Hypothesis Testing Of Means Research Articles

Hypothesis testing for the population mean and variance based on r-size biased samples

The present research deals with hypothesis testing for the population mean and variance based on r-size biased samples. Specifically, consistent and asymptotically normally distributed estimators of the mean and the variance of a population are proposed and utilized in developing hypothesis tests for the mean and the variance of a distribution. Two different approaches originating, respectively, from plug-in and bootstrap ideas are developed. A Monte Carlo study is carried out to examine the performance of both methods on controlling type I error rate as well as evaluating their power. Finally, the analysis of a real world data set illustrates the benefits incurred from utilizing the proposed methodology.

Mean and Variance of Phylogenetic Trees.

We describe the use of the Fréchet mean and variance in the Billera-Holmes-Vogtmann (BHV) treespace to summarize and explore the diversity of a set of phylogenetic trees. We show that the Fréchet mean is comparable to other summary methods, and, despite its stickiness property, is more likely to be binary than the majority-rule consensus tree. We show that the Fréchet variance is faster and more precise than commonly used variance measures. The Fréchet mean and variance are more theoretically justified, and more robust, than previous estimates of this type and can be estimated reasonably efficiently, providing a foundation for building more advanced statistical methods and leading to applications such as mean hypothesis testing and outlier detection.

INFERENSI STATISTIK DARI DISTRIBUSI NORMAL DENGAN METODE BAYES UNTUK NON-INFORMATIF PRIOR

One of the method that can be used in statistical inference is Bayesian method. It combine sample distribution and prior distribution to get a posterior distribution. In this paper, sample distribution used is univariate normal distribution. Prior distribution used is non-informative prior. Determination technique of non-informative prior use Jefrrey’s method from univariate normal distribution. After got the posterior distribution, find the marginal distribution of mean and variance. So that will get the parameter estimation of interval for mean and variance. Hypothesis testing for mean and variance can find from parameter estimation of formed interval. Keywords : Bayesian method, non-informatif prior, Jeffrey’s method, Parameter Estimation of Interval, Hypothesis test

Gross errors detection of industrial data by neural network and cluster techniques

This article describes the application of a three-layer feed-forward neural network to analyze industrial plant data. To adjust mathematical models (for control or optimization purposes) from plant data, it is necessary to analyze and detect outliers and systematic errors and to remove them. The system studied is the feed preparation of an isoprene production unit and represents a multivariable problem. To detect outliers in a multivariable system is not an easy task. The technique used in this paper is able to identify this kind of error. The methodology employed involves construction of a reliable neural network model to represent the process and its training with a few iterations (a few thousand). Thus, the points at which errors between the experimental and calculated data appear to be scattered far from the majority of the values are probably outliers. In some cases, outlier points can be easily detected, but in others, they are not so obvious. In these cases, they are separated and a cluster with other similar data is built. After analyzing these clusters based on the similarity principle or by hypothesis tests for means, it is then decided whether or not these points can be excluded. At the same time the process is checked for any abnormalities recorded during the specific period. Three year's worth of process data were analyzed and about 30% of the data were excluded.

Classification of fermentation performance by multivariate analysis based on mean hypothesis testing

Multivariate analysis, such as principal component analysis and artificial autoassociative neural networks, is currently extensively applied to feature capturing, physiological state recognition, fault detection and bioprocess control. However, it is not clear which process variable should be selected as an important input for multivariate analysis to analyze physiological conditions and/or bioprocess performance a priori. An efficacious method to select more informative process variables from the repository of historical data is highly desired. In this study, we focused on a premodeling step. Mean hypothesis testing (MHT) was used to select appropriate variables for multivariate analysis. Fermentation data sets were classified into two classes “good” and “bad” according to the MHT results. The results showed that selecting discriminating process variables from the historical database by MHT enhanced the overall effectiveness of multivariate analysis prior to principal component analysis and artificial autoassociative neural network model creation.

Classification of Fermentation Performance by Multivariate Analysis Based on Mean Hypothesis Testing

Multivariate analysis, such as principal component analysis and artificial autoassociative neural networks, is currently extensively applied to feature capturing, physiological state recognition, fault detection and bioprocess control. However, it is not clear which process variable should be selected as an important input for multivariate analysis to analyze physiological conditions and/or bioprocess performance a priori. An efficacious method to select more informative process variables from the repository of historical data is highly desired. In this study, we focused on a premodeling step. Mean hypothesis testing (MHT) was used to select appropriate variables for multivariate analysis. Fermentation data sets were classified into two classes "good" and "bad" according to the MHT results. The results showed that selecting discriminating process variables from the historical database by MHT enhanced the overall effectiveness of multivariate analysis prior to principal component analysis and artificial autoassociative neural network model creation.

Effect size, power, and sample size determination for structured means modeling and mimic approaches to between-groups hypothesis testing of means on a single latent construct

While effect size estimates, post hoc power estimates, and a priori sample size determination are becoming a routine part of univariate analyses involving measured variables (e.g., ANOVA), such measures and methods have not been articulated for analyses involving latent means. The current article presents standardized effect size measures for latent mean differences inferred from both structured means modeling and MIMIC approaches to hypothesis testing about differences among means on a single latent construct. These measures are then related to post hoc power analysis, a priori sample size determination, and a relevant measure of construct reliability.

Identifying and discriminating seismic patterns leading flank eruptions at Mt. Etna Volcano during 1981–1996

Seismicity affecting Mt. Etna Volcano (Italy) has been investigated in order to identify and discriminate seismic patterns precursory to flank eruptions. An intense period (1981–1996) of seismicity and volcanism, during which eight flank eruptions occurred has been considered. Two statistical methods are used: mean hypothesis testing and entropic decision trees. The results of the two methods are consistent and reveal a pattern of ‘deep’ and ‘western’ events, prior to the flank eruptions that can be used as a predictive tool as well as a physical modeling constraint.

Two-sample hypothesis tests of means of a fuzzy random variable

Abstract In this paper we will consider some two-sample hypothesis tests for means concerning a fuzzy random variable in two populations. For this purpose, we will make use of a generalized metric for fuzzy numbers, and we will develop an exact study for the case of normal fuzzy random variables and an asymptotic study for the case of simple general fuzzy random variables.

Mining of Biological Data I: Identifying Discriminating Features Via Mean Hypothesis Testing

Large volumes of data are routinely collected during bioprocess operations and, more recently, in basic biological research using genomics-based technologies. While these data often lack sufficient detail to be used for mechanism identification, it is possible that the underlying mechanisms affecting cell phenotype or process outcome are reflected as specific patterns in the overall or temporal sensor logs. This raises the possibility of identifying outcome-specific fingerprints that can be used for process or phenotype classification and the identification of discriminating characteristics, such as specific genes or process variables. The aim of this work is to provide a systematic approach to identifying and modeling patterns in historical records and using this information for process classification. This approach differs from others in that emphasis is placed on analyzing the data structure first and thereby extracting potentially relevant features prior to model creation. The initial step in this overall approach is to first identify the discriminating features of the relevant measurements and time windows, which can then be subsequently used to discriminate among different classes of process behavior. This is achieved via a mean hypothesis testing algorithm. Next, the homogeneity of the multivariate data in each class is explored via a novel cluster analysis technique called PC1 Time Series Clustering to ensure that the data subsets used accurately reflect the variability displayed in the historical records. This will be the topic of the second paper in this series. We present here the method for identifying discriminating features in data via mean hypothesis testing along with results from the analysis of case studies from industrial fermentations

Identifying seismicity patterns leading flank eruptions at Mt. Etna Volcano during 1981–1996

Seismicity time properties of the Etna Volcano (Italy) are investigated through a systematic pattern recognition analysis. Mean Hypothesis Testing (MHT) has been applied to a long time database of instrumental data recorded from 1981 to 1996 to identify relevant correlation among seismic patterns, main seismogenic volumes and the eight flank eruptions occured in the same period. Time evolution of the test statistic (T‐Ratio), calculated on a temporal window starting 75 days prior to a volcanic eruption and extending 25 days after, reveals that there is a pattern of seismic activity prior to the eruptions that can be used as a diagnostic tool as well as a physical modeling support in eruption forecasting.

The Effect of a Variable Data Point on Hypothesis Tests for Means

The Effect of a Variable Data Point on Hypothesis Tests for Means

The Effect of a Variable Data Point on Hypothesis Tests for Means

Abstract The effect of a single variable data point, x, on the usual test statistics for traditional hypothesis tests for means is analyzed. It is shown that an outlier may have a profound and unexpected effect on the test statistic. Although it might appear that an outlier would tend to lend support to the alternate hypothesis, it may in fact detract from the significance of the test. In one-population tests and analysis of variance (ANOVA), the value of x that maximizes the significance of the test statistic is given. This value does not have to be unusually large or small. In fact, it often falls within the range of the other sample points. In the general one-population case, the limiting value for the test statistic is shown to be +1. In the case involving more than one population, it is shown that the limiting value of the test statistic is a function only of the number of members in the samples and not their relative values. Special cases are identified in which the test statistic is shown to have u...