Applied Statistics Commons^™

Longitudinal Sport Science Implementation In American Collegiate Men’S Basketball, Jason Stone

Graduate Theses, Dissertations, and Problem Reports

The expanding opportunities to implement sport science frameworks in elite-level basketball environments coincide with the sport’s increasing global prominence. Concomitant to these opportunities is the continual growth of the sport technology market (e.g., wearables, force plates) and computational power (e.g., data management tools, coding capabilities), which yields solutions and challenges for both athletes and practitioners. Due to the rapid influx of new sport technologies in high performance environments, particularly American Collegiate Men’s Basketball, more formal and ecologically valid research on how to effectively utilize data derived from them, particularly over long periods of time (i.e., multiple seasons) is needed. To …

Introduction To Research Statistical Analysis: An Overview Of The Basics, Christian Vandever

HCA Healthcare Journal of Medicine

This article covers many statistical ideas essential to research statistical analysis. Sample size is explained through the concepts of statistical significance level and power. Variable types and definitions are included to clarify necessities for how the analysis will be interpreted. Categorical and quantitative variable types are defined, as well as response and predictor variables. Statistical tests described include t-tests, ANOVA and chi-square tests. Multiple regression is also explored for both logistic and linear regression. Finally, the most common statistics produced by these methods are explored.

The Andersen Likelihood Ratio Test With A Random Split Criterion Lacks Power, Georg Krammer

Journal of Modern Applied Statistical Methods

The Andersen LRT uses sample characteristics as split criteria to evaluate Rasch model fit, or theory driven hypothesis testing for a test. The power and Type I error of a random split criterion was evaluated with a simulation study. Results consistently show a random split criterion lacks power.

A More Powerful Unconditional Exact Test Of Homogeneity For 2 × C Contingency Table Analysis, Louis Ehwerhemuepha, Heng Sok, Cyril Rakovski

Mathematics, Physics, and Computer Science Faculty Articles and Research

The classical unconditional exact p-value test can be used to compare two multinomial distributions with small samples. This general hypothesis requires parameter estimation under the null which makes the test severely conservative. Similar property has been observed for Fisher's exact test with Barnard and Boschloo providing distinct adjustments that produce more powerful testing approaches. In this study, we develop a novel adjustment for the conservativeness of the unconditional multinomial exact p-value test that produces nominal type I error rate and increased power in comparison to all alternative approaches. We used a large simulation study to empirically estimate the …

Daily And Seasonal Variability Of Offshore Wind Power On The Central California Coast And Statewide Demand, Matthew Douglas Kehrli

Physics

No abstract provided.

Sample Size For Non-Inferiority Tests For One Proportion: A Simulation Study, Özlem Güllü, Mustafa Agah Tekindal

Journal of Modern Applied Statistical Methods

The objective of non-inferiority trials is to demonstrate the efficiency of a novel treatment whether it is acceptably less or more efficient than a control or active (existing) treatment. They are employed in situations where, when compared to the active treatment, the novel treatment is to be advantageous with higher rates of reliability, compatibility, cost-efficiency, etc. Odds ratio is the most significant measure used in investigating the size of efficiency of treatments relative to one another. The purpose of the study is to calculate and evaluate the sample size under different scenarios based on three different test statistics in non-inferiority …

Outlier Impact And Accommodation On Power, Hongjing Liao, Yanju Li, Gordon P. Brooks

Journal of Modern Applied Statistical Methods

The outliers’ influence on power rates in ANOVA and Welch tests at various conditions was examined and compared with the effectiveness of nonparametric methods and Winsorizing in minimizing the impact of outliers. Results showed that, considering both power and Type I error, a nonparametric test is the safest choice to control the inflation of Type I error with a decent sample size and yield relatively high power.

Comparing The Structural Components Variance Estimator And U-Statistics Variance Estimator When Assessing The Difference Between Correlated Aucs With Finite Samples, Anna L. Bosse

Theses and Dissertations

Introduction: The structural components variance estimator proposed by DeLong et al. (1988) is a popular approach used when comparing two correlated AUCs. However, this variance estimator is biased and could be problematic with small sample sizes.

Methods: A U-statistics based variance estimator approach is presented and compared with the structural components variance estimator through a large-scale simulation study under different finite-sample size configurations.

Results: The U-statistics variance estimator was unbiased for the true variance of the difference between correlated AUCs regardless of the sample size and had lower RMSE than the structural components variance estimator, providing better type 1 error …

Resolving The Issue Of How Reliability Is Related To Statistical Power: Adhering To Mathematical Definitions, Donald W. Zimmerman, Bruno D. Zumbo

Journal of Modern Applied Statistical Methods

Reliability in classical test theory is a population-dependent concept, defined as a ratio of true-score variance and observed-score variance, where observed-score variance is a sum of true and error components. On the other hand, the power of a statistical significance test is a function of the total variance, irrespective of its decomposition into true and error components. For that reason, the reliability of a dependent variable is a function of the ratio of true-score variance and observed-score variance, whereas statistical power is a function of the sum of the same two variances. Controversies about how reliability is related to statistical …

Spss Programs For Addressing Two Forms Of Power For Multiple Regression Coefficients, Christopher Aberson

Journal of Modern Applied Statistical Methods

This paper presents power analysis tools for multiple regression. The first takes input of correlations between variables and sample size and outputs power for multiple predictors. The second addresses power to detect significant effects for all of the predictors in the model. Both employ user-friendly SPSS Custom Dialogs.

An Assessment Of The Performances Of Several Univariate Tests Of Normality, James Olusegun Adefisoye

FIU Electronic Theses and Dissertations

The importance of checking the normality assumption in most statistical procedures especially parametric tests cannot be over emphasized as the validity of the inferences drawn from such procedures usually depend on the validity of this assumption. Numerous methods have been proposed by different authors over the years, some popular and frequently used, others, not so much. This study addresses the performance of eighteen of the available tests for different sample sizes, significance levels, and for a number of symmetric and asymmetric distributions by conducting a Monte-Carlo simulation. The results showed that considerable power is not achieved for symmetric distributions when …

Meta-Analysis Of Type I Error Rates For Detecting Differential Item Functioning With Logistic Regression And Mantel-Haenszel In Monte Carlo Studies, Eva Van De Water Ph. D.

Eva Van De Water

Differential item functioning (DIF) occurs when individuals from different groups who have equal levels of a latent trait fail to earn commensurate scores on a testing instrument. Type I error occurs when DIF-detection methods result in unbiased items being excluded from the test while a Type II error occurs when biased items remain on the test after DIF-detection methods have been employed. Both errors create potential issues of injustice amongst examinees and can result in costly and protracted legal action. The purpose of this research was to evaluate two methods for detecting DIF: logistic regression (LR) and Mantel-Haenszel (MH).

To …

Likelihood Ratio Type Test For Linear Failure Rate Distribution Vs. Exponential Distribution, R R. L. Kantam, M C. Priya, M S. Ravikumar

Journal of Modern Applied Statistical Methods

The Linear Failure Rate Distribution (LFRD) is considered. The graphs of its probability density function are examined for selected parameter combinations. Some of them are similar to the well-known exponential distribution. Incidentally exponential distribution is one of the two component models of the LFRD model. In view of the simpler form of exponential model as applicable in inference, looking at the frequency curves of LFRD, a test statistic is proposed based on ratio of likelihood functions containing the standard forms of the density functions of both LFRD and Exponential to discriminate between LFRD and exponential models. The critical values and …

Examining Multiple Comparison Procedures According To Error Rate, Power Type And False Discovery Rate, Guven Ozkaya, Ilker Ercan

Journal of Modern Applied Statistical Methods

Examining pairwise differences between means is a common practice of applied researchers, and the selection of an appropriate multiple comparison procedure (MCP) is important for analyzing pairwise comparisons. This study examines the performance of MCPs under the assumption of homogeneity of variances for various numbers of groups with equal and unequal sample sizes via a simulation study. MCPs are compared according to type I error rate, power type and false discovery rate (FDR). Results show that the LSD and Duncan procedures have high error rates and Scheffe’s procedure has low power; no remarkable differences between the other procedures considered were …

Modified Edf Goodness Of Fit Tests For Logistic Distribution Under Srs And Rss, S. A. Al-Subh, M. T. Alodat, Kamaruzaman Ibrahim, Abdul Aziz Jemain

Journal of Modern Applied Statistical Methods

Modified forms of goodness of fit tests are presented for the logistic distribution using statistics based on the empirical distribution function (EDF). A method to improve the power of the modified EDF goodness of fit tests is introduced based on Ranked Set sampling (RSS). Data are collected via the Ranked Set Sampling (RSS) technique (McIntyre, 1952). Critical values for the logistic distribution with unknown parameters are provided and the powers of the tests are given for a number of alternative distributions. A simulation study is presented to illustrate the power of the new method.

Jmasm31: Manova Procedure For Power Calculations (Spss), Alan Taylor

Journal of Modern Applied Statistical Methods

D’Amico, Neilands & Zambarano (2001) showed how the SPSS MANOVA procedure can be used to conduct power calculations for research designs. This article demonstrates a simple way of entering data required for power calculations into SPSS and provides examples that supplement those given by D’Amico, Neilands & Zambarano.

Notes On Hypothesis Testing Under A Single-Stage Design In Phase Ii Trial, Kung-Jong Lui

Journal of Modern Applied Statistical Methods

A primary objective of a phase II trial is to determine future development is warranted for a new treatment based on whether it has sufficient activity against a specified type of tumor. Limitations exist in the commonly-used hypothesis setting and the standard test procedure for a phase II trial. This study reformats the hypothesis setting to mirror the clinical decision process in practice. Under the proposed hypothesis setting, the critical points and the minimum required sample size for a desired power of finding a superior treatment at a given α -level are presented. An example is provided to illustrate how …

Generalized Variances Ratio Test For Comparing K Covariance Matrices From Dependent Normal Populations, Marcelo Angelo Cirillo, Daniel Furtado Ferreira, Thelma Sáfadi, Eric Batista Ferreira

Journal of Modern Applied Statistical Methods

New tests based on the ratio of generalized variances are presented to compare covariance matrices from dependent normal populations. Monte Carlo simulation concluded that the tests considered controlled the Type I error, providing empirical probabilities that were consistent with the nominal level stipulated.

On Testing For Significant Quantitative Trait Loci (Qtl) Effects When Variances Are Unequal, Pradeep Singh, Shesh N. Rai

Conference on Applied Statistics in Agriculture

The basic theory of QTL (Quantitative Trait Loci) mapping is to score a population for a quantitative trait according to the marker genotype, and then to use statistics to identify differences associated with the markers and the quantitative trait of interest. Permutation based methods have been used to estimate threshold values for quantitative mapping. The permutation test based on the Student t-test for equality of means does not control Type I error rate to its nominal value when variances are unequal. In this study we propose a modification of the Student t-test based on the jackknife estimator of population variance. …

Detecting Lag-One Autocorrelation In Interrupted Time Series Experiments With Small Datasets, Clare Riviello, S. Natasha Beretvas

Journal of Modern Applied Statistical Methods

The power and type I error rates of eight indices for lag-one autocorrelation detection were assessed for interrupted time series experiments (ITSEs) with small numbers of data points. Performance of Huitema and McKean’s (2000) z_HM statistic was modified and compared with the z_HM, five information criteria and the Durbin-Watson statistic.

Quel Test For Two Linear Restrictions In The Nonlinear Models, Krishna K. Saha

Journal of Modern Applied Statistical Methods

An alternative Wald type test called the quel test is developed for two linear restrictions by finding the critical region based on the quel utilizing the repeated values of estimated parameters of interest under the null. Simulation shows evidence that the full quel test performs best in that it holds nominal level well and shows monotonic increasing power properties.

Comparative Power Of The Independent T, Permutation T, And Wilcoxontests, Michèle Weber, Shlomo Sawilowsky

Journal of Modern Applied Statistical Methods

The nonparametric Wilcoxon Rank Sum (also known as the Mann-Whitney U) and the permutation t-tests are robust with respect to Type I error for departures from population normality, and both are powerful alternatives to the independent samples Student’s t-test for detecting shift in location. The question remains regarding their comparative statistical power for small samples, particularly for non-normal distributions. Monte Carlo simulations indicated the rank-based Wilcoxon test was found to be more powerful than both the t and the permutation t-tests.

Robustness To Non-Independence And Power Of The I Test For Trend In Construct Validity, John L. Cuzzocrea, Shlomo Sawilowsky

Journal of Modern Applied Statistical Methods

The Multitrait-Multimethod Matrix is used to evaluate construct validity; Sawilowsky (2002) created the I test to analyze the matrix. This article examined the robustness and power of the Sawilowsky I test. Ad hoc critical values were determined to improve the statistical power of the technique for analyzing the Multitrait-Multimethod Matrix.

Comparing Different Methods For Multiple Testing In Reaction Time Data, Massimiliano Pastore, Massimo Nucci, Giovanni Galfano

Journal of Modern Applied Statistical Methods

Reaction times were simulated for examining the power of six methods for multiple testing, as a function of sample size and departures from normality. Power estimates were low for all methods for non-normal distributions. With normal distributions, even for small sample sizes, satisfactory power estimates were observed, especially for FDR-based procedures.

Tests For 2 X 2 Tables In Clinical Trials, Vic Hasselblad, Yulia Lokhnygina

Journal of Modern Applied Statistical Methods

Five standard tests are compared: chi-squared, Fisher's exact, Yates’ correction, Fisher’s exact mid-p, and Barnard’s. Yates’ is always inferior to Fisher’s exact. Fisher’s exact is so conservative that one should look for alternatives. For certain sample sizes, Fisher’s mid-p or Barnard’s test maintain the nominal alpha and have superior power.

Sample Size Determination In Animal Health Studies, Zhanglin Cui, Alan G. Zimmermann, Daniel H. Mowrey

Conference on Applied Statistics in Agriculture

Oftentimes in animal health studies, a treatment group is randomly assigned to a pen of animals, and the pen of animals as a whole is treated (fed the same medicated feed or water) together. In this scenario, the pen of animals is the experimental unit and the individual animal may be an observational unit. In addition to having the pen as the experimental unit, if multiple sites are used and site is treated as a random factor, this adds complexity to the study. To properly design the study, it is necessary to determine the number of animals in a pen, …

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.

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.

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.

A Different Future For Social And Behavioral Science Research, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

The dissemination of intervention and treatment outcomes as effect sizes bounded by conf idence intervals in order to think meta-analytically was promoted in a recent article in Educational Researcher. I raise concerns with unfettered reporting of effect sizes, point out the con in confidence interval, and caution against thinking meta-analytically. Instead, cataloging effect sizes is recommended for sample size estimation and power analysis to improve social and behavioral science research.