Hotelling's T2 Test Research Articles

A genome-wide association scan for rheumatoid arthritis data by Hotelling's T2tests

We performed a genome-wide association scan on the North American Rheumatoid Arthritis Consortium (NARAC) data using Hotelling's T2 tests, i.e., TH based on allele coding and TG based on genotype coding. The objective was to identify associations between single-nucleotide polymorphisms (SNPs) or markers and rheumatoid arthritis. In specific candidate gene regions, we evaluated the performance of Hotelling's T2 tests. Then Hotelling's T2 tests were used as a tool to identify new regions that contain SNPs showing strong associations with disease. As expected, the strongest association evidence was found in the region of the HLA-DRB1 locus on chromosome 6. In the region of the TRAF1-C5 genes, we identified two SNPs, rs2900180 and rs3761847, with the largest and the second largest TH and TG scores among all SNPs on chromosome 9. We also identified one SNP, rs2476601, in the region of the PTPN22 gene that had the largest TH score and the second largest TG score among all SNPs on chromosome 1. In addition, SNPs with the largest TH score on each chromosome were identified. These SNPs may be located in the regions of genes that have modest effects on rheumatoid arthritis. These regions deserve further investigation.

Hotelling T2 test and multivariated analysis of variance to analyzing nurse job burnout datum

Objective To investigate the statistical.method for analyzing nurse job burnout Data. Methods Hotelling T2 test and multivariate analysis of variance(MANOVA)were used to analyze nurse job burnout datum. Results There was statistical significance between different cities,different ethnieities in the personal achievements,hut from three dimensions of the whole job burnout,there are no statistical sig-nificant differences among different cities, different ethnicities and different ages. Conclusions The use of Hotelling T2 test and multivariate analysis of variance to analyzing nurse job burnout data, not only ob-tain overall conclusion, and further use of single-variable analysis may also gain comparative results of each dimensions. Key words: Job burnout; Hotelling T2 test; Multivariate analysis of variance

Correction to Wu, L., Chuang, A., & Chen, P. (2008). Motivation for using search engines: A two factor model. Journal of American Society for Information Science and Technology, 59(11), 1829-1840.

Correction to Wu, L., Chuang, A., & Chen, P. (2008). Motivation for using search engines: A two factor model. Journal of American Society for Information Science and Technology, 59(11), 1829-1840.

Age and growth of bluemouth, Helicolenus dactylopterus, from the Portuguese continental slope

Abstract Sequeira, V., Neves, A., Vieira, A. R., Figueiredo, I., and Gordo, L. S. 2009. Age and growth of bluemouth, Helicolenus dactylopterus, from the Portuguese continental slope. – ICES Journal of Marine Science, 66: 524–531. In all, 933 bluemouth (Helicolenus dactylopterus) were obtained from bottom-trawl research surveys along the Portuguese continental slope between October 2005 and February 2007 and from commercial landings. Age was determined by reading whole sagittal otoliths, and age estimates were validated by daily growth increment (DGI) analysis. Fish ranged from 5.2 to 44.9 cm, which corresponded to fish between 0 and 30 years old. The mean total length obtained from DGI analysis for age class 1 fish was 8.6 cm, corresponding to otoliths with a mean radius of 1.8 mm. As no statistical differences between sex were observed, the von Bertalanffy growth equation fitted was Lt = 45.50[1 − e−0.05(t+4.01)]. Comparisons with other studies using Hotelling's T2 test and the growth perform index (Ф) are drawn. The growth rates estimated in this study using whole otolith readings were the lowest of all the studies available, and the estimated L∞ is lower then those obtained for Azorean waters and higher than those published for the Mediterranean.

M-quantile Regression Analysis of Temporal Gene Expression Data

In this paper, we explore the use of M-quantile regression and M-quantile coefficients to detect statistical differences between temporal curves that belong to different experimental conditions. In particular, we consider the application of temporal gene expression data. Here, the aim is to detect genes whose temporal expression is significantly different across a number of biological conditions. We present a new method to approach this problem. Firstly, the temporal profiles of the genes are modelled by a parametric M-quantile regression model. This model is particularly appealing to small-sample gene expression data, as it is very robust against outliers and it does not make any assumption on the error distribution. Secondly, we further increase the robustness of the method by summarising the M-quantile regression models for a large range of quantile values into an M-quantile coefficient. Finally, we fit a polynomial M-quantile regression model to the M-quantile coefficients over time and employ a Hotelling T(2)-test to detect significant differences of the temporal M-quantile coefficients profiles across conditions. Extensive simulations show the increased power and robustness of M-quantile regression methods over standard regression methods and over some of the previously published methods. We conclude by applying the method to detect differentially expressed genes from time-course microarray data on muscular dystrophy.

Change Detection for the NASA Generic Transport Aircraft Model

This paper reports our initial effort on change detection performed on the residuals of sets of probing outputs to monitor the health of a simulated generic transport aircraft model provided by NASA. The probing outputs are estimates of small signal impulse responses generated based on a pulse-compression principle, and designed to be independent of other applied signals around the aircraft control loop. The residuals are the difference between the probing outputs of a potentially faulty system and the stored or calculated probing outputs of a normal system. The samples of residuals are evaluated using the Hotelling's T2-test which rejects or accepts the null hypothesis that the samples are from an F-distribution. The paper focuses its discussion on the attempt to reduce detection delay, and presents a simplified analysis on detection threshold, detection delay, and miss detection rate.

Relationship between segmental and whole-body phase angle in peritoneal dialysis patients

The relation between the right-side (RS) electrical impedance phase angle (PA) and segmental PA in five configurations at 50 kHz was analyzed in 23 peritoneal dialysis male patients before complete drainage of the abdominal cavity. The impedance vector (Z/H) components were standardized by the height H of the subjects (R/H and Xc/H). BIVA software was used to analyze the individual RS vector. The Pearson correlation was used to analyze the correlation between RS and segmental configurations. Student's t test and Hotelling's T2 test were used to analyze the separation of groups obtained by BIVA. The highest significant Pearson correlation was between RS and right leg total (RLEGT) in a longitudinal direction (r = 0.925, P < 0.001). We obtained a significant difference (P < 0.05) in R/H, Xc/H (for RS and RLEGT) using Hotelling's T2 test, and in PA using Student's t test. The transverse measurement in the leg (RTRLEG) showed the lowest correlation (r = 0.261). In conclusion, we can obtain similar information through the phase angle, whether RS is measured or if we measure on RLEGT. The phase angle of the transverse measurements provides different information from the phase angle of the longitudinal measurements.

Gender Differences In Mathematics Performance: Some Fresh Insights

The widespread belief that males outperform females has been of interest not only to the social researcher but to the general public as well. It is in this view that the researchers decided to investigate if there is a significance difference in mathematics performance by gender at least at the tertiary level. Data was obtained from the Department of Mathematics and Statistics (UCC). All level 200 students who took mathematics courses constituting of 384 and 416 students for the 2004/2005 and 2005/2006 academic years respectively were used for the study. The analysis made use of the Hotelling's T test of difference of mean vectors and the chi-squared test of independence. The results of the study showed that more males offer mathematics courses more than females. However, the grades obtained did not depend on gender. The research also revealed that there is no significant difference in the performance of mathematics by gender. This and many other interesting findings are presented in this paper. Keywords: Mathematics performance, Hotelling's T2 test, Chi-Squared test of independence Gender and Behaviour Vol. 6 (1) 2008: pp. 1519-1531

Effect of the ethinylestradiol/norelgestromin contraceptive patch on body composition. Results of bioelectrical impedance analysis in a population of Italian women

BackgroundAs weight gain is one of the most frequently cited reasons for not using and for discontinuing hormonal contraceptives, in an open-label, single-arm, multicentre clinical study we evaluated the effect of the ethinylestradiol/norelgestromin contraceptive patch (EVRA, Janssen-Cilag International, Belgium) on body composition using bioelectrical impedance analysis (BIA).MethodsBody weight and impedance vector components (resistance (R) and reactance (Xc), at 50 kHz frequency, Akern-RJL Systems analyzer) were recorded before entry, after 1, 3 and 6 months in 182 Italian healthy women aged 29 yr (18 to 45), and with BMI 21.8 kg/m2 (16 to 31). Total body water (TBW) was estimated with a BIA regression equation. Vector BIA was performed with the RXc mean graph method and the Hotelling's T2 test for paired and unpaired data.ResultsAfter 6 months body weight increased by 0.64 kg (1.1%) and TBW increased by 0.51 L (1.7%). The pattern of impedance vector displacement indicated a small increase in soft tissue hydration (interstitial gel fluid). Body composition changes did not significantly differ among groups of previous contraceptive methods. Arterial blood pressure did not significantly change over time.ConclusionAfter 6 months of treatment with the ethinylestradiol/norelgestromin contraceptive patch we found a minimal, clinically not relevant, increase in body weight less than 1 kg that could be attributed to an adaptive interstitial gel hydration. This fluctuation is physiological as confirmed by the lack of any effect on blood pressure. This could be useful in increasing women's choice, acceptability and compliance of the ethinylestradiol/norelgestromin contraceptive patch.

Multivariate attribute control chart using Mahalanobis D 2 statistic

Process control involves repeated hypothesis testing based on several samples. However, process control is not exactly hypothesis testing as such since it deals with detection of non-random patterns of variation as well in a fleeting kind of population. Compare this with hypothesis testing which is principally meant for a stagnant population. Dr Walter A. Shewhart introduced a graphic method for doing this testing in a fleeting population in 1924. This graphic method came to be known as control chart and is widely used throughout the world today for process management purposes. Subsequently there was much advancement in process control techniques. In particular, when more than one variable was involved, process control techniques were developed mainly by Hicks (1955), Jackson (1956 and 1959) and Montgomery and Wadsworth (1972) based on the pioneering work of Hotelling in 1931. Most of them have worked in the area of multivariate variable control chart with the underlying distribution as multivariate normal. When more than one attribute variables are involved some works relating to test of hypothesis was done by Mahalanobis (1946). These works were also based on the Hotelling T2 test. This paper expands the concept of ‘Mahalanobis Distance’ in case of a multinomial distribution and thereby proposes a multivariate attribute control chart.

Two-stage analysis strategy for identifying the IgM quantitative trait locus.

Genetic association studies offer an opportunity to find genetic variants underlying complex human diseases. Various tests have been developed to improve their power. However, none of these tests is uniformly best and it is usually unclear at the outset what test is best for a specific dataset. For example, Hotelling's T2 test is best for normally distributed data, but it can lose considerable power when normality is not met. To achieve satisfactory power in most cases, without compromising the overall significance level, we propose to adopt a two-stage adaptive analysis strategy - several statistics are compared on a portion of the samples at the first stage and the most powerful statistic is then used for the remaining samples. We evaluated this procedure by mapping the quantitative trait locus of IgM with the simulated data in Genetic Analysis Workshop 15 Problem 3. The results show that the gain in power of the two-stage adaptive analysis procedure could be considerable when the initial choice of test statistic is wrong, whereas the loss is relatively small in the case that the optimal test chosen initially is correct.

A framework for significance analysis of gene expression data using dimension reduction methods.

BackgroundThe most popular methods for significance analysis on microarray data are well suited to find genes differentially expressed across predefined categories. However, identification of features that correlate with continuous dependent variables is more difficult using these methods, and long lists of significant genes returned are not easily probed for co-regulations and dependencies. Dimension reduction methods are much used in the microarray literature for classification or for obtaining low-dimensional representations of data sets. These methods have an additional interpretation strength that is often not fully exploited when expression data are analysed. In addition, significance analysis may be performed directly on the model parameters to find genes that are important for any number of categorical or continuous responses. We introduce a general scheme for analysis of expression data that combines significance testing with the interpretative advantages of the dimension reduction methods. This approach is applicable both for explorative analysis and for classification and regression problems.ResultsThree public data sets are analysed. One is used for classification, one contains spiked-in transcripts of known concentrations, and one represents a regression problem with several measured responses. Model-based significance analysis is performed using a modified version of Hotelling's T2-test, and a false discovery rate significance level is estimated by resampling. Our results show that underlying biological phenomena and unknown relationships in the data can be detected by a simple visual interpretation of the model parameters. It is also found that measured phenotypic responses may model the expression data more accurately than if the design-parameters are used as input. For the classification data, our method finds much the same genes as the standard methods, in addition to some extra which are shown to be biologically relevant. The list of spiked-in genes is also reproduced with high accuracy.ConclusionThe dimension reduction methods are versatile tools that may also be used for significance testing. Visual inspection of model components is useful for interpretation, and the methodology is the same whether the goal is classification, prediction of responses, feature selection or exploration of a data set. The presented framework is conceptually and algorithmically simple, and a Matlab toolbox (Mathworks Inc, USA) is supplemented.

Gastric emptying: a comparison of three methods

Objective. A better understanding of the clinical relevance of delayed gastric emptying (e.g. in diabetes) requires a simple, easily accessible and inexpensive method for measuring it. Two “new” methods for measuring gastric emptying of liquids (the paracetamol absorption test and the 13C-acetate breath test) are compared with the gold standard (gastric emptying scintigraphy (GES)). Material and methods. The three techniques were used simultaneously in 10 healthy subjects. A gastric emptying time-retention curve was drawn for each technique and the results were compared at the 75%, 50% and 25% retention quartiles. Results. Agreement was found between the paracetamol absorption test and GES (p=0.95; Hotelling's T2 test). Using the Wagner-Nelson one compartment correction produced a retention curve for the 13C-acetate breath test statistically significantly below GES (p<0.01). Conclusion. In healthy subjects, the paracetamol absorption test produced results comparable to those of liquid GES, but not to the results of the 13C-acetate breath test.

Multivariate statistical methods applied to biomonitoring studies

This work describes the use of some multivariate statistical methods for retrieving the information present in a typical dataset coming from a biomonitoring study applied to trace metals measured on Patella caerulea and Monodonta turbinata samples. These samples were collected at five stations in Linosa Island in the Sicilian Channel (Mediterranean Sea) and the multivariate statistical methods applied were Principal Component Analysis (PCA), Hotelling T² test and Discriminant Analysis by means of Mahalanobis Distance (DAMD). Using PCA it is possible to have in a single and fast step, a direct insight into the structure of data, and thus obtain peculiar information that allows the different accumulation characteristics of the two types of mollusc to be seen. PCA also gives information about the metals that cause the peculiar accumulation characteristics of each mollusc. Hotelling's T² and DAMD are other important multivariate methods that confirm the results of PCA and also give complementary information for the interpretation of experimental data.

Integration of mobility and intrusion detection for wireless ad hoc networks

AbstractOne of the main challenges in building intrusion detection systems (IDSs) for mobile ad hoc networks (MANETs) is to integrate mobility impacts and to adjust the behaviour of IDSs correspondingly. In this paper, we first introduce two different approaches, a Markov chain‐based approach and a Hotelling's T2 test based approach, to construct local IDSs for MANETs. We then demonstrate that nodes' moving speed, a commonly used parameter in tuning IDS performances, is not an effective metric to tune IDS performances under different mobility models. To solve this problem, we further propose an adaptive scheme, in which suitable normal profiles and corresponding proper thresholds can be selected adaptively by each local IDS through periodically measuring its local link change rate, a proposed unified performance metric. We study the proposed adaptive mechanism at different mobility levels, using different mobility models such as random waypoint model, random drunken model, and obstacle mobility model. Simulation results show that our proposed adaptive scheme is less dependent on the underlying mobility models and can further reduce false positive ratio. Copyright © 2006 John Wiley &amp; Sons, Ltd.

Exploiting the full power of temporal gene expression profiling through a new statistical test: Application to the analysis of muscular dystrophy data

BackgroundThe identification of biologically interesting genes in a temporal expression profiling dataset is challenging and complicated by high levels of experimental noise. Most statistical methods used in the literature do not fully exploit the temporal ordering in the dataset and are not suited to the case where temporal profiles are measured for a number of different biological conditions. We present a statistical test that makes explicit use of the temporal order in the data by fitting polynomial functions to the temporal profile of each gene and for each biological condition. A Hotelling T2-statistic is derived to detect the genes for which the parameters of these polynomials are significantly different from each other.ResultsWe validate the temporal Hotelling T2-test on muscular gene expression data from four mouse strains which were profiled at different ages: dystrophin-, beta-sarcoglycan and gamma-sarcoglycan deficient mice, and wild-type mice. The first three are animal models for different muscular dystrophies. Extensive biological validation shows that the method is capable of finding genes with temporal profiles significantly different across the four strains, as well as identifying potential biomarkers for each form of the disease. The added value of the temporal test compared to an identical test which does not make use of temporal ordering is demonstrated via a simulation study, and through confirmation of the expression profiles from selected genes by quantitative PCR experiments. The proposed method maximises the detection of the biologically interesting genes, whilst minimising false detections.ConclusionThe temporal Hotelling T2-test is capable of finding relatively small and robust sets of genes that display different temporal profiles between the conditions of interest. The test is simple, it can be used on gene expression data generated from any experimental design and for any number of conditions, and it allows fast interpretation of the temporal behaviour of genes. The R code is available from V.V. The microarray data have been submitted to GEO under series GSE1574 and GSE3523.

A Multivariate Two‐Sample Mean Test for Small Sample Size and Missing Data

We develop a new statistic for testing the equality of two multivariate mean vectors. A scaled chi-squared distribution is proposed as an approximating null distribution. Because the test statistic is based on componentwise statistics, it has the advantage over Hotelling's T2 test of being applicable to the case where the dimension of an observation exceeds the number of observations. An appealing feature of the new test is its ability to handle missing data by relying on only componentwise sample moments. Monte Carlo studies indicate good power compared to Hotelling's T2 and a recently proposed test by Srivastava (2004, Technical Report, University of Toronto). The test is applied to drug discovery data.

Craniofacial morphometric analysis of mandibular prognathism

The purpose of this study was to provide more information about the morphological characteristics of the craniofacial complex in mandibular prognathism. Forty young adult males having mandibular prognathism were compared with 40 having normal occlusion. This was conducted to carry out geometric morphometric assessments to localize alterations, using Procrustes analysis and thin-plate spline analysis, in addition to conventional cephalometric techniques. Procrustes analysis indicated that the mean craniofacial, midfacial and mandibular morphology was significantly different in prognathic subjects compared with normal controls. This finding was corroborated by the multivariate Hotelling T(2)-test of cephalometric variables. Mandibular prognathism demonstrated a shorter and slightly retropositioned maxilla, a greater total length and anterior positioning of the mandible. Thin-plate spline analysis revealed a developmental diminution of the palatomaxillary region anteroposteriorly and a developmental elongation of the mandible anteroposteriorly, leading to the appearance of a prognathic mandibular profile. In conclusion, thin-plate spline analysis seems to provide a valuable supplement for conventional cephalometric analysis because the complex patterns of craniofacial shape change are visualized suggestive by means of grid deformations.

A Nonparametric Test for the One-Sample Bivariate Location Problem

SYNOPTIC ABSTRACTA nonparametric test is proposed for the bivariate one-sample location problem. The proposed test is robust in nature. The asymptotic distribution of the test statistic is computed as Chi-square. The power of the proposed test statistic is compared with Hotelling's T2 test statistic, Mardia's (1967) test statistic, Blumen's (1958) test statistic, and Wilcoxon's rank sum test statistic using Monte Carlo techniques. The proposed test statistic performs better than its competitors considered here under almost all the underlying distributions used for the power study. The application of the test is illustrated using a bivariate one sample data.

Effect of Temperature on the Longitudinal Variability of Quantitative Ultrasound Variables

It is unclear whether longitudinal change in phantom measurements bears any relation to the long-term in vivo instrument performance of quantitative ultrasound devices. Longitudinal quantitative ultrasound phantom data were obtained by measuring the manufacturer-provided phantom at ambient temperature and two different sets of Leeds phantoms at either ambient temperature or following a phantom temperature-control protocol. Measurements were performed using the Achilles Plus bone densitometer. Changes in longitudinal phantom data were compared to in vivo quantitative ultrasound data obtained from seven healthy, young volunteers. A cosinor model with linear trend and Hotelling's T2-test were used to quantify seasonal rhythms and long-term drift in quantitative ultrasound variables. Temperature effects and marked seasonal rhythms on quantitative ultrasound phantom measurements were evident but were far less apparent in vivo. Longitudinal precision of quantitative ultrasound variables was poorer for the manufacturer-provided phantom than for phantoms that were subjected to a temperature-control protocol or for healthy volunteers. This study has shown that longitudinal precision and longitudinal change differs between in vivo and phantom data. Longitudinal quantitative ultrasound measurements for monitoring change in skeletal status cannot, as yet, be properly controlled.