Popular Statistical Software Packages Research Articles

Handling missing data in longitudinal clinical trials: three examples from the pediatric psychology literature.

Researchers by default tend to choose complex models when analyzing nonindependent response variable data, this may be particularly applicable in the analysis of longitudinal trial data, possibly due to the ability of such models to easily address missing data by default. Both maximum-likelihood (ML) estimation and multiple imputation (MI) are well-known to be acceptable methods for handling missing data, but much of the recently published quantitative literature has addressed questions regarding the research designs and circumstances under which one should be chosen over the other. The purpose of this article is threefold. First, to clearly define the assumptions underlying three common longitudinal trial data analysis models for continuous dependent variable data: repeated measures analysis of covariance (RM-ANCOVA), generalized estimating equation (GEE), and a longitudinal linear mixed model (LLMM). Second, to clarify when ML or MI should be chosen, and to introduce researchers to an easy-to-use, empirically well-validated, and freely available missing data multiple imputation program: BLIMP. Third, to show how missing longitudinal trial data can be handled in the three data analysis models using three popular statistical analysis software packages (SPSS, Stata, and R) while keeping the published quantitative research in mind.

Evaluating the median p-value method for assessing the statistical significance of tests when using multiple imputation

Rubin’s Rules are commonly used to pool the results of statistical analyses across imputed samples when using multiple imputation. Rubin’s Rules cannot be used when the result of an analysis in an imputed dataset is not a statistic and its associated standard error, but a test statistic (e.g. Student’s t-test). While complex methods have been proposed for pooling test statistics across imputed samples, these methods have not been implemented in many popular statistical software packages. The median p-value method has been proposed for pooling test statistics. The statistical significance level of the pooled test statistic is the median of the associated p-values across the imputed samples. We evaluated the performance of this method with nine statistical tests: Student’s t-test, Wilcoxon Rank Sum test, Analysis of Variance, Kruskal-Wallis test, the test of significance for Pearson’s and Spearman’s correlation coefficient, the Chi-squared test, the test of significance for a regression coefficient from a linear regression and from a logistic regression. For each test, the empirical type I error rate was higher than the advertised rate. The magnitude of inflation increased as the prevalence of missing data increased. The median p-value method should not be used to assess statistical significance across imputed datasets.

Accounting for uncertainty: an application of Bayesian methods to accruals models

We provide an applied introduction to Bayesian estimation methods for empirical accounting research. To showcase the methods, we compare and contrast the estimation of accruals models via a Bayesian approach with the literature’s standard approach. The standard approach takes a given model of normal accruals for granted and neglects any uncertainty about the model and its parameters. By contrast, our Bayesian approach allows incorporating parameter and model uncertainty into the estimation of normal accruals. This approach can increase power and reduce false positives in tests for opportunistic earnings management as a result of better estimates of normal accruals and more robust inferences. We advocate the greater use of Bayesian methods in accounting research, especially since they can now be easily implemented in popular statistical software packages.

Comparing multiple statistical software for multiple-indicator, multiple-cause modeling: an application of gender disparity in adult cognitive functioning using MIDUS II dataset

BackgroundThe multiple-indicator, multiple-cause model (MIMIC) incorporates covariates of interest in the factor analysis. It is a special case of structural equation modeling (SEM), which is modeled under latent variable framework. The MIMIC model provides rigorous results and becomes broadly available in multiple statistical software. The current study introduces the MIMIC model and how it can be implemented using statistical software packages SAS CALIS procedure, R lavaan package, and Mplus version 8.0.MethodsIn this paper, we first discussed the formulation of the MIMIC model with regard to model specification and identification. We then demonstrated the empirical application of the MIMIC model with the Midlife in the United States II (MIDUS II) Study (N = 4109) using SAS CALIS procedure, R lavaan package and Mplus version 8.0 to examine gender disparities in cognitive functioning. The input, output, and diagram syntaxes of the three statistical software packages were also presented.ResultsIn terms of data structure, all three statistical programs can be conducted using both raw data and empirical covariance matrix. SAS and R are comprehensive statistical analytic packages and encompass numerous data manipulation capacities. Mplus is designed primarily for latent variable modeling and has far more modeling flexibility compared to SAS and R, but limited in data manipulation. Differences in model results from the three statistical programs are trivial. Overall, the results show that while men show better performance in executive function than women, women demonstrate better episodic memory than men.ConclusionsOur study demonstrates the utility of the MIMIC model in its empirical application, fitted with three popular statistical software packages. Results from our models align with empirical findings from previous research. We provide coding procedures and examples with detailed explanations in the hopes of providing a concise tutorial for researchers and methodologists interested in incorporating latent constructs with multiple indicators and multiple covariates in their research projects. Future researchers are encouraged to adopt this flexible and rigorous modeling approach.

Statistical methodological review for time-series data

Numerous literatures on statistical methods for Time-Series (TS) data have been published. In this paper, a literature of the TS data analysis methods is reviewed. We organize the review based on the basic three-family category of TS models: The Exponential Smoothing Model (ESM) family, the Auto-Regressive Integrated Moving Average (ARIMA) model family, and the Unobserved Component Model (UCM) family. A roadmap is provided in a diagram format to these TS methods which are translatable into nowadays computing statements. Further, the execution of these methods in SAS commands (as one of the most popular nowadays statistical software packages) is also presented. This paper will be very beneficial for practitioners, forecasters, and researchers in diverse fields of study (such as business, management, finance, economics, etc.) to determine which TS data analysis method (along with the corresponding SAS command) are ready to use.

Computing the exact distribution of the Bartlett's test statistic by numerical inversion of its characteristic function

Application of the exact statistical inference frequently leads to non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by their characteristic functions, as is the case for the null distribution of the Bartlett's test statistic. However, analytical inversion of the characteristic function, if possible, frequently leads to complicated expressions for computing the distribution function and the corresponding quantiles. An efficient alternative is the well-known method based on numerical inversion of the characteristic functions, which is, however, ignored in popular statistical software packages. In this paper, we present the explicit characteristic function of the corrected Bartlett's test statistic together with the computationally fast and efficient implementation of the approach based on numerical inversion of this characteristic function, suggested for evaluating the exact null distribution used for testing homogeneity of variances in several normal populations, with possibly unequal sample sizes.

New Approaches for Estimation of Effect Sizes and their Confidence Intervals for Treatment Effects from Randomized Controlled Trials.

Although Cohen's d and the growth modeling analysis (GMA) d from linear models are common standardized effect sizes used to convey treatment effects, popular statistical software packages do not include them in their standard outputs. This article demonstrated the use of statistical software with user-prescribed parameter functions (e.g., Mplus) to produce d for treatment effects from both classical analysis and GMA--along with their associated standard errors (SEs) and confidence intervals (CIs). A Monte Carlo study was conducted to examine bias in the SE and CI for GMA d obtained with Mplus and found that both estimates were more accurate when calculated by the software with the standard bootstrap than with the delta method, but the delta method estimates were less biased than respective estimates from extant post hoc equations. Thus, users of many statistical software packages (including SAS, R, and LISREL) should obtain d or GMA d and associated CIs directly. Researchers employing less versatile software--and meta-analysts including ds and GMA ds in their syntheses of treatment effects--should continue to use the conventional post hoc equations. Biases in SEs and CIs for effect sizes obtained with them are ignorable and point estimates of d and GMA d are the same whether obtained directly from the software or with post hoc equations.

Accounting for Uncertainty: An Application of Bayesian Methods to Accruals Models

We provide an applied introduction to Bayesian estimation methods for empirical accounting research. To showcase the methods, we compare and contrast the estimation of accruals models via a Bayesian approach with the literature’s standard approach. The standard approach takes a given model of normal accruals for granted and neglects any uncertainty about the model and its parameters. By contrast, our Bayesian approach allows incorporating parameter and model uncertainty into the estimation of normal accruals. This approach can increase power and reduce false positives in tests for opportunistic earnings management as a result of better estimates of normal accruals and more robust inferences. We advocate the greater use of Bayesian methods in accounting research, especially since they can now be easily implemented in popular statistical software packages.

Using the Linear Mixed-Effect Model Framework to Estimate Generalizability Variance Components in R

Abstract. Extending from classical test theory, G theory allows more sources of variations to be investigated and therefore provides the accuracy of generalizing observed scores to a broader universe. However, G theory has been used less due to the absence of analytic facilities for this purpose in popular statistical software packages. Besides, there is rarely a systematic G theory introduction in the linear mixed-effect model context, which is a widely taught technique in statistical analysis curricula. The present paper fits G theory into linear mixed-effect models and estimates the variance components via the well-known lme4 package in R. Concrete examples, modeling procedures, and R syntax are illustrated so that practitioners may use G theory for their studies. Realizing the G theory estimation in R provides more flexible features than other platforms, such that users need not rely on specialized software such as GENOVA and urGENOVA.

Statistical methodological review for time-to-event data

For Time-To-Event (TTE) data, various statistical methods have been discussed in the literature. In this article we give a review of the TTE data analysis methods. The review includes descriptive methods, such as Kaplan-Meier estimator and Life Table, as well as inferential methods, such as the Log-Rank test and the Cox (Proportional Hazard) model. We provide a roadmap in a figure or diagram format to which methods are practically available to use in the literature. In addition, the implementation of these methods in popular statistical software packages such as SAS is also presented. This article will be very helpful for practitioners, investigators, and researchers to determine which TTE data analysis method (along with the corresponding SAS code) are available to use in various fields of study such as clinical trials, epidemiology, etc., both for the design phase of a study in prospective study or retrospective study analysis.

Two-Stage Residual Inclusion Estimation in Health Services Research and Health Economics.

Empirical analyses in health services research and health economics often require implementation of nonlinear models whose regressors include one or more endogenous variables-regressors that are correlated with the unobserved random component of the model. In such cases, implementation of conventional regression methods that ignore endogeneity will likely produce results that are biased and not causally interpretable. Terza etal. (2008) discuss a relatively simple estimation method that avoids endogeneity bias and is applicable in a wide variety of nonlinear regression contexts. They call this method two-stage residual inclusion (2SRI). In the present paper, I offer a 2SRI how-to guide for practitioners and a step-by-step protocol that can be implemented with any of the popular statistical or econometric software packages. We introduce the protocol and its Stata implementation in the context of a real data example. Implementation of 2SRI for a very broad class of nonlinear models is then discussed. Additional examples are given. We analyze cigarette smoking as a determinant of infant birthweight using data from Mullahy (1997). It is hoped that the discussion will serve as a practical guide to implementation of the 2SRI protocol for applied researchers.

A Comprehensive Review of the Two-Sample Independent or Paired Binary Data, with or without Stratum Effects

Various statistical hypotheses testing for discrete or categorical or binary data have been extensively discussed in the literature. A comprehensive review is given for the two-sample binary or categorical data testing methods on data with or without Stratum Effects. The review includes traditional methods such as Fisher’s Exact, Pearson’s Chi-Square, McNemar, Bowker, Stuart-Maxwell, Breslow-Day and, Cochran-Mantel-Haenszel, as well as newly developed ones. We also provide the roadmap, in a figure or diagram format to which methods are available in the literature. In addition, the implementation of these methods in popular statistical software packages such as SAS and/or R is also presented. This will be helpful for researchers to determine which (categorical-data) testing method is available to use in various fields of study such as clinical trials, epidemiology, etc., both for the design phase of a study in prospective study, cross-sectional or retrospective study analysis.

Fooled by Pseudo-Randomness

Random numbers are important to conducting surveys, simulations, and other economic and statistical analysis. Despite their importance, many people using popular statistical software packages to generate random numbers are often uninformed about how the software creates a (supposedly) random number. This lack of knowledge can inadvertently lead the user to use “random” numbers that fail important tests for randomness and are therefore not really random. Unbeknownst to many users, the random number generators in some commercial software programs are seriously flawed; they simply fail to generate numbers that are randomly drawn, resulting in serious unintended consequences for the study being performed. In this paper, we introduce the concept of random numbers in layman’s terms. We describe a number of different methods for drawing random numbers in several popular statistical software packages frequently used by economists. We then discuss errors commonly committed by economists and analysts unfamiliar with the algorithms used by their software package of choice. Next we describe flaws contained in the random number functions in some popular software packages. Finally, we discuss better random number functions also found in commonly used software.

Estimating predicted probabilities from logistic regression: different methods correspond to different target populations

We review three common methods to estimate predicted probabilities following confounder-adjusted logistic regression: marginal standardization (predicted probabilities summed to a weighted average reflecting the confounder distribution in the target population); prediction at the modes (conditional predicted probabilities calculated by setting each confounder to its modal value); and prediction at the means (predicted probabilities calculated by setting each confounder to its mean value). That each method corresponds to a different target population is underappreciated in practice. Specifically, prediction at the means is often incorrectly interpreted as estimating average probabilities for the overall study population, and furthermore yields nonsensical estimates in the presence of dichotomous confounders. Default commands in popular statistical software packages often lead to inadvertent misapplication of prediction at the means. Using an applied example, we demonstrate discrepancies in predicted probabilities across these methods, discuss implications for interpretation and provide syntax for SAS and Stata. Marginal standardization allows inference to the total population from which data are drawn. Prediction at the modes or means allows inference only to the relevant stratum of observations. With dichotomous confounders, prediction at the means corresponds to a stratum that does not include any real-life observations. Marginal standardization is the appropriate method when making inference to the overall population. Other methods should be used with caution, and prediction at the means should not be used with binary confounders. Stata, but not SAS, incorporates simple methods for marginal standardization.

The analysis of asbestos count data with “nondetects”: The example of asbestos fiber concentrations in the lungs of brake workers

In the analysis of tissue for asbestos fibers, some measurements may be below the analytical detection limit (nondetects). The use of maximum likelihood and survival analysis methods have been recommended to perform comparisons between subjects in the presence of nondetects. When the data consist of "counts" another method is useful. This method is discussed, and illustrated with an analysis of asbestos lung burden data among brake mechanics previously analyzed by other methods. Statistical models for count data, namely Poisson and negative binomial regression, were used to compare the asbestos fiber concentrations in the lungs of brake mechanics with those of control subjects. The fit of the models was assessed with an analysis of residuals. The negative binomial regression models fit the data well. The concentrations of Quebec asbestos fibers in the lungs of the brake mechanics were significantly higher than in the control population. Helsel recommended the use of maximum likelihood and survival analysis methods to perform comparisons in the presence of nondetects. When analyzing asbestos fiber count data, or other count data arising in occupational or environmental health, the use of models such as the Poisson and negative binomial may be added to the analyst's toolbox. Benefits are that neither of these methods requires the substitution of arbitrary values for the nondetects and that programs for the computation of count data models are contained in popular statistical software packages.

What can be learnt from nothing? – A statistical perspective

No observed event is a special, but not uncommon, result in patch test studies. The interpretation of such findings depends critically on the sample size (n) of the investigation, and is statistically addressed by the use of confidence intervals (CIs). To define the statistically correct method of calculating a CI with a confidence level of 1 - α, where α denotes the tolerated statistical error probability, for an observed prevalence of 0%. A literature survey and evaluation of the statistical methods was conducted. The popular statistical software packages SPSS™ and SAS™ were examined with regard to the methods implemented, and the results obtained, for estimating such CIs in this special case. The evaluation identified [0; 1 - α(1/n) ], which is well approximated by [0; 3/n] for α = 0.05, as an appropriate method to compute a CI with a confidence level of 1 - α. The resulting CI is an exact one, and more efficient than standard solutions. Popular statistical software such as SPSS™ and SAS™ offers only various inefficient or even invalid procedures, but does not include this method. It is easy to calculate a CI for an observed prevalence of 0% obtained in some studies. Such a CI facilitates the interpretation of such a finding, as it puts the observed zero result into adequate statistical perspective.

SPSS and SAS programs for comparing Pearson correlations and OLS regression coefficients

Several procedures that use summary data to test hypotheses about Pearson correlations and ordinary least squares regression coefficients have been described in various books and articles. To our knowledge, however, no single resource describes all of the most common tests. Furthermore, many of these tests have not yet been implemented in popular statistical software packages such as SPSS and SAS. In this article, we describe all of the most common tests and provide SPSS and SAS programs to perform them. When they are applicable, our code also computes 100 × (1 - α)% confidence intervals corresponding to the tests. For testing hypotheses about independent regression coefficients, we demonstrate one method that uses summary data and another that uses raw data (i.e., Potthoff analysis). When the raw data are available, the latter method is preferred, because use of summary data entails some loss of precision due to rounding.

RT4Win: A Windows-Based Program for Randomization Tests

A randomization test (RndT) is a statistical significance test for which the validity is based on the random assignment of experimental units in a designed experiment. In a random sampling setting, it can also be applied in a very general way because its validity does not rely on distributional assumptions, homogeneity of variances, or independence of errors. However, the use of RndTs did not receive much attention in applied research because RndTs rely on computationally intensive algorithms and most popular and common statistical software packages do not provide facilities to easily perform randomization tests. In order to fill this gap, we present a software package, RT4Win. Unlike most stand-alone software and programs for RndTs, RT4Win is a fast Windows-based program with a user-friendly interface. It provides a facility to carry out RndTs in a series of experimental designs, for both systematic and Monte Carlo data partition methods. The program is free of charge and available upon request from the authors.

AnSPSSR-Menu for Ordinal Factor Analysis

Exploratory factor analysis is a widely used statistical technique in the social sciences. It attempts to identify underlying factors that explain the pattern of correlations within a set of observed variables. A statistical software package is needed to perform the calculations. However, there are some limitations with popular statistical software packages, like SPSS. The R programming language is a free software package for statistical and graphical computing. It offers many packages written by contributors from all over the world and programming resources that allow it to overcome the dialog limitations of SPSS. This paper offers an SPSS dialog written in the R programming language with the help of some packages, so that researchers with little or no knowledge in programming, or those who are accustomed to making their calculations based on statistical dialogs, have more options when applying factor analysis to their data and hence can adopt a better approach when dealing with ordinal, Likert-type data.

The uses and benefits of cluster analysis in pharmacy research

Purpose Cluster analysis (CA) refers to a set of analytic procedures that reduce complex multivariate data into smaller subsets or groups. Compared with other data reduction methods, such as factor analysis, CA yields groupings that are based on the similarity of whole cases, as opposed to the individual variables that comprise those cases. CA represents a valuable analytic tool for the health sciences, and may be used to devise patient or consumer profiles, or in the development of classification systems or taxonomies. CA has become a more widely used analytic tool because before the advent of personal computers with high processing power, CA methods were too complex to be time efficient. Yet in the past few decades, interest in and the applied use of CA have advanced considerably. CA tools are now integrated into most popular statistical software packages and are therefore more accessible. Methods The authors provide a discussion of CA that seeks to introduce the various methods, issues, and considerations to the researcher who is largely unfamiliar with CA. A conceptual understanding of CA is guided through breaking down CA into a series of steps and issues to consider including composition of the dataset, selection of variables, decisions about standardizing variables, selecting a measure of association, selecting a clustering method, determining the number of clusters, and interpretation. Results/Conclusions Because the range of CA methods is diverse, and because the steps within each method are so varied, an attempt to offer a complete “how-to” process in a single article is imprudent. Rather, the novice reader will be able to use this article as a starting point for conducting his or her own particular CA study.