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Methods for the presentation and display of multivariate data are discussed with emphasis placed on the multivariate analysis of variance problems and the Hotelling T(2) solution in the two-sample case. The methods utilize the concepts of stepwise discrimination analysis and the computation of partial correlation coefficients.
Observations of large amplitude MHD waves upstream of Jupiter's bow shock are analyzed. The waves are found to be right circularly polarized in the solar wind frame, which suggests that they are propagating in the fast magnetosonic mode. A complete spectral and minimum variance eigenvalue analysis of the data was performed. The power spectrum of the magnetic fluctuations contains several peaks. The fluctuations at 2.3 MHz have a direction of minimum variance anti-parallel to the direction of the average magnetic field. Several harmonics at 6, 9, and 12 MHz are also present. The direction of minimum variance of these fluctuations lies at approximately 40 deg to the magnetic field. It is argued that these fluctuations are waves excited by protons reflected off the Jovian bow shock. The inferred speed of the reflected protons is about two times the solar wind speed in the solar wind frame. A linear instability analysis is presented that suggests an explanation for many of the observed features of the observations. The fluctuations apparently contain a significant fraction of magnetic energy that is linearly polarized and in the Alfven mode.
Observations of large amplitude magnetohydrodynamics (MHD) waves upstream of Jupiter's bow shock are analyzed. The waves are found to be right circularly polarized in the solar wind frame which suggests that they are propagating in the fast magnetosonic mode. A complete spectral and minimum variance eigenvalue analysis of the data was performed. The power spectrum of the magnetic fluctuations contains several peaks. The fluctuations at 2.3 mHz have a direction of minimum variance along the direction of the average magnetic field. The direction of minimum variance of these fluctuations lies at approximately 40 deg. to the magnetic field and is parallel to the radial direction. We argue that these fluctuations are waves excited by protons reflected off the Jovian bow shock. The inferred speed of the reflected protons is about two times the solar wind speed in the plasma rest frame. A linear instability analysis is presented which suggests an explanation for many of the observed features of the observations.
Microvariability consists of small timescale variations of low amplitude in the photometric light curves of quasars and represents an important tool to investigate their inner core. Detection of quasar microvariations is challenging because of their non-periodicity, as well as the need for high monitoring frequency and a high signal-to-noise ratio. Statistical tests developed for the analysis of quasar differential light curves usually show either low power or low reliability, or both. In this paper we compare two statistical procedures to perform tests on several stars with enhanced power and high reliability. We perform light curve simulations of variable quasars and non-variable stars and analyze them with statistical procedures developed from the F-test and the analysis of variance. The results show a large improvement in the power of both statistical probes and a larger reliability when several stars are included in the analysis. The results from the simulations agree with those obtained from observations of real quasars. The high power and high reliability of the tests discussed in this paper improve the results that can be obtained from short and long timescale variability studies. These techniques are not limited to quasar variability; on the contrary, they can be easily implemented for other sources, such as variable stars. Their applications to future research and to the analysis of large-field photometric monitoring archives could reveal new variable sources.
By conservation of mass, the mass of wildland fuel that is pyrolyzed and combusted must equal the mass of smoke emissions, residual char and ash. For a given set of conditions, these amounts are fixed. This places a constraint on smoke emissions data which violates statistical assumptions for many of the methods currently used to analyze these data such as linear regression, analysis of variance, and t-tests. These data are inherently multivariate and non-negative parts of a whole. This paper introduces the field of compositional data analysis to the emissions community and provides examples of appropriate statistical treatment of emissions data. It is shown that modified combustion efficiency should not be used as a predictor variable for other smoke emissions because it is not an independent variable. An alternative method based on compositional linear trends to estimate trace gas composition using CO and CO2 is presented. The data used in this paper resulted from projects the DOD/DOE/EPA Strategic 586 Environmental Research and Development Program projects RC-1648 and 1649. The senior 587 author appreciates the guidance and R scripts provided by Prof. Girty at San Diego State 588 University to estimate linear trends by perturbation. J. P.-A. was supported by the Spanish 589 Ministry of Science, Innovation and Universities under the project CODAMET (RTI2018-590 095518-B-C21, 2019-2021). The data used in this study have been previously published and are 591 available in the original publications. DRW conceived the initial manuscript (70 percent) and 592 performed the bulk of the data analysis. JPA provided statistical guidance and compositional data 593 expertise and contributed 20 percent of the manuscript. TJJ and HJ were extensively involved in 594 the study that provided the data. TJJ provide smoke emissions expertise and HJ provided 595 combustion expertise. The authors declare that they have no conflict of interest. The use of trade 596 or firm names in this publication is for reader information and does not imply endorsement by 597 the U.S. Department of Agriculture of any product or service.
The task involved the control of two simulated aircraft targets per trial, in a 37.0 -km radius terminal area, by means of conventional radar vectoring and/or speed control. The goal was to insure that the two targets crossed the Missed Approach Point (MAP) at the runway threshold exactly 60 sec apart. The effects on controller performance of the MLS configuration under wind and no-wind conditions were examined. The data for mean separation time between targets at the MAP and the range about that mean were analyzed by appropriate analyses of variance. Significant effects were found for mean separation times as a result of the configuration of the MLS and for interaction between the configuration and wind conditions. The analysis of variance for range indicated significantly poorer performance under the wind condition. These findings are believed to be a result of certain perceptual factors involved in radar air traffic control (ATC) using the MLS with separation of targets in time.
This paper analyzes operator's error rate from experiments, depending on the expertise and simulator complexity. This study uses the Rancor Microworld, a simplified simulator developed by INL, and the Compact Nuclear Simulator (CNS), a less simplified simulator developed by the Korea Atomic Energy Research Institute (KAERI). The error rates were measured from simulation data of a total of 72 participants, and the collected error rate data were analyzed using analysis of variance (ANOVA) test.
The precise measurements of the synchrophasor and frequency from phasor measurement units (PMUs) are widely used in power grid applications. With the improvement of the technique, applications always require stable dynamic performance and higher accuracy for the synchrophasor and frequency measurements, which is challenging for PMU development. To evaluate the contribution of PMU hardware to measurement accuracy, this paper proposes a general-purpose sampling model to analyze the measurement error. In the proposed sampling model, a strict mathematical derivation is derived, where its error is purely determined by the parameters of the PMU hardware. The sensitivity analysis is carried out by three methods, including mathematical analysis, computer simulation, and variance-based sensitivity analysis. Through the sensitivity analysis, this paper establishes the systematic formulation and the inclusion of synchrophasor, frequency, and ROCOF. Experimental results based on the real-world testbench involving distribution-level PMUs match the mathematical analysis conclusion, which verifies the correctness of the general-purpose sampling model. Furthermore, a strategy for the optimal PMU design is proposed, which could guide PMU design in the future.
The metrological performance of a virtual flowmeter-based transducer for monitoring helium under cryogenic conditions is assessed. At this aim, an uncertainty model of the transducer, mainly based on a valve model, exploiting finite-element approach, and a virtual flowmeter model, based on the Sereg-Schlumberger method, are presented. The models are validated experimentally on a case study for helium monitoring in cryogenic systems at the European Organization for Nuclear Research (CERN). The impact of uncertainty sources on the transducer metrological performance is assessed by a sensitivity analysis, based on statistical experiment design and analysis of variance. In this way, the uncertainty sources most influencing metrological performance of the transducer are singled out over the input range as a whole, at varying operating and setting conditions. This analysis turns out to be important for CERN cryogenics operation because the metrological design of the transducer is validated, and its components and working conditions with critical specifications for future improvements are identified.
The CoRoT field LRa02 has been observed with the Berlin Exoplanet Search Telescope II (BEST II) during the southern summer 2007/2008. A first analysis of stellar variability led to the publication of 345 newly discovered variable stars. Now, a deeper analysis of this data set was used to optimize the variability search procedure. Several methods and parameters have been tested in order to improve the selection process compared to the widely used J index for variability ranking. This paper describes an empirical approach to treat systematic trends in photometric data based upon the analysis of variance statistics that can significantly decrease the rate of false detections. Finally, the process of reanalysis and method improvement has virtually doubled the number of variable stars compared to the first analysis by Kabath et al. A supplementary catalog of 272 previously unknown periodic variables plus 52 stars with suspected variability is presented. Improved ephemerides are given for 19 known variables in the field. In addition, the BEST II results are compared with CoRoT data and its automatic variability classification.
High altitude alpine meadows are experiencing considerably greater than average increases in soil surface temperature, potentially as a result of ongoing climate change. The effects of warming on plant productivity and soil edaphic variables have been established previously, but the influence of warming on soil microbial community structure has not been well characterized. Here, the impact of 15 months of soil warming (both + 1 and + 2 degrees C) on bacterial community structure was examined in a field experiment on a Tibetan plateau alpine meadow using bar-coded pyrosequencing. Warming significantly changed (P < 0.05) the structure of the soil bacterial community, but the alpha diversity was not dramatically affected. Changes in the abundance of the Actinobacteria and Alphaproteobacteria were found to contribute the most to differences between ambient (AT) and artificially warmed conditions. A variance partitioning analysis (VPA) showed that warming directly explained 7.15% variation in bacterial community structure, while warming-induced changes in soil edaphic and plant phenotypic properties indirectly accounted for 28.3% and 20.6% of the community variance, respectively. Interestingly, certain taxa showed an inconsistent response to the two warming treatments, for example Deltaproteobacteria showed a decreased relative abundance at + 1 degrees C, but a return to AT control relative abundance at + 2 degrees C. This suggests complex microbial dynamics that could result from conditional dependencies between bacterial taxa.
Human Factors Engineering (HFE) is a discipline whose goal is to engineer a safer, more efficient interface between humans and machines. HFE makes use of a wide range of tools and techniques to fulfill this goal. One of these tools is known as motion and time study, a technique used to develop time standards for given tasks. During the summer of 1995, a human factors motion and time study was initiated with the goals of developing a database of EVA task times and developing a method of utilizing the database to predict how long an EVA should take. Initial development relied on the EVA activities performed during the STS-61 (Hubble) mission. The first step of the study was to become familiar with EVA's, the previous task-time studies, and documents produced on EVA's. After reviewing these documents, an initial set of task primitives and task-time modifiers was developed. Data was collected from videotaped footage of two entire STS-61 EVA missions and portions of several others, each with two EVA astronauts. Feedback from the analysis of the data was used to further refine the primitives and modifiers used. The project was continued during the summer of 1996, during which data on human errors was also collected and analyzed. Additional data from the STS-71 mission was also collected. Analysis of variance techniques for categorical data was used to determine which factors may affect the primitive times and how much of an effect they have. Probability distributions for the various task were also generated. Further analysis of the modifiers and interactions is planned.
Purpose: To investigate the significance of using pinpoint ionization chambers (IC) and RadCalc (RC) in determining the quality of lung SBRT VMAT plans with low dose deviation pass percentage (DDPP) as reported by ScandiDos Delta4 (D4). To quantify the relationship between DDPP and point dose deviations determined by IC (ICDD), RadCalc (RCDD), and median dose deviation reported by D4 (D4DD). Methods: Point dose deviations and D4 DDPP were compiled for 45 SBRT VMAT plans. Eighteen patients were treated on Varian Truebeam linear accelerators (linacs); the remaining 27 were treated on Elekta Synergy linacs with Agility collimators. A one-way analysis of variance (ANOVA) was performed to determine if there were any statistically significant differences between D4DD, ICDD, and RCDD. Tukey’s test was used to determine which pair of means was statistically different from each other. Multiple regression analysis was performed to determine if D4DD, ICDD, or RCDD are statistically significant predictors of DDPP. Results: Median DDPP, D4DD, ICDD, and RCDD were 80.5% (47.6%–99.2%), −0.3% (−2.0%–1.6%), 0.2% (−7.5%–6.3%), and 2.9% (−4.0%–19.7%), respectively. The ANOVA showed a statistically significant difference between D4DD, ICDD, and RCDD for a 95% confidence interval (p < 0.001). Tukey’s test revealed a statistically significant difference between two pairs of groups, RCDD-D4DD and RCDD-ICDD (p < 0.001), but no difference between ICDD-D4DD (p = 0.485). Multiple regression analysis revealed that ICDD (p = 0.04) and D4DD (p = 0.03) are statistically significant predictors of DDPP with an adjusted r{sup 2} of 0.115. Conclusion: This study shows ICDD predicts trends in D4 DDPP; however this trend is highly variable as shown by our low r{sup 2}. This work suggests that ICDD can be used as a method to verify DDPP in delivery of lung SBRT VMAT plans. RCDD may not validate low DDPP discovered in D4 QA for small field SBRT treatments.
Purpose: To determine causal factors related to high frame definition error when treating GK patients using a pre-planning workflow. Methods: 160 cases were retrospectively reviewed. All patients received treatment using a pre-planning workflow whereby stereotactic coordinates are determined from a CT scan acquired after framing using a fiducial box. The planning software automatically detects the fiducials and compares their location to expected values based on the rigid design of the fiducial system. Any difference is reported as mean and maximum frame definition error. The manufacturer recommends these values be less than 1.0 mm and 1.5 mm. In this study, frame definition error was analyzed in comparison with a variety of factors including which neurosurgeon/oncologist/physicist was involved with the procedure, number of post used during framing (3 or 4), type of lesion, and which CT scanner was utilized for acquisition. An analysis of variance (ANOVA) approach was used to statistically evaluate the data and determine causal factors related to instances of high frame definition error. Results: Two factors were identified as significant: number of post (p=0.0003) and CT scanner (p=0.0001). Further analysis showed that one of the four scanners was significantly different than the others. This diagnostic scanner was identified as an older model with localization lasers not tightly calibrated. The average value for maximum frame definition error using this scanner was 1.48 mm (4 posts) and 1.75 mm (3 posts). For the other scanners this value was 1.13 mm (4 posts) and 1.40 mm (3 posts). Conclusion: In utilizing a pre-planning workflow the choice of CT scanner matters. Any scanner utilized for GK should undergo routine QA at a level appropriate for radiation oncology. In terms of 3 vs 4 post, it is hypothesized that three posts provide less stability during CT acquisition. This will be tested in future work.
It is important to accurately evaluate depletion uncertainties that exist due to the limitations of a computer code on accuracy in a nuclear depletion calculation for criticality safety analysis. In this work, the bias and bias uncertainty in the effective neutron multiplication factor (k{sub eff}) for the generic 32 PWR-assembly burnup credit (GBC-32) cask system were assessed using the Monte Carlo uncertainty sampling method for three different burnups and the isotopic biases and uncertainties obtained with the calculated and measured isotopic concentrations. The PLUS7 used nuclear fuel assemblies discharged from the Hanbit Nuclear Power Plant Unit 3 were assumed to be loaded into the GBC-32 cask. In addition, the statistical F-test in the two-way analysis of variance (ANOVA) was suggested to efficiently estimate the statistically converged total depletion uncertainty in k{sub eff}, with a significant reduction of computing efforts in the Monte Carlo criticality calculations, and it was applied to the GBC-32 cask system after a sensitivity analysis was performed to select the important nuclides having significant contributions to the total depletion uncertainty. With the statistical F-tests in the two-way ANOVA, 100 criticality calculations were needed to get a statistically converged total depletion uncertainty for 10 and 30 GWD/MTU, while 120 criticality calculations were needed for 50 GWD/MTU. (authors)
Losses of photoreceptor cells (rods) from the retinas of New Zealand white (NZW) rabbits were detectable within 2 years after localized acute irradiation of optic and proximal tissues with greater than or equal to 7 Gy of 530 MeV u(exp -1) Ar-40 ions or greater than or equal to 2 Gy of 465 MeV u(exp -1) Fe-56 ions in the Bragg plateau region of energy deposition. Those limits were determined only from an analysis of variance of dose groups because the shapes of the dose response curves at early post-irradiation times are not known, a concern being addressed by experiments in progress. Losses of photoreceptor cells for the period 0.5-2.5 years post-irradiation, determined by provisional linear regression analysis, were approxiamtely 1.7% Gy(exp -1) and 2.5% Gy(exp.-1) for Ar-40 and Fe-56 ions, respectively.
The present analysis uses the Monte Carlo method to solve the problem of rarefied diffusion between parallel walls. The diffusing molecules are evaporated or emitted from one of two parallel walls and diffused through another molecular species. The analysis treats the diffusing molecule as undergoing a Markov random walk and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs the expected Markov walk payoff is retained but its variance is reduced so that the M. C. result has a much smaller error.
The problem of rarefied diffusion between parallel walls is solved using the Monte Carlo method. The diffusing molecules are evaporated or emitted from one of the two parallel walls and diffuse through another molecular species. The Monte Carlo analysis treats the diffusing molecule as undergoing a Markov random walk, and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs, the expected Markov walk payoff is retained but its variance is reduced so that the Monte Carlo result has a much smaller error.