Hotelling's Test Research Articles

Multivariate test applied to single Pu isotopic composition measurement

The determination of the plutonium isotopic composition by gamma spectrometry is one of the tasks performed by nuclear inspectors. It is typically measured using planar germanium detectors. The spectra are analysed with deconvolution codes, which calculate all isotopic abundances. The experimental results are then compared with the declared values and the acceptance criterion is often based on one unique isotope, 240Pu, to distinguish between reactor and weapon grade Pu.If the measurement is a part of a measurement series, it is possible to calculate covariance terms and carry out a more comprehensive comparison using Hotelling's test as recently presented in Berndt and Mortreau (2023) [1]. In this study, it was shown that the T2 test often rejects simulated false cases which are accepted if only the 240Pu abundance is considered. Hence, the T2 test should be preferred to the 240Pu criterion.In case of a single measurement, which is typical for inspections, the co-variance cannot be determined and the comprehensive calculation of the T2 test as performed in Berndt and Mortreau (2023) [1] cannot be applied. The purpose of the present paper is to consider approximations of the variance-covariance matrix to allow the application of the T2 test to isolated measurements. The results were then applied to more than 400 single measurements of Pu samples covering many different experimental conditions.

A Pairwise Hotelling Method for Testing High-Dimensional Mean Vectors

For high-dimensional small sample size data, Hotelling's T2 test is not applicable for testing mean vectors due to the singularity problem in the sample covariance matrix. To overcome the problem, there are three main approaches in the literature. Note, however, that each of the existing approaches may have serious limitations and only works well in certain situations. Inspired by this, we propose a pairwise Hotelling method for testing high-dimensional mean vectors, which, in essence, provides a good balance between the existing approaches. To effectively utilize the correlation information, we construct the new test statistics as the summation of Hotelling's test statistics for the covariate pairs with strong correlations and the squared $t$ statistics for the individual covariates that have little correlation with others. We further derive the asymptotic null distributions and power functions for the proposed Hotelling tests under some regularity conditions. Numerical results show that our new tests are able to control the type I error rates, and can achieve a higher statistical power compared to existing methods, especially when the covariates are highly correlated. Two real data examples are also analyzed and they both demonstrate the efficacy of our pairwise Hotelling tests.

PENERAPAN RME BERBASIS BUDAYA PEKALONGAN TERHADAP KEMAMPUAN PEMAHAMAN KONSEP MAHASISWA PADA MATA KULIAH STATISTIK

Multivariate Statistics and Educational Research Statistics courses are useful courses for students, so students need the ability to understand concepts in mastering statistical material. This research aims to determine the average ability of students to understand concepts in Multivariate Statistics and Educational Research Statistics courses by implementing the RME approach based on Pekalongan culture. This research is quantitative research with the form of an experimental design, namely quasi experimental design. The subjects in the research consisted of 15 students taking Multivariate Statistics and Educational Research Statistics courses at the Mathematics Education Study Program, Pekalongan University. The data collection technique was carried out by testing the ability to understand concepts accompanied by problems in the cultural context of Pekalongan. The data analysis technique was carried out using multivariate analysis using the Hotelling's Trace test (T2 Hotelling), with a prerequisite test in the form of a multivariate normality test. The results of the research show that the average students' conceptual understanding ability in the Multivariate Statistics and Educational Research Statistics courses can reach a score of 70. If we look at the results obtained, the average conceptual understanding ability in the Multivariate Statistics and Educational Research Statistics courses is 80 and 85,333. These results indicate that the implementation of learning using the RME approach based on Pekalongan culture is effective in students' ability to understand concepts.

Implementation of Electronic Module Based Multiple Representation on Buffer Solution Materials to Improve Students’ Self-Regulated Learning and Cognitive Learning Outcomes

This research aims to determine the differences between self-regulated learning (SRL) and cognitive learning outcomes (CLO) of students who use multiple representation-based e-modules with students who use other teaching materials without being based on multiple representations on buffer solution materials and to determine the percentage of effective contribution. The subjects of this study were students of class XI MIPA at one of the high schools in Yogyakarta. The sampling technique carried out is cluster random sampling with a quasi-experiment method by posttest-only control group design. The instruments used are questionnaires on self-regulated learning and cognitive learning outcomes. The data analysis technique used in the field test results used Hotelling's Trace test and the results of effective contribution were obtained from the Partial Eta Squared value. The results showed that the significance value of 0.000 < 0.05 so that H0 was rejected, which means that there are differences in SRL and CLO of students between students who use multiple representation-based e-modules and students who use other teaching materials without multiple representations based on buffer solution materials. The percentage of effective contribution of the use of e-modules to SRL by 16.5%, CLO by 11.8%, and SRL and CLO by 20.3%.

T2-DAG: a powerful test for differentially expressed gene pathways via graph-informed structural equation modeling.

A major task in genetic studies is to identify genes related to human diseases and traits to understand functional characteristics of genetic mutations and enhance patient diagnosis. Compared with marginal analyses of individual genes, identification of gene pathways, i.e. a set of genes with known interactions that collectively contribute to specific biological functions, can provide more biologically meaningful results. Such gene pathway analysis can be formulated into a high-dimensional two-sample testing problem. Given the typically limited sample size of gene expression datasets, most existing two-sample tests tend to have compromised powers because they ignore or only inefficiently incorporate the auxiliary pathway information on gene interactions. We propose T2-DAG, a Hotelling's T2-type test for detecting differentially expressed gene pathways, which efficiently leverages the auxiliary pathway information on gene interactions from existing pathway databases through a linear structural equation model. We further establish its asymptotic distribution under pertinent assumptions. Simulation studies under various scenarios show that T2-DAG outperforms several representative existing methods with well-controlled type-I error rates and substantially improved powers, even with incomplete or inaccurate pathway information or unadjusted confounding effects. We also illustrate the performance of T2-DAG in an application to detect differentially expressed KEGG pathways between different stages of lung cancer. The R (R Development Core Team, 2021) package T2DAG which implements the proposed T2-DAG test is available on Github at https://github.com/Jin93/T2DAG. Supplementary data are available at Bioinformatics online.

Efektivitas Pendekatan CTL Dan Discovery Terhadap Kemampuan Berpikir Kreatif Dalam Pemecahan Masalah Mahasiswa PGSD UMKO

This study compares the effects of the contextual teaching and learning (CTL) approach and the discovery approach, the name by providing problem-solving problems in mathematics learning on the creative thinking abilities of PGSD students at Muhammadiyah University, Kotabumi. This type of research is a quasi-experimental research with a pretest and posttest nonequivalent group design. The subjects in this study were students of class A and class B PGSD, Muhammadiyah University, Kotabumi, 2019/2020 academic year. Instruments / measuring instruments in this study are in the form of questions that require problem-solving, the questions given have also been validated by mathematicians as a reference for measuring students' creative thinking abilities. In the next stage, the data that has been obtained by the researcher is analyzed using descriptive analysis test, inferential analysis test which includes the normality test, homogeneity, and Hotelling's test. From the results of the requirements test that are normally distributed and homogeneous, a significance level of 5% is obtained, this indicates that the contextual teaching and learning (CTL) approach and the discovery approach are equally effective as methods of learning mathematics for UMKO PGSD Students to improve creative thinking skills. Students who are use to solve mathematics problems.

Robust Two-Sample Location Testing via Probability Measure Transform

This paper deals with the problem of testing for equality between the location parameters of two unknown symmetric distributions that may belong to different families. Under this framework, we develop a new robust extension of the two-sample Hotelling test (HT). The proposed extension, called measure-transformed HT (MT-HT), operates by applying a transform to the probability measures of some reshaped versions of the two compared data sets. The considered measure transform is structured by a non-negative function, called MT-function, that weights the data points. In the paper we show that proper selection of the involved MT-functions can result in significant enhancement of the decision performance in the presence of non-Gaussian distributions with heavy tails. The advantages of the proposed MT-HT are illustrated in simulation studies that involve synthetic measurements. Additionally, the MT-HT is illustrated for anomaly detection in a blurred and noisy video stream.

Tsunami Understanding Media: Android-Physics Mobile Learning to Improve Problem Solving-Skills and Natural Disaster Preparedness

This research aimed to determine the effectiveness of the implementation of tsunami understanding media through Android-based physics mobile learning in improving students' problem-solving skills and natural disaster preparedness. This study employed quasi-experiment research with a non-equivalent control group design. This research subjects were fifty-six students of class XI IPA at SMA N 1 Kretek, Bantul, Yogyakarta. The sampling technique employed in this research was the simple random sampling technique to determine the experimental and control groups. The research data had been obtained through pretest and posttest in the form of essay tests. The data obtained were then analyzed using N-gain. The analysis results were used to determine the effectiveness of the media using the Hotelling's Trace test in MANOVA test analysis. Normally distributed and homogeneous data are required to perform the multivariate analysis. The results showed that the tsunami understanding media through Android-based physics mobile learning improved students' problem-solving skills and natural disaster preparedness compared to the learning using PowerPoint presentation. The research decisions were based on the significant value that was smaller than 0.05 (0.0000.05), and the value of the Partial Eta Squared was 0.359 in the broad category.

Generalized Hotelling's test for paired compositional data with application to human microbiome studies.

The human microbiome is a dynamic system that changes due to diseases, medication, change in diet, etc. The paired design is a common approach to evaluate the microbial changes while controlling for the inherent differences between people. For example, microbiome data may be collected from the same individuals before and after a treatment. Two challenges exist in analyzing this type of data. First, microbiome data are compositional such that the reads for all taxa in each sample are constrained to sum to a constant. Second, the number of taxa can be much larger than the sample size. Few statistical methods exist to analyze such data besides methods that test one taxon at a time. In this paper, we propose to first conduct a log-ratio transformation of the compositions, and then develop a generalized Hotelling's test (GHT) to evaluate whether the average microbiome compositions are equivalent in the paired samples. We replace the sample covariance matrix in standard Hotelling's statistic by a shrinkage-based covariance, calculated as a weighted average of the sample covariance and a positive definite target matrix. The optimal weighting can be obtained for many commonly used target matrices. We develop a permutation procedure to assess the statistical significance. Extensive simulations show that our proposed method has well-controlled type I error and better power than a few ad hoc approaches. We apply our method to examine the vaginal microbiome changes in response to treatments for menopausal hot flashes. An R package " GHT" is freely available at https://github.com/zhaoni153/GHT.

Diachronic changes in size and shape of human proximal tibia in Central Europe during the latest 1200 years

During the past twelve centuries, the stature of Central European inhabitants has increased significantly with corresponding changes in the size of lower limb bones. The aim of our study was to determine whether these changes have occurred strictly in relation to size or if the shape of skeletal structures has been altered simultaneously. Diachronic size and shape changes in the proximal part of tibia in a Central European population (Czech Republic) were studied using geometric morphometrics (principal components analysis, Hotelling's test, linear discriminant analysis). The study sample consisted of 183 three-dimensional (3D) models of adult tibiae dating to the early Middle Ages (N=65), early 20th century (N=60), and from a modern Czech population (N=57). A positive secular trend in size manifested only between the two modern Czech populations (the 20th century vs. the 21st century), a time range shorter than one century. By contrast, landmark-based shape analyses revealed significant differences in tibial morphology over the three periods covered in the study. In particular, progressive changes were observed in the position of tibial tuberosity (shifted medially), the inclination of the line connecting tuberosity with anterior edge of the tibial plateau (sloped down), the reshaping of the lower back condyle boundary (shifted posteriorly), and reshaping of the medial contour of the medial condyle (shifted anteriorly). Changes in the shape of the proximal tibial extremity across the chronologically distinct groups indicated the existence of discreet but convincing microevolutionary trends involving this anatomical structure.

On the robustness to symmetry of some nonparametric multivariate one-sample sign-type tests

ABSTRACTMany nonparametric multivariate one-sample tests in the literature require the assumption of symmetry or directional symmetry to be distribution-free. Examples include the bivariate sign test of Blumen [A new bivariate sign test. J Am Stat Assoc. 1958;53(282):448–456], the bivariate sign test of Brown and Hettmansperger [An affine invariant bivariate version of the sign Test. J R Stat Soc B. 1989;51(1):117–125], the multivariate sign test of Randles [A simpler, affine invariant, multivariate, distribution-free sign test. J Am Stat Assoc. 2000;95:1263–1268] and the multivariate signed-rank test of Oja and Randles [Multivariate nonparametric tests. Stat Sci. 2004;19:598–605]. In the current literature, it is not known how robust these tests are to the assumption of (directional) symmetry. When the symmetry assumption is not satisfied, the observed or attained significance level (the type I error probability or the size) of these tests may be unacceptably different from the specified nominal value. In this paper, we examine this robustness issue for the four nonparametric multivariate one-sample sign-type tests cited above in a simulation study, using data from several families of distributions. The popular parametric Hotelling's test included as a benchmark. Conclusions and recommendations are offered.

Exploring the relationship between entheseal changes and physical activity: a multivariate study.

Analyses of entheseal changes (EC) in identified skeletal samples employ a common research strategy based on the comparison between occupations grouped on the basis of shared biomechanical and/or social characteristics. Results from this approach are often ambiguous, with some studies that point to differences in EC between occupational samples and others failing to provide evidence of behavioral effects on EC. Here we investigate patterns of EC among documented occupations by means of a multivariate analysis of robusticity scores in nine postcranial entheses from a large (N = 372) contemporary skeletal sample including specimens from one Italian and two Portuguese identified collections. Data on entheseal robusticity, analyzed by pooled sides as well by separated sides and levels of asymmetry, are converted in binary scores and then analyzed through nonlinear principal component analysis and hierarchical cluster analysis. Results of these analyses are then used for the classification of occupations. Differences between occupational classes are tested by MANOVA and pairwise Hotelling's test. Results evidence three classes which separate occupations related to farming, physically demanding but generalized occupation, and physically undemanding occupations, with the more consistent differences between the first and the last classes. Our results are consistent with differences in biomechanical behavior between the occupations included in each class, and point to the physical and social specificity of farming activities. On the other hand, our study exemplifies the usefulness of alternative analytical protocols for the investigation of EC, and the value of research designs devoid of a priori assumptions for the test of biocultural hypotheses.

In vivo 1H MRS study in microlitre voxels in the hippocampus of a mouse model of Down syndrome at 11.7 T.

In this article, we report in vivo (1)H MRS performed in 1.8-μL voxels in a mouse model of Down syndrome (DS). To characterise the excitation-inhibition imbalance observed in DS, metabolite concentrations in the hippocampi of adult Ts65Dn mice, which recapitulate features of DS, were compared with those of their euploid littermates at a voxel 42-fold smaller than in a previously published study. Quantification of the metabolites was performed using a linear combination model. We detected 16 metabolites in the right and left hippocampi. Principal component analysis revealed that the absolute concentrations of the 16 detected metabolites could differentiate between Ts65Dn and euploid hippocampi. Although measurements in the left and right hippocampi were highly correlated, the concentration of individual metabolites was sometimes significantly different in the left and right structures. Thus, bilateral values from Ts65Dn and euploid mice were further compared with Hotelling's test. The level of glutamine was found to be significantly lower, whereas myo-inositol was significantly higher, in the hippocampi of Ts65Dn relative to euploid mice. However, γ-aminobutyric acid (GABA) and glutamate levels remained similar between the groups. Thus, the excitation-inhibition imbalance described in DS does not appear to be related to a radical change in the levels of either GABA or glutamate in the hippocampus. In conclusion, microliter MRS appears to be a valuable tool to detect changes associated with DS, which may be useful in investigating whether differences can be rescued after pharmacological treatments or supplementation with glutamine.

Impact of modified radical mastectomy on health-related quality of life in women with early stage breast cancer.

Systematic reviews favor a better body image and sexual activity in patients who have undergone conservative breast surgery (BCS) compared to modified radical mastectomy (MRM). In those patients with the same survival, MRM remains the surgical choice among both surgeons and patients in Iran as well as in many other countries. This cross-sectional study focuses on health-related quality of life in early stage breast cancer patients following BCS and MRM. From all post-op patients who referred to the Motahari Clinic, Shiraz, Iran, we used a convenient sampling method to select 160 MRM patients and 127 who underwent BCS. Translated copies of the EORTC QLQ-C30 (version 3) and the EORTC QLQ-BR23 questionnaires, in addition to a third questionnaire which was customized and prepared for this study, were completed by the patients under our supervision The two groups were compared by a multivariate method (Hotelling's trace test) after controlling for variables with unequal values such as disease stage, hormonal and radiotherapy treatments, and patients' role in the choice of surgery. We noted a significant difference (P < 0.001) attributed to a significantly better BI in the BCS group (average: 78.49 ± 23.14) compared to the MRM group (average: 60.71 ± 23.14). We concluded that in terms of body image, BCS has a better impact on health-related quality of life.

P02-78 - The impact of escitalopram on sleep problems of depressive patients in real-life clinical practice in greece

IntroductionThere is a bidirectional relationship between depression and insomnia, the latter being both a risk factor for the development of depression and a consequence of depression itself. Since depressive patients with residual symptoms of insomnia are at higher risk for disease recurrence, dealing successfully with sleep disorders during antidepressive treatment is of great importance.ObjectivesThe aim of the current study was to evaluate the effectiveness and tolerability of escitalopram on both depressive symptoms and sleep problems of depressive patients.MethodsAn observational, open-label, 3-month study was conducted in Greece.Effectiveness was assessed using the CGI-S and AIS (Athens Insomnia Scale) scales. Tolerability was evaluated by spontaneously reported adverse events and treatment discontinuation rates.ResultsThe study included 2,103 patients (mean age 51 ± 15 years, 64.0% women).Patients showed significant improvement during the treatment period for both depressive symptoms and sleep problems. Mean CGI-S scores decreased from 4.2 ± 0.8 to 2.2 ± 1.0 and total AIS score decreased from 13.6 ± 4.9 to 3.5 ± 3.8 (repeated measures analysis of variance Hotelling's test, p &lt; 0.001). The positive effect of escitalopram treatment was significant both on “night sleep” and “behaviour on the following days”. Moreover, the percentage of patients suffering from insomnia (AIS score &gt;=6) decreased from 89.1% to 22.1% (Cochran's Q test p &lt; 0.001). Escitalopram was also well tolerated, as 1909 (90.8%) patients successfully completed the study and 39 patients (1.85%) discontinued due to adverse events.ConclusionsEscitalopram combines significant effectiveness on both depressive symptoms and sleep problems with good tolerability.

The Role of the Magnetite-Based Receptors in the Beak in Pigeon Homing

Magnetite-containing structures in the upper beak of birds have been described as putative magnetoreceptors [1-4], but so far, all positive evidence indicating their influence on behavior has come from laboratory studies using rather unnatural stimuli (e.g., [5-7]). Here, we demonstrate these receptors' possible role in a natural situation: we released pigeons with these receptors deactivated by a local anesthetic within and outside a magnetic anomaly, together with untreated control birds. Within the anomaly, the untreated birds showed unusually long vanishing intervals and scattered bearings, indicating confusion by the anomalous magnetic conditions. Anesthesia of the beak suppressed this adverse effect. Outside the anomaly, in contrast, the treatment had little effect. These findings indicate that the receptors in the beak mediate magnetic "map" information and that this information is normally included in the navigational process yet can be replaced by nonmagnetic factors at most sites.

PW01-79 - Effect of memantine treatment in cognitive and behavioral symptoms of Alzheimer disease patients

PurposeThis study investigated the efficacy of memantine alone or in combination for the treatment of patients with Alzheimer's disease (AD) in a naturalistic setting, specifically for the cognitive and behavioural symptom domains.MethodsOpen-label, 6-month observational study, conducted at 110 sites in Greece. Efficacy was based on the MMSE and NPI scales at baseline, 3 months, and 6 months. Statistical analysis was made on a modified intent-to-treat dataset (ITT: at least one valid post-baseline measurement) using last observation carried forward (LOCF), and observed cases (OC, defined as patients assessed at all 3 visits).Results1,469 patients were enrolled. Their mean age was 75.7±6.5 years and the majority were women (52.7%). At baseline the average scores were 17.6 (±5.3) for the MMSE and 30.6 (±25.9) for the NPI. 285 patients (19.4%), received combination treatment (a second AD medication) during the observation period.Both cognitive and behavioral symptoms were improved at the end of the study, as measured by the MMSE and NPI scales (repeated measures analysis of variance Hotelling's test, p-value&lt; 0.001, both ITT, LOCF and OC analyses). After 3 and 6 months, cognitive function improved for 50.3% and 55.8% of the patients (ITT, LOCF), while behavioral symptoms improved for 56.8% and 62%, respectively.Memantine was well tolerated, with 3.5% (52) of patients withdrawing from the study for any reason and 7.6% reporting adverse events.ConclusionMemantine treatment resulted in significant improvement of cognitive and behavioral symptoms in patients with AD and was well tolerated based on patient withdrawals.

다변량 자료에서 위치모수에 대한 로버스트 검정

This work propose a robust test for location parameters in multivariate data based on MVE and MCD with the affine equivariance and the high-breakdown properties. We consider the hypothesis testing satisfying high efficiency and high test power simultaneously to bring in the one-step reweighting procedure upon high-breakdown estimators, which generally suffer from the low efficiency and, as a result, usually used only in the exploratory analysis. Monte Carlo study shows that the suggested method retains nominal significance levels and higher testing power without regard to various population distributions than a Hotelling's test. In an example, a data set containing known outliers does not make an influence toward our proposal, while it renders a Hotelling's useless.

Spatial vision in the purple sea urchinStrongylocentrotus purpuratus(Echinoidea)

Recent evidence that echinoids of the genus Echinometra have moderate visual acuity that appears to be mediated by their spines screening off-axis light suggests that the urchin Strongylocentrotus purpuratus, with its higher spine density, may have even more acute spatial vision. We analyzed the movements of 39 specimens of S. purpuratus after they were placed in the center of a featureless tank containing a round, black target that had an angular diameter of 6.5 deg. or 10 deg. (solid angles of 0.01 sr and 0.024 sr, respectively). An average orientation vector for each urchin was determined by testing the animal four times, with the target placed successively at bearings of 0 deg., 90 deg., 180 deg. and 270 deg. (relative to magnetic east). The urchins showed no significant unimodal or axial orientation relative to any non-target feature of the environment or relative to the changing position of the 6.5 deg. target. However, the urchins were strongly axially oriented relative to the changing position of the 10 deg. target (mean axis from -1 to 179 deg.; 95% confidence interval +/- 12 deg.; P<0.001, Moore's non-parametric Hotelling's test), with 10 of the 20 urchins tested against that target choosing an average bearing within 10 deg. of either the target center or its opposite direction (two would be expected by chance). In addition, the average length of the 20 target-normalized bearings for the 10 deg. target (each the vector sum of the bearings for the four trials) were far higher than would be expected by chance (P<10(-10); Monte Carlo simulation), showing that each urchin, whether it moved towards or away from the target, did so with high consistency. These results strongly suggest that S. purpuratus detected the 10 deg. target, responding either by approaching it or fleeing it. Given that the urchins did not appear to respond to the 6.5 deg. target, it is likely that the 10 deg. target was close to the minimum detectable size for this species. Interestingly, measurements of the spine density of the regions of the test that faced horizontally predicted a similar visual resolution (8.3+/-0.5 deg. for the interambulacrum and 11+/-0.54 deg. for the ambulacrum). The function of this relatively low, but functional, acuity - on par with that of the chambered Nautilus and the horseshoe crab - is unclear but, given the bimodal response, is likely to be related to both shelter seeking and predator avoidance.

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