A Permutation Test for Multivariate Matched-Pair Analyses: Comparisons with Hotelling's Multivariate Matched-Pair T2 Test

Mathematics is often considered a difficult and boring subject. However, with the right approach, mathematics can foster logical dan systematic thinking in problem-solving. This study aims to investigate: 1) the effect of RME approach on mathematical procedural fluency and student learning motivation, 2) the effect of RME approach on mathematical procedural fluency, 3) the effect of RME approach on student learning motivation. The method used was quasi-experiment with post-test only control group design. Research instruments included a written a test to measure procedural fluency, and a questionnaire to assess learning motivation. Data analysis techniques in this study used multivariate and univariate analysis with R software. The results showed that: 1) there is a significant difference simultaneously with Hotelling's T² test with p-value 0.02256 < 0.05, 2) there is a significant difference in procedural fluency with t-Independent test shows p-value 0.01019 < 0.05, 3) there is a significant difference in procedural fluency with Mann-Whitney test shows p-value 0.1249 > 0.05. These findings indicate that cognitive aspects and affective aspects have an attachment in achieving effective learning. Therefore, the RME approach can be considered an alternative learning strategy that teachers can use to develop residual mathematical abilities more optimally.

This paper describes the procedures that may be used to compute Hotelling's T2 for matched group designs using the RELIABILITY routine of SPSS. Modifications of a normal SPSS job necessary for the test are described. An example data set is used to illustrate the procedure.

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

SUMMARY It is often necessary to determine if, and to what extent, an incident A is related to a set of environmental random variables X = (Xl, ..., Xk)'. In this paper we assume that in the general population, X is normally distributed with mean ,u and covariance matrix E. A sample of X will be taken from the incident and nonincident groups, and, assuming that the incident rate p is approximately a linear function of X1, ..., Xk, we can determine the sample sizes for detecting the dependence between A and X without any prior knowledge of the unknowns , and E. Let Pi be the average incident rate in the population and 0 and po be two given numbers with po <Pl. The sample size is then determined so that the dependence relation between A and X will be detected with small error if a fraction 0 or more of the population live in an environment which has incident rate no greater than po. Some key worde: Correlation analysis; Hotelling's T2 test; Selection of sample size.

Mono-frequency (50 kHz) whole-body and segmental bioimpedance is measured before sport training in 14 high performance athletes. The athletes are classified in two groups according to the team sport: football and basketball. Bioelectrical impedance vector analysis (BIVA) method is used to obtain the individual whole-body impedance and 6 segmental impedance vectors in the main muscular groups in the lower-limbs. The whole-body vector is analyzed in the tolerance ellipses of the reference population. Individual impedance vector components are standardized by the height H of the subject, (R/H and Xc/H) to obtain the impedance vector (Z/H) of each segment. The hypotheses of the study are: 1) Not all the sports have the same pattern of bioimpedance vector by muscle group. 2) In elite well trained athletes their muscle groups are symmetrical (right and left sides), thus each athlete is its own reference for future comparisons. 3) We expect a change in the two components of bioimpedance vector (R/H and Xc/H) in front of a muscle injury. In order to compare the differences between the complex Z/H vector (R/H, Xc/H) we use Hotelling's T2 test. Preliminary results show a significant difference (P < 0.05) in bioimpedance vectors between groups according to the team sport, and also between normal muscle condition and after muscle injury producing hyper-hydration.

Background/Objectives: Energy availability (EA) is associated with Relative Energy Deficiency in Sport syndrome. This study assessed the EA, body composition, and phase angle (φ) of adolescent artistic gymnasts during a competitive season. Methods: Thirty non-elite artistic gymnasts aged 11-14 years participated in this cross-sectional study. Anthropometric data were collected and body mass index (BMI) was assessed using the World Health Organization growth charts. Bioelectrical impedance analysis was performed and diet and physical activity were recorded for three days. Dietary and physical activity records were analyzed to estimate energy intake, total energy expenditure (TEE), and exercise energy expenditure, from which energy balance (EB) and EA were calculated. The 95% confidence ellipses of the impedance (Z) vectors were compared with a reference population using the two-sample Hotelling's T2 test. Correlations between variables were examined by Pearson's or Spearman's correlation analysis. Statistical significance was set at α = 0.05. Results: All participants were classified within the normal BMI category, except for one who was classified as being overweight. Mean (± SD) fat mass, fat-free mass (FFM), and φ were 16.1 ± 3.4%, 83.9 ± 3.4%, and 6.0 ± 0.6°, respectively. The 95% confidence ellipses of Z vectors differed significantly from the reference population. Energy balance was 32 ± 223 kcal/day and EA was 49.2 ± 11.4 kcal/kg FFM/day. Energy availability was significantly correlated with EB, TEE, and body composition variables. Conclusions: Adolescent non-elite artistic gymnasts showed no clear indications of LEA and exhibited a normal body composition and φ during the competitive season, consistent with their EA.

Center of pressure (COP) trajectories summarize the complex mechanical interaction between the foot and a contacted surface. Each trajectory itself is also complex, comprising hundreds of instantaneous vectors over the duration of stance phase. To simplify statistical analysis often a small number of scalars are extracted from each COP trajectory. The purpose of this paper was to demonstrate how a more objective approach to COP analysis can avoid particular sensitivities of scalar extraction analysis. A previously published dataset describing the effects of walking speed on plantar pressure (PP) distributions was re-analyzed. After spatially and temporally normalizing the data, speed effects were assessed using a vector-field paired Hotelling's T2 test. Results showed that, as walking speed increased, the COP moved increasingly posterior at heel contact, and increasingly laterally and anteriorly between ∼60 and 85% stance, in agreement with previous independent studies. Nevertheless, two extracted scalars disagreed with these results. Furthermore, sensitivity analysis found that a relatively small coordinate system rotation of 5.5° reversed the mediolateral null hypothesis rejection decision. Considering that the foot may adopt arbitrary postures in the horizontal plane, these sensitivity results suggest that non-negligible uncertainty may exist in mediolateral COP effects. As compared with COP scalar extraction, two key advantages of the vector-field approach are: (i) coordinate system independence, (ii) continuous statistical data reflecting the temporal extents of COP trajectory changes.

Efficacy of specific bioelectrical impedance vector analysis (BIVA) for assessing body composition in the elderly.

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.

The aim was to study short and medium-term effects of a structured achievement motivation course on the achievement motivation of adolescent women. Hypotheses were that (a) achievement motivation could be experimentally aroused by means of the course and, (b) experimentally aroused achievement motivation would persist over the medium term, i.e., for six months following the course. The research group consisted of 121 adolescent women students at a military training unit. Subjects were divided into an experimental group ( n = 58) and a control group ( n = 63). Both groups participated in four testing sessions which were scheduled for January, before and after the experimental intervention in June, and December. The experimental intervention was an adaptation of McClelland's original achievement motivation course. Questionnaires constructed to assess cognitive conscious dimensions of achievement motivation were used as dependent variable measures. Dimensions assessed were autonomous and social achievement values, hope of success and fear of failure, internal and external locus of control, sensitivity to rejection, and affiliation tendency, as well as dogmatism, level of autonomy, and values. Data were analysed by means of Hotelling's T2 test. No significant differences existed between levels of achievement motivation for the experimental and control groups in January or before the intervention in June. The hypothesis that the course would cause a significant increase in the level of achievement motivation of the experimental group was not supported. The results suggested that situational factors and personal characteristics of the experimental group contributed to the failure of the experimental intervention.

Background and Purpose: This study was conducted to adapt the Medication Information Literacy Scale for Pregnant Women into Turkish. Methods: This study was designed as a methodological study, and the sample consisted of 279 pregnant women. Results: Confirmatory factor analysis revealed that the fit indices were within acceptable ranges. For reliability evaluation, the internal consistency coefficient (Cronbach's alpha = .872), intraclass correlation coefficient (.872), Hotelling's T2 test (F = 21.252, p = .000), standard error of measurement (5.11 ≤ 7.9), and floor-ceiling effect analysis (min. frequency = 0.4%, max. frequency = 0.4%) were assessed. Conclusion: The Medication Information Literacy Scale for Pregnant Women, consisting of 5 subdimensions and 20 items, was found to be a valid and reliable measurement tool.

The chemical bonding material is a concept that requires visualization. For students to comprehend chemical bonding concepts better, molecular forms must be depicted in the materials. Consequently, a learning module that can show 3D things made from molecular structures is necessary. This study aims to create and evaluate an augmented reality-based learning module on chemical bonds while examining the similarities and differences between students' interests and learning motivation before and after utilizing the augmented reality-based learning modules. The product is designed utilizing a 4-D model, and this study uses a research and development model. A quasi-experimental method and one group pretest and posttest design were used to evaluate the module involving 53 students chosen randomly. A sample of Hotelling's T2 test was used to analyze the student responses to the questionnaire about interest and motivation for learning. Descriptive quantitative analysis was used to analyze the data from the product quality assessment. The results showed that the developed augmented reality-supported chemical bonding learning module was very suited for chemistry learning and that there were variations between pre- and post-usage in student interest and motivation to study simultaneously or separately

This chapter introduces permutation methods for matched-pairs tests. Included in this chapter are six example analyses illustrating computation of exact permutation probability values for matched-pairs tests, calculation of measures of effect size for matched-pairs tests, the effect of extreme values on conventional and permutation matched-pairs tests, exact and Monte Carlo permutation procedures for matched-pairs tests, application of permutation methods to matched-pairs rank-score data, and analysis of matched-pairs multivariate data. Included in this chapter are permutation versions of Student’s matched-pairs t test, Wilcoxon’s signed-ranks test, the sign test, Hotelling’s multivariate T2 test for two matched samples, and a permutation-based alternative for the two conventional measures of effect size for matched pairs: Cohen’s \(\hat {d}\) and Pearson’s r2.

Powder blending was monitored on-line by taking near-infrared measurements at regular time intervals during the mixing process. The average standard deviation between the measurements taken at each time and the dissimilarity between each mixture spectrum and the ideal mixture spectrum were used to monitor the changes in the powder blend over time. The distribution of the pure compounds in the blend can be investigated by looking at the score plot for the first two principal components (PCs), the contribution of each variable to the dissimilarity and, in particular, the contrasts between two characteristic wavelengths for each compound. Statistical process monitoring charts were used to determine the blending time at which the mixture was within (spectroscopic) specifications. Shewhart charts monitor the blend at characteristic wavelengths for each substance separately. The Hotelling's T 2 test defines a multivariate confidence interval. For spectral data, feature reduction is needed. This procedure is accomplished by using characteristic wavelengths for the pure compounds or the significant PCs after performing principal components analysis (PCA).

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.