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Articles 31 - 60 of 134
Full-Text Articles in Statistical Theory
Statistical Tests, Tests Of Significance, And Tests Of A Hypothesis Using Excel, David A. Heiser
Statistical Tests, Tests Of Significance, And Tests Of A Hypothesis Using Excel, David A. Heiser
Journal of Modern Applied Statistical Methods
Microsoft’s spreadsheet program Excel has many statistical functions and routines. Over the years there have been criticisms about the inaccuracies of these functions and routines (see McCullough 1998, 1999). This article reviews some of these statistical methods used to test for differences between two samples. In practice, the analysis is done by a software program and often with the actual method used unknown. The user has to select the method and variations to be used, without full knowledge of just what calculations are used. Usually there is no convenient trace back to textbook explanations. This article describes the Excel algorithm …
Obituary: Cliff Lunneborg, Jmasm Editors
Obituary: Cliff Lunneborg, Jmasm Editors
Journal of Modern Applied Statistical Methods
No abstract provided.
Pietro Paoli, Italian Algebraist, John L. Cuzzocrea, Shlomo S. Sawilowsky
Pietro Paoli, Italian Algebraist, John L. Cuzzocrea, Shlomo S. Sawilowsky
Journal of Modern Applied Statistical Methods
Pietro Paoli was a leading Italian mathematician in the late 18th century. His signed letter pertaining to the death of astronomer Giuseppe Antonio Slop is translated from Italian to flowing (American) English.
Robust Confidence Intervals For Effect Size In The Two-Group Case, H. J. Keselman, James Algina, Katherine Fradette
Robust Confidence Intervals For Effect Size In The Two-Group Case, H. J. Keselman, James Algina, Katherine Fradette
Journal of Modern Applied Statistical Methods
The probability coverage of intervals involving robust estimates of effect size based on seven procedures was compared for asymmetrically trimming data in an independent two-groups design, and a method that symmetrically trims the data. Four conditions were varied: (a) percentage of trimming, (b) type of nonnormal population distribution, (c) population effect size, and (d) sample size. Results indicated that coverage probabilities were generally well controlled under the conditions of nonnormality. The symmetric trimming method provided excellent probability coverage. Recommendations are provided.
Sample Size Calculation And Power Analysis Of Time-Averaged Difference, Honghu Liu, Tongtong Wu
Sample Size Calculation And Power Analysis Of Time-Averaged Difference, Honghu Liu, Tongtong Wu
Journal of Modern Applied Statistical Methods
Little research has been done on sample size and power analysis under repeated measures design. With detailed derivation, we have shown sample size calculation and power analysis equations for timeaveraged difference to allow unequal sample sizes between two groups for both continuous and binary measures and explored the relative importance of number of unique subjects and number of repeated measurements within each subject on statistical power through simulation.
Testing Normality Against The Laplace Distribution, Taisuke Otsu
Testing Normality Against The Laplace Distribution, Taisuke Otsu
Journal of Modern Applied Statistical Methods
Some normality test statistics are proposed by testing non-nested hypotheses of the normal distribution and the Laplace distribution. If the null hypothesis is normal, the proposed non-nested tests are asymptotically equivalent to Geary’s (1935) normality test. The proposed test statistics are compared by the method of approximate slopes and Monte Carlo experiments.
Testing For Aptitude-Treatment Interactions In Analysis Of Covariance And Randomized Block Designs Under Assumption Violations, Tim Moses, Alan Klockars
Testing For Aptitude-Treatment Interactions In Analysis Of Covariance And Randomized Block Designs Under Assumption Violations, Tim Moses, Alan Klockars
Journal of Modern Applied Statistical Methods
This study compared the robustness of two analysis strategies designed to detect Aptitude-Treatment Interactions to two of their similarly-held assumptions, normality and residual variance homogeneity. The analysis strategies were the test of slope differences in analysis of covariance and the test of the Block-by- Treatment interaction in randomized block analysis of variance. With equal sample sizes in the treatment groups the results showed that residual variance heterogeneity has little effect on either strategy but nonnormality makes the test of slope differences liberal and the test of the Block-by-Treatment interaction conservative. With unequal sample sizes in the treatment groups the often-reported …
Type I Error Of Four Pairwise Mean Comparison Procedures Conducted As Protected And Unprotected Tests, J. Jackson Barnette, James E. Mclean
Type I Error Of Four Pairwise Mean Comparison Procedures Conducted As Protected And Unprotected Tests, J. Jackson Barnette, James E. Mclean
Journal of Modern Applied Statistical Methods
Type I error control accuracy of four commonly used pairwise mean comparison procedures, conducted as protected or unprotected tests, is examined. If error control philosophy is experimentwise, Tukey’s HSD, as an unprotected test, is most accurate and if philosophy is per-experiment, Dunn-Bonferroni, conducted as an unprotected test, is most accurate.
Kim And Warde’S Mixed Randomized Response Technique For Complex Surveys, Amitava Saha
Kim And Warde’S Mixed Randomized Response Technique For Complex Surveys, Amitava Saha
Journal of Modern Applied Statistical Methods
The randomized response (RR) technique introduced by Warner (1965) was found to be an effective method for reducing answer bias and ensuring better respondent cooperation in estimating the proportion of people in a community bearing a sensitive attribute. Chaudhuri (2001a, 2001b, 2002, 2003) extended Warner’s method and several other well-known RR devices to complex surveys adopting a varying probability sampling design. Kim and Warde (2004) proposed an RR model assuming that the sample is selected with simple random sampling (SRS) with replacement (SRSWR). Here, the method of estimation is presented when sample is chosen with varying selection probabilities and Kim …
A Nonrigorous Approach Of Incorporating Sensitizing Rules Into Multivariate Control Charts, Michael B. C. Khoo
A Nonrigorous Approach Of Incorporating Sensitizing Rules Into Multivariate Control Charts, Michael B. C. Khoo
Journal of Modern Applied Statistical Methods
Multivariate control charts are becoming more important in the monitoring of processes in manufacturing industries because the quality of a process is usually determined by several correlated variables (quality characteristics). The most popular multivariate process control procedure is based on the Hotelling control chart. It is used to monitor the mean vector of a process. A nonrigorous approach of using four sensitizing rules is introduced to improve the performance of a conventional Hotelling chart. The use of these rules on a conventional Hotelling chart do not require a transformation of the T2 statistics into normal random variables. Thus, the …
Sample Size Selection For Pair-Wise Comparisons Using Information Criteria, Xuemei Pan, C. Mitchell Dayton
Sample Size Selection For Pair-Wise Comparisons Using Information Criteria, Xuemei Pan, C. Mitchell Dayton
Journal of Modern Applied Statistical Methods
This article provides results for rates of correct identifications of paired-comparison information criteria and Tukey HSD as functions of the pattern of mean differences and of sample size. Therefore, the tables provided are useful for selecting sample sizes in real world applications.
Quasi-Maximum Likelihood Estimation For Latent Variable Models With Mixed Continuous And Polytomous Data, Jens C. Eickhoff
Quasi-Maximum Likelihood Estimation For Latent Variable Models With Mixed Continuous And Polytomous Data, Jens C. Eickhoff
Journal of Modern Applied Statistical Methods
Latent variable modeling is a multivariate technique commonly used in the social and behavioral sciences. The models used in such analysis relate all observed variables to latent common factors. In many situations, however, some outcome variables are in polytomous form while other outcomes are measured on a continuous scale. Maximum likelihood estimation for latent variable models with mixed polytomous and continuous outcomes is computationally intensive and may become difficult to implement in many applications. In this article, a computationally practical, yet efficient, Quasi- Maximum Likelihood approach for latent variable models with mixed continuous and polytomous variables is proposed. Asymptotic properties …
Determination Of Optimal Block Designs With Pre-Assigned Variance For Elementary Contrasts, Seemon Thomas, Alex Thannippara, S. C. Bagui, D. K. Ghosh
Determination Of Optimal Block Designs With Pre-Assigned Variance For Elementary Contrasts, Seemon Thomas, Alex Thannippara, S. C. Bagui, D. K. Ghosh
Journal of Modern Applied Statistical Methods
A method for obtaining optimal designs from the class of variance balanced and connected designs was developed for comparing treatment effects with a pre-assigned variance. The properties of the C-matrix of a block design are employed in developing this method. Some new results concerning the design parameters and the non-zero characteristic root of the C-matrix are also presented.
A Bayesian Subset Analysis Of Sensory Evaluation Data, Balgobin Nandram
A Bayesian Subset Analysis Of Sensory Evaluation Data, Balgobin Nandram
Journal of Modern Applied Statistical Methods
In social sciences it is easy to carry out sensory experiments using say a J-point hedonic scale. One major problem with the J-point hedonic scale is that a conversion from the category scales to numeric scores might not be sensible because the panelists generally view increments on the hedonic scale as psychologically unequal. In the current problem several products are rated by a set of panelists on the J-point hedonic scale. One objective is to select the best subset of products and to assess the quality of the products by estimating the mean and standard deviation response …
Estimating The Slope Of Simple Linear Regression In The Presence Of Outliers, Mohammed Al-Haj Ebrahem, Amjad D. Al-Nasser
Estimating The Slope Of Simple Linear Regression In The Presence Of Outliers, Mohammed Al-Haj Ebrahem, Amjad D. Al-Nasser
Journal of Modern Applied Statistical Methods
In this article, an estimation procedure to simple linear regression in the presence of outliers is proposed. The performance of the proposed estimator, the AM estimator, is compared with other traditional estimators: least squares, Theil type repeated median, and geometric mean. A numerical example is given to illustrate the proposed estimator. Simulation results indicate that the proposed estimator is accurate and has a high precision in the presence of outliers.
Selection Of Independent Binary Features Using Probabilities: An Example From Veterinary Medicine, Ludmila I. Kuncheva, Zoë S.J. Hoare, Peter D. Cockcroft
Selection Of Independent Binary Features Using Probabilities: An Example From Veterinary Medicine, Ludmila I. Kuncheva, Zoë S.J. Hoare, Peter D. Cockcroft
Journal of Modern Applied Statistical Methods
Supervised classification into c mutually exclusive classes based on n binary features is considered. The only information available is an n×c table with probabilities. Knowing that the best d features are not the d best, simulations were run for 4 feature selection methods and an application to diagnosing BSE in cattle and Scrapie in sheep is presented.
Training Statisticians To Be Alert To The Dangers Of Misapplying Statistical Methods, Vance W. Berger
Training Statisticians To Be Alert To The Dangers Of Misapplying Statistical Methods, Vance W. Berger
Journal of Modern Applied Statistical Methods
Statisticians are faced with a variety of challenges. Their ability to cope successfully with these challenges depends, in large part, on the quality of their training. It is not the purpose of this article to present a comprehensive training plan that will overhaul the standard curriculum a statistician might follow under current training regimens (i.e., in a degree program). Rather, the objective is to point out important areas that appear to be under-represented in standard curricula and correspondingly overlooked too often in practice. The hope is that these areas might be better integrated into the training of the next generation …
Power Of The T Test For Normal And Mixed Normal Distributions, Marilyn S. Thompson, Samuel B. Green, Yi-Hsin Chen, Shawn Stockford, Wen-Juo Lo
Power Of The T Test For Normal And Mixed Normal Distributions, Marilyn S. Thompson, Samuel B. Green, Yi-Hsin Chen, Shawn Stockford, Wen-Juo Lo
Journal of Modern Applied Statistical Methods
Previous research suggests that the power of the independent-samples t test decreases when population distributions are mixed normal rather than normal, and that robust methods have superior power under these conditions. However, under some conditions, the power for the independent-samples t test can be greater when the population distributions for the independent groups are mixed normal rather than normal. The implications of these results are discussed.
Misconceptions Leading To Choosing The T Test Over The Wilcoxon Mann-Whitney Test For Shift In Location Parameter, Shlomo S. Sawilowsky
Misconceptions Leading To Choosing The T Test Over The Wilcoxon Mann-Whitney Test For Shift In Location Parameter, Shlomo S. Sawilowsky
Journal of Modern Applied Statistical Methods
There exist many misconceptions in choosing the t over the Wilcoxon Rank-Sum test when testing for shift. Examples are given in the following three groups: (1) false statement, (2) true premise, but false conclusion, and (3) true statement irrelevant in choosing between the t test and the Wilcoxon Rank Sum test.
Jmasm21: Pcic_Sas: Best Subsets Using Information Criteria, C. Mitchell Dayton, Xuemei Pan
Jmasm21: Pcic_Sas: Best Subsets Using Information Criteria, C. Mitchell Dayton, Xuemei Pan
Journal of Modern Applied Statistical Methods
PCIC_SAS is a SAS program for identifying optimal subsets of means based on independent groups. All possible configurations of ordered subsets of groups are considered and a best model is identified using both the AIC and BIC information criteria. Results for models with homogeneous variances as well as models with heterogeneity of variance in the same pattern as the means are reported.
End Matter, Jmasm Editors
End Matter, Jmasm Editors
Journal of Modern Applied Statistical Methods
No abstract provided.
Second-Order Accurate Inference On Simple, Partial, And Multiple Correlations, Robert J. Boik, Ben Haaland
Second-Order Accurate Inference On Simple, Partial, And Multiple Correlations, Robert J. Boik, Ben Haaland
Journal of Modern Applied Statistical Methods
This article develops confidence interval procedures for functions of simple, partial, and squared multiple correlation coefficients. It is assumed that the observed multivariate data represent a random sample from a distribution that possesses infinite moments, but there is no requirement that the distribution be normal. The coverage error of conventional one-sided large sample intervals decreases at rate 1√n as n increases, where n is an index of sample size. The coverage error of the proposed intervals decreases at rate 1/n as n increases. The results of a simulation study that evaluates the performance of the proposed intervals is …
A Method For Analyzing Unreplicated Experiments Using Information On The Intraclass Correlation Coefficient, Jamis J. Perrett
A Method For Analyzing Unreplicated Experiments Using Information On The Intraclass Correlation Coefficient, Jamis J. Perrett
Journal of Modern Applied Statistical Methods
Many studies are performed on units that cannot be replicated; however, there is often an abundance of subsampling. By placing a reasonable upper bound on the intraclass correlation coefficient (ICC), it is possible to carry out classical tests of significance that have conservative levels of significance.
Ab/Ba Crossover Trials - Binary Outcome, James F. Reed Iii
Ab/Ba Crossover Trials - Binary Outcome, James F. Reed Iii
Journal of Modern Applied Statistical Methods
On occasion, the response to treatment in an AB/BA crossover trial is measured on a binary variable - success or failure. It is assumed that response to treatment is measured on an outcome variable with (+) representing a treatment success and a (-) representing a treatment failure. Traditionally, three tests for comparing treatment effect have been used (McNemar’s, Mainland-Gart, and Prescott’s). An issue arises concerning treatment comparisons when there may be a residual effect (carryover effect) of a previous treatment affecting the current treatment. A general consensus as to which procedure is preferable is debatable. However, if both group and …
Joseph Liouville’S ‘Mathematical Works Of Évariste Galois’, Shlomo S. Sawilowsky, John L. Cuzzocrea
Joseph Liouville’S ‘Mathematical Works Of Évariste Galois’, Shlomo S. Sawilowsky, John L. Cuzzocrea
Journal of Modern Applied Statistical Methods
Liouville’s 1846 introduction to the mathematical works of Galois is translated from French to flowing (American) English. It gave an overview of the tragic circumstances of the undergraduate mathematician whose originality led to major advances in abstract Algebra.
Interaction Graphs For 4R2N-P Fractional Factorial Designs, M. L. Aggarwal, S. Roy Chowdhury, Anita Bansal, Neena Mital
Interaction Graphs For 4R2N-P Fractional Factorial Designs, M. L. Aggarwal, S. Roy Chowdhury, Anita Bansal, Neena Mital
Journal of Modern Applied Statistical Methods
Interaction graphs have been developed for two-level and three-level fractional factorial designs under different design criteria. A catalogue is presented of all possible non-isomorphic interaction graphs for 4r2n-p (r=1; n=2,…, 10; p=1,…,8 and r=2; n=1,…, 7; p=1,…,7) fractional factorial designs, and nonisomorphic interaction graphs for asymmetric fractional factorial designs under the concept of combined array.
Jmasm24: Numerical Computing For Third-Order Power Method Polynomials (Excel), Todd C. Headrick
Jmasm24: Numerical Computing For Third-Order Power Method Polynomials (Excel), Todd C. Headrick
Journal of Modern Applied Statistical Methods
The power method polynomial transformation is a popular procedure used for simulating univariate and multivariate non-normal distributions. It requires software that solves simultaneous nonlinear equations. Potential users of the power method may not have access to commercial software packages (e.g., Mathematica, Fortran). Therefore, algorithms are presented in the more commonly available Excel 2003 spreadsheets. The algorithms solve for (1) coefficients for polynomials of order three, (2) intermediate correlations and Cholesky factorizations for multivariate data generation, and (3) the values of skew and kurtosis for determining if a transformation will produce a valid power method probability density function (pdf). The Excel …
A Discretized Approach To Flexibly Fit Generalized Lambda Distributions To Data, Steve Su
A Discretized Approach To Flexibly Fit Generalized Lambda Distributions To Data, Steve Su
Journal of Modern Applied Statistical Methods
This article presents a flexible approach to fit statistical distribution to data. It optimizes the bin-width of data histogram to find a suitable generalized lambda distribution. In addition to the default optimization, this approach provides additional flexibility akin to the concepts of loess and kernel smoothing, which allow the users to determine the amount of details they would like to smooth over the data. The approach presented in this article will allow users to visually compare and choose the parameters of generalized lambda distribution that best suit their purposes of study.
A Single, Powerful, Nonparametric Statistic For Continuous-Data Telecommunications Parity Testing, J. D. Opdyke
A Single, Powerful, Nonparametric Statistic For Continuous-Data Telecommunications Parity Testing, J. D. Opdyke
Journal of Modern Applied Statistical Methods
Since the enactment of the Telecommunications Act of 1996, extensive expert testimony has justified use of the modified t statistic (Brownie et al., 1990) for performing two-sample hypothesis tests comparing Bell companies’ CLEC and ILEC performance measurement data (known as parity testing). However, Opdyke (Telecommunications Policy, 2004) demonstrated this statistic to be potentially manipulable and to have literally zero power to detect inferior CLEC service provision under a wide range of relevant data conditions. This article develops a single, nonparametric statistic that is easily implemented (i.e., not computationally intensive) and typically provides dramatic power gains over the modified t while …
Testing Goodness Of Fit Of The Geometric Distribution: An Application To Human Fecundability Data, Sudhir R. Paul
Testing Goodness Of Fit Of The Geometric Distribution: An Application To Human Fecundability Data, Sudhir R. Paul
Journal of Modern Applied Statistical Methods
A measure of reproduction in human fecundability studies is the number of menstrual cycles required to achieve pregnancy which is assumed to follow a geometric distribution with parameter p. Tests of heterogeneity in the fecundability data through goodness of fit tests of the geometric distribution are developed, along with a likelihood ratio test statistic and a score test statistic. Simulations show both are liberal, and empirical level of the likelihood ratio statistic is larger than that of the score test statistic. A power comparison shows that the likelihood ratio test has a power advantage. A bootstrap p-value procedure using the …