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Using software to teach statistical inference in introductory courses opens the door for methods and practices that are more conceptually appealing to students. With an increasing number of fields requiring competency in statistics including data science, natural and social sciences, public health and more, it is crucial that we as instructors deliver the basic concepts of statistics effectively. In line with guidelines presented in the GAISE College Report, this article demonstrates intuitive approaches to teaching proportion and mean inference that take advantage of statistical software and emphasize conceptual understanding. The article recommends putting aside asymptotic-based methods for proportion inference and using the exact binomial method. Regarding mean inference, we propose a more contextualized and simplified process that uses the distribution of the sample mean directly and avoids standardized statistics such as z or t. In both the proportion and mean inference contexts, we discuss the benefits of the proposed approaches and provide detailed examples that demonstrate the methods using the Rguroo statistical software. [ABSTRACT FROM AUTHOR]

Test of homogeneity of covariances (or homoscedasticity) among several groups has many applications in statistical analysis. In the context of incomplete data analysis, tests of homoscedasticity among groups of cases with identical missing data patterns have been proposed to test whether data are missing completely at random (MCAR). These tests of MCAR require large sample sizes "n" and/or large group sample sizes "n [subscript i]", and they usually fail when applied to nonnormal data. Hawkins (Technometrics 23:105-110, "1981") proposed a test of multivariate normality and homoscedasticity that is an exact test for complete data when "n [subscript i]" are small. This paper proposes a modification of this test for complete data to improve its performance, and extends its application to test of homoscedasticity and MCAR when data are multivariate normal and incomplete. Moreover, it is shown that the statistic used in the Hawkins test in conjunction with a nonparametric "k"-sample test can be used to obtain a nonparametric test of homoscedasticity that works well for both normal and nonnormal data. It is explained how a combination of the proposed normal-theory Hawkins test and the nonparametric test can be employed to test for homoscedasticity, MCAR, and multivariate normality. Simulation studies show that the newly proposed tests generally outperform their existing competitors in terms of Type I error rejection rates. Also, a power study of the proposed tests indicates good power. The proposed methods use appropriate missing data imputations to impute missing data. Methods of multiple imputation are described and one of the methods is employed to confirm the result of our single imputation methods. Examples are provided where multiple imputation enables one to identify a group or groups whose covariance matrices differ from the majority of other groups. (Contains 6 tables and 7 figures.)

Incomplete or missing data is a common problem in almost all areas of empirical research. It is well known that simple and ad hoc methods such as complete case analysis or mean imputation can lead to biased and/or inefficient estimates. The method of maximum likelihood works well; however, when the missing data mechanism is not one of missing completely at random (MCAR) or missing at random (MAR), it too can result in incorrect inference. Statistical tests for MCAR have been proposed, but these are restricted to a certain class of problems. The idea of sensitivity analysis as a means to detect the missing data mechanism has been proposed in the statistics literature in conjunction with selection models where conjointly the data and missing data mechanism are modeled. Our approach is different here in that we do not model the missing data mechanism but use the data at hand to examine the sensitivity of a given model to the missing data mechanism. Our methodology is meant to raise a flag for researchers when the assumptions of MCAR (or MAR) do not hold. To our knowledge, no specific proposal for sensitivity analysis has been set forth in the area of structural equation models (SEM). This article gives a specific method for performing postmodeling sensitivity analysis using a statistical test and graphs. A simulation study is performed to assess the methodology in the context of structural equation models. This study shows success of the method, especially when the sample size is 300 or more and the percentage of missing data is 20% or more. The method is also used to study a set of real data measuring physical and social self-concepts in 463 Nigerian adolescents using a factor analysis model. (Contains 2 figures and 3 tables.)

Describes the maximum likelihood (ML) estimation of mean and covariance structure models when data are missing. Describes expectation maximization (EM), generalized expectation maximization, Fletcher-Powell, and Fisher-scoring algorithms for parameter estimation and shows how software can be used to implement each algorithm. (Author/SLD)

This paper reviews various methods of identifying missing data mechanisms. The three well-known mechanisms of missing completely at random ( MCAR), missing at random ( MAR), and missing not at random ( MNAR) are considered. A number of tests deem rejection of homogeneity of means and/or covariances ( HMC) among observed data patterns as a means to reject MCAR. Utility of these tests as well as their shortcomings are discussed. In particular, examples of MAR and MNAR data with homogeneous means and covariances between their observed data patterns are provided for which tests of HMC fail to reject MCAR. More generally, tests of homogeneity of parameter estimates between various subsets of data are reviewed and their utility as tests of MCAR and MAR (in special cases) is pointed out. Since many tests of MCAR assume multinormality, methods to assess this assumption in the context of incomplete data are reviewed. Tests of homogeneity of distributions among observed data patterns for MCAR are also considered. A new nonparametric test of this type is proposed on the basis of pairwise comparison of marginal distributions. Finally, methods of examining missing data mechanism based on sensitivity analysis including methods that model missing data mechanism based on logistic, probit, and latent variable regression models, as well as methods that do not require modeling of missing data mechanism are reviewed. The paper concludes with some practical comments about the validity and utility of tests of missing data mechanism. WIREs Comput Stat 2014, 6:56-73. doi: 10.1002/wics.1287 Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website. [ABSTRACT FROM AUTHOR]

Research on multiple comparison during the past 50 years or so has focused mainly on the comparison of several population means. Several years ago, Spurrier considered the multiple comparison of several simple linear regression lines. He constructed simultaneous confidence bands for all of the contrasts of the simple linear regression lines over the entire range (-∞, ∞) when the models have the same design matrices. This article extends Spurrier's work in several directions. First, multiple linear regression models are considered and the design matrices are allowed to be different. Second, the predictor variables are either unconstrained or constrained to finite intervals. Third, the types of comparison allowed can be very flexible, including pairwise, many-one, and successive. Two simulation methods are proposed for the calculation of critical constants. The methodologies are illustrated with examples. [ABSTRACT FROM AUTHOR]