Thursday, Aug 7: 10:30 AM - 12:20 PM
4226
Contributed Papers
Music City Center
Room: CC-211
Main Sponsor
IMS
Presentations
In many scientific studies, researchers need to test whether correlations among pairs of variables show specific orders across different study groups. For instance, in biomedical research, it may be hypothesized that correlations among certain groups of commensal bacteria decrease monotonically from healthy individuals to those with progressive stages disease, reflecting systematic shifts in biological relationships with health status. We propose a constrained statistical inference procedure to test these order-based hypotheses about correlations to detect systematic changes in correlation patterns. This approach allows for more precise testing of ordered relationships and provides theoretical guarantees on its performance, including robustness and power under different scenarios. We apply this method to several simulated datasets and two real datasets, MACS Cohort HIV-1 data and Breast Cancer Cell Line data.
Keywords
Correlation coefficient
Constrained Statistical Inference
PAVA algorithm
Group restricted ordering
The problem of testing and interval estimating the reliability parameter R=P( Y1>Y2), where Y1 and Y2 are independent normal random variables with unknown means and variances, is considered. We first observe that the problem of estimating R is equivalent to estimating the coefficient of variation of the distribution of Y1-Y2. On the basis of this relation, we propose an improved approximate method to make inference on R and compare it with two existing approximate methods and a fiducial method. Approximate closed-form confidence bounds for the reliability parameter are provided. Approximate tolerance intervals for Y1-Y2 are also given. The results are extended to the case where Y1 and Y2 depend on some explanatory variables. Examples with real data are given to illustrate the methods and some recommendations are made for applications.
Keywords
fiducial test
parametric bootstrap
quantile
Satterthwaite approximation
tolerance limits
This study presents a Shiny app designed to compute statistical power and visualize the non-central F distribution in the context of ANOVA. The app allows users to explore power analysis by manipulating key parameters, including population means, a single population standard deviation, sample sizes, and significance levels. By providing an interactive tool, students can dynamically adjust these inputs and observe the effects on statistical power, reinforcing their understanding of experimental design. The app aligns with the GAISE guidelines, supporting student learning through hands-on exploration of power analysis in one-way completely randomized designs. Additionally, the connection between non-centrality parameters and test statistics is illustrated, demonstrating how the pooled variance t-test is a special case of the F-test when comparing two treatments. This interactive approach enables students to design experiments with appropriate power and gain deeper insights into hypothesis testing.
Keywords
Statistical Power
Shiny App
Non-central F Distribution
Significance Level
Experimental Design
This paper presents some new parametric test statistics for hypothesis testing population variances. These statistics are based on mean absolute deviations from the population mean, sample mean, and median. They are designed for single and two-independent-sample scenarios. The asymptotic distributions are derived, and test statistics are obtained in both absolute and ordered forms. Challenges associated with having an acceptable Type 1 error of the test statistics in small sample situations necessitated their modifications. The modifier is a function of the sample size(s) and another parameter d, 0<=d<=1. The value(s) of d at which the test statistics produced an acceptable Type 1 error rate were determined through Monte Carlo Simulation Studies, and their power and robustness were also examined and compared with the existing ones. The modified test statistics provide better Type 1 error, power, and robustness compared to existing ones. Results from real-life data applications support the simulation studies.
Keywords
New Parametric Test statistics
Variance
Monte Carlo Simulation Studies
Type I error
Power
Robustness
A member of the family of transmuted distributions is introduced, namely the transmuted Gumbel-Weibull distribution. Some statistical properties of the distribution are presented, including the mean deviations, moments, and entropy. The method of maximum likelihood is proposed for parameter estimation and multiple datasets are used to illustrate the usefulness of using this method in application.
Keywords
T-R{Y}
transmuted distributions
estimation
generalized distribution
This paper simulates the performance of two pairwise comparison procedures when distributions are normal mixtures (sometimes exhibiting heteroscedasticity and/or skewness). The two procedures are Tukey's (1949) using the Hayter-Fisher (1986) adjustment (HFF) compared to a novel procedure we name EHF that adjusts for heteroscedasticity based on the methods of Brown-Forsythe (1974), Mehrotra (1997), and Games-Howell (1976). The heterogeneity adjustments of EHF provide the expected protection against Type I errors but with a loss of power. The HFF procedure is acceptably robust and more powerful in most cases, with the exception being small sample sizes, extreme heteroscedasticity, and maximized difference in skewness and kurtosis among the populations. The direction of skewness, along with the configuration of means, surprisingly effects the power of the procedures resulting from the effect of the skewness on the correlation of mean square treatment (MST) and mean square error (MSE), the numerator and denominator in analysis of variance (ANOVA) F tests.
Keywords
ANOVA methods
power and robustness
computer simulation procedures
assumption violations