دانلود رایگان ترجمه مقاله روشی دو مرحله ای جهت تبدیل متغیرهای پیوسته به معمولی – Semanticscholar 2011

یک رویکرد دو مرحله ای برای تبدیل متغیر های پیوسته به متغیر های نرمال: اهمیت ها و توصیه ها برای تحقیقات IS

A Two-Step Approach for Transforming Continuous Variables to Normal: Implications and Recommendations for IS Research

Abstract

This article describes and demonstrates a two-step approach for transforming non-normally distributed continuous variables to become normally distributed. Step 1 involves transforming the variable into a percentile rank, which will result in uniformly distributed probabilities. Step 2 applies the inverse-normal transformation to the results of the first step to form a variable consisting of normally distributed z-scores. The approach is little-known outside the statistics literature, has been scarcely used in the social sciences, and has not been used in any IS study. The article illustrates how to implement the approach in Excel, SPSS, and SAS and explains implications and recommendations for IS research.

1 Introduction

Traditionally, data transformations (e.g., power and logarithm) have been pursued by improving normality incrementally using a trial-and-error approach. Unfortunately, it is rarely the occasion that a researcher may actually achieve statistical normality as indicated by accepted diagnostics tests (e.g., Kolmogorov-Smirnov, P-P plot, skewness, kurtosis). This research demonstrates a simple yet powerful approach herein referred to as the TwoStep, which may be used to transform many non-normally distributed continuous variables toward statistical normality (i.e., satisfies the preponderance of appropriate diagnostics tests for normality). The proposed transformation can achieve statistically acceptable kurtosis, skewness, and an overall normality test in many situations and improve normality in many others. With the exception of two limitations described later, the approach optimizes normality of the resulting variable distribution. The Two-Step offers an ideal standard for transforming variables toward normality and a new perspective on MIS research. In studies on the effects of non-normality on association tests, prior research has used simulated data [e.g., Figelman, 2009], whereas the proposed Two-Step procedure will enable the use of observed variables. For example, the Productivity Paradox is a term that describes the perplexing inability of information systems (IS) 1 researchers to uncover relationships between a range of information technology (IT) investment criteria and organizational productivity. Within this topic, a tremendous amount of multidisciplinary scholarly effort has been expended to better understand specific streams, such as the relationship between IT investment and financial performance [Brynjolfsson and Hitt, 2003]. Despite the enormity of effort and its prominence across disciplines, very little resolution has been made to the Paradox and, surprisingly, studies on the subject rarely mention the distributional aspects of underlying data. Simulation studies, which use data devoid of theory to study normality implications, cannot directly advance the Paradox stream. By contrast, the Two-Step offers the potential to transform observed variables toward statistical normality and the realization of downstream effects on study findings, such as main effect sizes. Among the dozens of generic distributions available, the normal distribution has the most applications in quantitative research. Many parametric statistical procedures (e.g., multiple regression, factor analysis) used in quantitative research are sensitive to normality. For instance, the presence of normality has been shown to improve the detection of between-groups differences in both covariance and components-based structural equation modeling [Qureshi and Compeau, 2009]. Improved normality will reduce the heteroscedasticity shown in P-P plots [Hair et al., 2010], thereby increasing the level of statistical correlation observed between two variables. The proposed approach addresses at least four voids that may be observed in IS research. First, as will be demonstrated in the following section, normality has barely been addressed in IS studies that should address the issue. Second, the Two-Step transformation approach presented here has not been used at all in IS research to date. Consequently, researchers have had no exposure and have been unaware of the technique. For the first time, this tutorial makes the approach available to the IS community as a method and subject of research. Third, recent trends in pervasive computing, remote sensing, and cloud computing are making dramatically more data available to more organizations and members of the ―information society.‖ The greater availability of data will only increase the societal reliance on analyses of such data. For example, data mining is proliferating and raising the importance of causal testing in practice. Fourth, due to the availability of less expensive and more comprehensive electronic databases, researchers are more interested in data reduction than ever. Consequently, rigorous formative index construction studies, which rely heavily on the results of intercorrelation tests between logically grouped variables, is more important. While the Two-Step approach is relevant in studies utilizing any continuous data, it is perhaps more useful to those in the highly multidisciplinary IS research community. The purpose of this tutorial is to illuminate a transformation approach that promises to help advance any topic constrained by the non-normality of continuous data. The significance of the article is in its description of a novel procedure and its potential for providing a new perspective on IS research. While each step has been used disparately in the social sciences, the originality of this manuscript lies in its description of two steps for transforming observed variables toward normality. In particular, the algorithm introduced here has not been described or studied in published research. Therefore, the article serves as a means by which IS researchers can access the approach to determine if it will improve theoretical understandings and rates of scientific advancement in the IS discipline. This article provides a background of foundational concepts, explains a logical algorithm researchers may follow, illustrates its use in three common software applications, and provides examples of its application to observed data. The article then discusses its implications for IS scholarship, uses of the approach and recommendations for researchers, and a brief conclusion.