hierarchically, each as a function of two random effects, representing the genetic and environmental sources of variability, respectively. The genetic random effects are allowed to be correlated, leading to a correlation within and between clusters. The environmental effects are introduced by independent residual terms, accounting for overdispersion above that caused by extra-zeros. In addition, an inter correlation structure between random genetic effects affecting mixture and Poisson parameters is used to infer pleiotropy, an expression of the extent to which these parameters are influenced by common genes. The methods described here are illustrated with data on number of mastitis cases from Norwegian Red cows. Bayesian analysis yields posterior distributions useful for studying environmental and genetic variability, as well as genetic correlation.

Abstract: A new rank-based test statistics are proposed for the problem of a possible change in the distribution of independent observations. We extend the two-sample test statistic of Damico (2004) to the change point setup. The finite sample critical values of the proposed tests is estimated. We also conduct a Monte Carlo simulation to compare the powers of the new tests with their competitors. Using the Nile data of Cobb (1978), we demonstrate the applicability of the new tests.