Finite Sample Distribution-Free Test Statistics for Nested Structural Models

The asymptotically distribution free (ADF) method is often used to estimate parameters or test models without a normal distribution assumption on variables, both in covariance structure analysis and in correlation structure analysis. However, little has been done to study the differences in behaviors of the ADF method in covariance versus correlation structure analysis. The behaviors of 3 test statistics frequently used to evaluate structural equation models with nonnormally distributed variables, χ2 test TAGLS and its small-sample variants TYB and TF(AGLS) were compared. Results showed that the ADF method in correlation structure analysis with test statistic TAGLS performs much better at small sample sizes than the corresponding test for covariance structures. In contrast, test statistics TYB and TF(AGLS) under the same conditions generally perform better with covariance structures than with correlation structures. It is proposed that excessively large and variable condition numbers of weight matrices are a cause of poor behavior of ADF test statistics in small samples, and results showed that these condition numbers are systematically increased with substantial increase in variance as sample size decreases. Implications for research and practice are discussed.

Considerations of sample size in medical research

Determining whether sample differences in central tendency represent real differences in parent populations is a typical issue in applied research. If the conditions of normality, homogeneity of variance, and independence of errors are met, the t-test can be used for a two sample instance (two groups). However, the nonparametric equivalent is taken into account when these presumptions are violated. In order to determine which test is most effective and resilient to a certain distribution and sample size when samples are obtained from separate populations, the study compares the effectiveness and sensitivity of power of four test statistics. These tests were examined under normal and some skew distributions at sample size of 5, 10, 15, 20, 25, 30, 40, 45, and 50 using simulation. The most effective test for a given distribution and sample size was chosen using the power of each test computed. The study found that when data are taken from a normal distribution and tested at small and large sample sizes, respectively, the t-test and Welch test have the highest power, while the Median is the most resistant to uniform and gamma, and the Man-Whitney test is the most reliable for exponential distributions.

Relatively few empirical studies have examined the performance of enumeration indices in correctly identifying longitudinal population heterogeneity when present, and these studies have produced mixed results. In light of these findings, Muthén (2003) suggested that the inclusion of time-invariant (antecedent) and time-varying (concurrent) covariates, as well as allowing the extracted growth mixture classes to predict a distal outcome (consequent covariate), could improve the performance of enumeration indices. This Monte Carlo simulation study examined the performance of a large set of enumeration indices within these generalized growth mixture model (GGMM) conditions, as suggested by Muthén, by manipulating 4 design conditions: (a) sample size, (b) separation distance between adjacent latent growth trajectories, (c) growth trajectory membership proportions, and (d) the amount of mixture model variance explained by the covariates. The findings suggest: (a) at smaller (N = 500) sample sizes, enumeration indices were much more likely to select an incorrect model than the correct one, (b) at larger (N = 3,000) sample sizes, correct model identification occurred only in the largest separation distance and trajectory membership equality conditions, and (c) the inclusion of covariates had a negligible effect at smaller sample sizes, but covariate inclusion had a more favorable effect on data generation model identification in the largest sample size, largest trajectory separation distance, and equal trajectory membership proportions conditions. Suggestions for researchers and future empirical study possibilities are discussed.

Some Thoughts About Data Type, Distribution, and Statistical Significance

The reversed intrinsic phenomenon/ curve and voltage dependence of ultra-low k IMD (Inter-Metal Dielectric) were investigated by experiments with large sample sizes using high and low voltage stresses for both 40nm and 28nm ultra-low k dielectrics. Using large sample sizes, we observed that the reversed intrinsic curve only exists for the stresses at high voltages, but not for the low voltage stress tests. This phenomenon should be caused by the difference in percolation paths at high and low electric fields. At low voltage stresses, the dielectric breakdown is dominated by the accumulative percolation path as what in the traditional non-low k dielectrics. On the other hand, at high voltage stresses, the geometric IMD spacing-dominate breakdowns happen and it leads to the breakdowns showing the “reversed intrinsic curve” (which the earlier portion of the fitting curve with a larger slope). We propose that the reversed intrinsic curve does not represent a true failure mechanism at the field operation conditions. From our experiments, we also found, in the tests with small sample sizes at high voltages, we cannot see a clear reversed intrinsic curve, which will result in bi-modal distributions with small R squares (coefficient of determination). The low voltage PLR (Package-Level Reliability) test will be a better solution to assess ultra-low k dielectric reliability even at a small sample size.

The Need for Large Clinical Studies in Perioperative Medicine

A Monte Carlo study was conducted to evaluate the performance of two-group multivariate tests on means under conditions of homogeneous and heterogeneous correlation structure and multivariate normality and nonnormality. The test statistics under study included those based on the work of Hotelling and alternative procedures proposed by James, Yao, Johansen, Nel and van der Merwe, and Kim. Results indicated that the F statistic based on Hotelling's T 2 was outperformed by the alternative procedures which showed good Type I error control under moderate to large sample sizes. Under small sample sizes, the alternative procedures tended to have unacceptable Type I error control. The F statistic based on Hotelling's T 2 is recommended for use when the sample size in each group is small (e.g., n = p + 1) and correlation heterogeneity is mild (<.3), or when groups are approximately equal in size. Though simulated conditions of multivariate nonnormality had some impact on the Type I error rates on some of the procedures, the impact was in general small and apparent only under the smaller sample size conditions.

“What should be the sample size for my study?” is a common question in the minds of every research at some point of the research cycle. Answering this question with confident is tough even for a seasoned researcher. Sample size determination, an important aspect of sampling design consideration of a study, is a factor which directly influences the internal and external validity of the study. Unless the sample size is of adequate size, the results of the study cannot be justified. Conducting a study in too small sample size or too large sample size have ethical, scientific, practical, and economic strings attached to it and have detrimental effects in the research outcomes. A myriad of factors including the study design, type of power analysis, sampling technique employed, and acceptable limits of error fixed play a decisive role in estimating the sample size. However, the advent of free to use software and websites for sample size estimation has actually diluted or sometimes complicated the whole process of sample size estimation as important factors or assumptions related to sample size are overlooked. Engaging a professional biostatistician from the very beginning of the research process would be a wise decision while conducting research. This article highlights the important concepts related to sample size estimation with emphasis on factors which influences it.

Population genetic studies provide insights into the evolutionary processes that influence the distribution of sequence variants within and among wild populations. FST is among the most widely used measures for genetic differentiation and plays a central role in ecological and evolutionary genetic studies. It is commonly thought that large sample sizes are required in order to precisely infer FST and that small sample sizes lead to overestimation of genetic differentiation. Until recently, studies in ecological model organisms incorporated a limited number of genetic markers, but since the emergence of next generation sequencing, the panel size of genetic markers available even in non-reference organisms has rapidly increased. In this study we examine whether a large number of genetic markers can substitute for small sample sizes when estimating FST. We tested the behavior of three different estimators that infer FST and that are commonly used in population genetic studies. By simulating populations, we assessed the effects of sample size and the number of markers on the various estimates of genetic differentiation. Furthermore, we tested the effect of ascertainment bias on these estimates. We show that the population sample size can be significantly reduced (as small as n = 4–6) when using an appropriate estimator and a large number of bi-allelic genetic markers (k>1,000). Therefore, conservation genetic studies can now obtain almost the same statistical power as studies performed on model organisms using markers developed with next-generation sequencing.

Causative agents of Kikuchi–Fujimoto disease (histiocytic necrotizing lymphadenitis): A meta-analysis

Great efforts have been made on the algorithms that deal with RNA-seq data to enhance the accuracy and efficiency of differential expression (DE) analysis. However, no consensus has been reached on the proper threshold values of fold change and adjusted p-value for filtering differentially expressed genes (DEGs). It is generally believed that the more stringent the filtering threshold, the more reliable the result of a DE analysis. Nevertheless, by analyzing the impact of both adjusted p-value and fold change thresholds on DE analyses, with RNA-seq data obtained for three different cancer types from the Cancer Genome Atlas (TCGA) database, we found that, for a given sample size, the reproducibility of DE results became poorer when more stringent thresholds were applied. No matter which threshold level was applied, the overlap rates of DEGs were generally lower for small sample sizes than for large sample sizes. The raw read count analysis demonstrated that the transcript expression of the same gene in different samples, whether in tumor groups or in normal groups, showed high variations, which resulted in a drastic fluctuation in fold change values and adjustedp-values when different sets of samples were used. Overall, more stringent thresholds did not yield more reliable DEGs due to high variations in transcript expression; the reliability of DEGs obtained with small sample sizes was more susceptible to these variations. Therefore, less stringent thresholds are recommended for screening DEGs. Moreover, large sample sizes should be considered in RNA-seq experimental designs to reduce the interfering effect of variations in transcript expression on DEG identification.

Liang과 Zeger는 이산형 혹은 연속형 반복측정자료를 분석하기 위한 일반화 추정방정식 (GEE)을 제안하였다 GEE모형은 범주형 반복측정자료의 모형으로 확장될 수 있으며, 이 GEE추정량은 대표본인 경우 다변량 정규분포를 따른다. 그러나 GEE는 대표본근사이론에 기초한다. 본 논문에서는 소표본인 경우 반복 측정된 순서자료에 대한 GEE추정량의 성질을 연구한다. 우리는 두가지 방법을 사용하여 두그룹의 반복 측정된 순서자료를 생성하며 모의실험을 통하여 소표본인 경우 여러 개 범주를 갖는 순서반응 자료에 대하여 GEE추정량의 1종 오류율, 검정력, 상대효율, 두 그룹의 표본크기가 다를 경우 효과, 그리고 분산 추정량의 성질등을 연구한다. Liang and Zeger proposed generalized estimating equations(GEE) for analyzing repeated data which is discrete or continuous. GEE model can be extended to model for repeated categorical data and its estimator has asymptotic multivariate normal distribution in large sample sizes. But GEE is based on large sample asymptotic theory. In this paper, we study the properties of GEE estimators for repeated ordinal data in small sample sizes. We generate ordinal repeated measurements for two groups using two methods. Through Monte Carlo simulation studies we investigate the empirical type 1 error rates, powers, relative efficiencies of the GEE estimators, the effect of unequal sample size of two groups, and the performance of variance estimators for polytomous ordinal response variables, especially in small sample sizes.

There are several misconceptions when interpreting the values of the coefficient of determination, R2, in simple linear regression. R2 is heavily dependent on sample size n and the type of data being analyzed but becomes insignificant when working with very large sample sizes. In this paper, we comment on these observations and develop a relationship between R2, n, and the level of significance α, for relatively small sample sizes. In addition, this paper provides a simplified version of the relationship between R2 and n, by comparing the standard deviation of the dependent variable, Sy, to the standard error of the estimate, Se. This relationship will serve as a safe lower bound to the values of R2. Computational experiments are performed to confirm the results from both models. Even though the focus of the paper is on simple linear regression, we present the groundwork for expanding our two models to the multiple regression case.

The processes by which plant spatial patterns are formed, and the effects of those patterns on plant community dynamics, remain important areas of research in plant ecology. Plant spatial pattern formation has been linked to many ecological processes that act to structure plant communities at different spatiotemporal scales. Past studies of pattern formation are common, but recent methodological advances in data collection and analysis have permitted researchers to conduct more advanced observational studies of pattern formation in space and time. While studies of the effects of plant spatial patterns were formally rare, they have increased in the last decade as new types of experiments and analysis have been developed to better understand the myriad effects of plant patterns on community dynamics. My dissertation research examined both the causes and consequences of plant spatial patterns in the context of natural and experimental Great Basin semi-arid plant communities. In both cases, I implemented novel methodologies for data collection, experimental design, and data analysis in an attempt to address current gaps in knowledge related to the processes by which plant spatial patterns are formed, as well as the effect of plant spatial patterns on community dynamics. The results inform both basic and applied plant ecology, and set the stage for further research on the causes and consequences of plant spatial patterns in semi-arid plant communities.