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NASA NTRS1985

The system of EAS time analysis

The extensive air showers' (EAS) front shape, angle of incidence, disk thickness, particle distribution along the shower, on the delayed and EAS front advancing particles were determined. The suggested system of the EAS time analysis allows determination of the whole EAS longitudinal structure at the observation points. The information from the detectors is continuously recorded in the memory with the memory cell switching in 5 ns, this enables fixation of the moment of pulse input from the detector with an accuracy to + or - 2.5 ns. Along with the fast memory, a slow memory with the cell switching in 1 micron s is introduced in the system, this permits observation of relatively large time intervals with respect to the trigger pulse with an appropriately lower accuracy.

Khalafyan, A. Z.↗

NASA NTRS1986

The fossil record of evolution: Data on diversification and extinction

Synoptic studies of the fossil record of complex life on Earth indicate increasingly that extinction, and especially mass extinction, were extremely important driving forces in the history of life. Analysis of a new compilation of geologic ranges for 25,000 genera of marine animals suggests that extinction events were much more frequent in occurrence and variable in magnitude than previously suspected. At least 30 well documented and potential mass extinctions were identified in the dataset. The most recent event, distributed over 260 to 0 ma. exhibit a stationary periodicity of 26.1 + or - 1 ma, implicating a cosmological forcing mechanism. Earlier events, especially in the 575 to 450 ma interval, are more frequent, possibly indicating either a breakdown of periodicity in the more distant past; and as yet undemonstrated diminution of the period length; or frequent aperiodic terrestrial perturbations of a less stable biota superimposed upon the cosmological periodicity.

Sepkoski, J. J., Jr.↗

NASA NTRS1992

Min and max are the only continuous ampersand-, V-operations for finite logics

Experts usually express their degrees of belief in their statements by the words of a natural language (like 'maybe', 'perhaps', etc.). If an expert system contains the degrees of beliefs t(A) and t(B) that correspond to the statements A and B, and a user asks this expert system whether 'A&B' is true, then it is necessary to come up with a reasonable estimate for the degree of belief of A&B. The operation that processes t(A) and t(B) into such an estimate t(A&B) is called an &-operation. Many different &-operations have been proposed. Which of them to choose? This can be (in principle) done by interviewing experts and eliciting a &-operation from them, but such a process is very time-consuming and therefore, not always possible. So, usually, to choose a &-operation, the finite set of actually possible degrees of belief is extended to an infinite set (e.g., to an interval (0,1)), define an operation there, and then restrict this operation to the finite set. Only this original finite set is considered. It is shown that a reasonable assumption that an &-operation is continuous (i.e., that gradual change in t(A) and t(B) must lead to a gradual change in t(A&B)), uniquely determines min as an &-operation. Likewise, max is the only continuous V-operation. These results are in good accordance with the experimental analysis of 'and' and 'or' in human beliefs.

Kreinovich, Vladik↗

NASA NTRS2000

On Utilization of NEXRAD Scan Strategy Information to Infer Discrepancies Associated With Radar and Rain Gauge Surface Volumetric Rainfall Accumulations

To evaluate the Tropical Rainfall Measuring Mission (TRMM) monthly Ground Validation (GV) rain map, 42 quality controlled tipping bucket rain gauge data (1 minute interpolated rain rates) were utilized. We have compared the gauge data to the surface volumetric rainfall accumulation of NEXRAD reflectivity field, (converting to rain rates using a 0.5 dB resolution smooth Z-R table). The comparison was carried out from data collected at Melbourne, Florida during the month of July 98. GV operational level 3 (L3 monthly) accumulation algorithm was used to obtain surface volumetric accumulations for the radar. The gauge records were accumulated using the 1 minute interpolated rain rates while the radar Volume Scan (VOS) intervals remain less than or equal to 75 minutes. The correlation coefficient for the radar and gauge totals for the monthly time-scale remain at 0.93, however, a large difference was noted between the gauge and radar derived rain accumulation when the radar data interval is either 9 minute, or 10 minute. This difference in radar and gauge accumulation is being explained in terms of the radar scan strategy information. The discrepancy in terms of the Volume Coverage Pattern (VCP) of the NEXRAD is being reported where VCP mode is ascertained using the radar tilt angle information. Hourly radar and gauge accumulations have been computed using the present operational L3 method supplemented with a threshold period of +/- 5 minutes (based on a sensitivity analysis). These radar and gauge accumulations are subsequently improved using a radar hourly scan weighting factor (taking ratio of the radar scan frequency within a time bin to the 7436 total radar scans for the month). This GV procedure is further being improved by introducing a spatial smoothing method to yield reasonable bulk radar to gauge ratio for the hourly and daily scales.

Roy, Biswadev↗

NASA NTRS2006

ALPS: The Age-Layered Population Structure for Reducing the Problem of Premature Convergence

To reduce the problem of premature convergence we define a new attribute of an individual, its age, and propose the Age-Layered Population Structure (ALPS), in which age is used to restrict competition and breeding between members of the population. ALPS differs from a typical EA by segregating individuals into different age-layers by their age - a measure of how long the genetic material has been in the population - and by regularly replacing all individuals in the bottom layer with randomly generated ones. The introduction of new, randomly generated individuals at regular intervals results in an EA that is never completely converged and is always looking at new parts of the fitness landscape. By using age to restrict competition and breeding search is able to develop promising young individuals without them being dominated by older ones. We demonstrate the effectiveness of the ALPS algorithm on an antenna design problem in which evolution with ALPS produces antennas more than twice as good as does evolution with two other types of EAs. Further analysis shows that the ALPS model does allow the offspring of newly generated individuals to move the population out of mediocre local-optima to better parts of the fitness landscape.

Hornby, Gregory S.↗

NASA NTRS2011

Nutrition Coupled with High-Load Traditional or Low-Load Blood Flow Restricted Exercise During Human Limb Suspension

High-load resistance exercise (HRE) and low-load blood flow restricted (BFR) exercise have demonstrated efficacy for attenuating unloading related muscle atrophy and dysfunction. In recreational exercisers, protein consumption immediately before and/or after exercise has been shown to increase the skeletal muscle anabolic response to resistance training. PURPOSE: To compare the skeletal muscle adaptations when chocolate milk intake was coupled with HRE or low-load BFR exercise [3 d/wk] during simulated lower limb weightlessness. METHODS: Eleven subjects were counterbalanced [based on age and gender] to HRE (31 +/- 14 yr, 170 +/- 13 cm, 71 +/- 18 kg, 2M/3W) or low-load BFR exercise (31 +/- 12 yr, 169 +/- 13 cm, 66 +/- 14 kg, 2M/4W) during 30 days of unilateral lower limb suspension (ULLS). Both HRE and BFR completed 3 sets of single leg press and calf raise exercise during ULLS. BFR exercise intensity was 20% of repetition maximum (1RM) with a cuff inflation pressure of 1.3 systolic blood pressure (143 4 mmHg). Cuff pressure was maintained during all 3 sets including rest intervals (90s). HRE intensity was 75% 1RM and was performed without cuff inflation. Immediately (<10 min) before and after exercise 8 fl oz of chocolate milk (150 kcal, 2.5g total fat, 22g total carbohydrate, 8g protein) was consumed to optimize acute exercise responses in favor of muscle anabolism. ULLS analog compliance was assessed from leg skin temperature recordings and plantar accelerometry. Muscle cross-sectional area (CSA) for knee extensor and plantar flexor muscle groups were determined from analysis of magnetic resonance images using ImageJ software. 1RM strength for leg press and calf raise was assessed on the Agaton exercise system. Muscular endurance during leg press and calf raise was evaluated from the maximal number of repetitions performed to volitional fatigue using 40% of pre-ULLS 1RM. RESULTS: Steps detected by plantar acceleometry declined by 98.9% during ULLS relative to an ambulatory control period. Average skin temperature of the unloaded calf declined from 27.4 C to 26.8 C (-2.1%), while there was a slight increase (+1.1%) in skin temperature in the loaded calf (27.6 C to 27.9 C). Collectively, these measures indicate strong subject compliance with the ULLS analog. Unloaded limb work performed during leg press (1514 +/- 334 vs. 576 +/- 103) and calf raise (2886 +/- 508 vs. 1233 +/- 153) exercises sessions was greater in HRE vs. BFR, respectively. Leg press training loads were 44 +/- 7 kg in HRE compared to 11 +/- 1 kg in BFR. Similarly, calf raise training loads were 81 +/- 11 kg in HRE and 16 +/- 1 kg in BFR. Pre to post-ULLS training adaptations in the unloaded leg are shown in the table. CONCLUSION: The preliminary results of this investigation suggest when HRE is optimized for muscle anabolism during unloading muscle size and strength are preserved (or enhanced) at the expense of muscle endurance. In contrast, when BFR exercise is optimized for muscle anabolism during unloading muscle endurance is preserved (or enhanced) at the expense of muscle size and strength

Hackney, K. J.↗

DOE OSTI2025

Design of a separate effects MiniFuel irradiation experiment investigating microstructure evolution in high burnup UO 2

The microstructural evolution of UO 2 fuel pellets during commercial operation in light water reactors (LWRs) is known to vary significantly across the pellet radius due to spatial variations in local temperature and burnup. The primary obstacle to extending LWR refueling cycles to 24-month intervals is the susceptibility of certain high burnup fuel microstructures to fuel fragmentation, relocation, and dispersal (FFRD) during a loss of coolant accident (LOCA). Although FFRD of the high burnup structure in the rim region of a pellet is well studied, the fine fragmentation that has been observed in a second region, near the midradius of the pellet (termed the “dark zone”) following mock LOCA testing of high burnup commercial fuel rods is less understood. This paper describes the design, analysis, and execution of a separate effects MiniFuel irradiation experiment that aims to identify the specific temperature and burnup regimes under which FFRD-susceptible dark zone microstructures form. The small disc specimens (3 mm diameter by ∼0.3 mm thick) enable more precise control of the relatively uniform temperature and burnup conditions. A total of 42 specimens were fabricated with typical LWR fuel densities (∼96%–98% of theoretical density) and grain sizes (∼12 μm) and are being irradiated over a range of temperatures (600°C–1000°C) and discharge burnups (50–72 MWd/kg-U) that bound the midradius region of high burnup LWR fuel. Fuel specimens with identical 235 U enrichments were inserted in two irradiation locations in the High Flux Isotope Reactor and are currently undergoing irradiation to further evaluate the impact of rate effects (fission rate, time at temperature) on the microstructural evolution. The fuel fabrication and the thermal and neutronic simulations used for designing the experiment are detailed in this paper. A secondary objective of the experiment is to observe fission gas release (FGR) under the various irradiation conditions, and this work provides first-order predictions of FGR from all fuel specimens. The insights gained from these experiments will inform future high burnup core designs that could minimize the formation of susceptible microstructures and ultimately enable 24-month refueling cycles while minimizing the fraction of the fuel susceptible to FFRD.

FFRD↗

DOE OSTI2023

Search for Higgs Boson Decay to a Charm Quark-Antiquark Pair in Proton-Proton Collisions at s = 13 TeV

A search for the standard model Higgs boson decaying to a charm quark-antiquark pair, $H → c\bar{c}$, produced in association with a leptonically decaying $V (W \text{or} Z)$ boson is presented. The search is performed with proton-proton collisions at $\sqrt{s}=13\,\text {TeV}$ collected by the CMS experiment, corresponding to an integrated luminosity of 138 fb -1 . Novel charm jet identification and analysis methods using machine learning techniques are employed. The analysis is validated by searching for $Z → c\bar{c}$ in $VZ$ events, leading to its first observation at a hadron collider with a significance of 5.7 standard deviations. The observed (expected) upper limit on $σ(VH)\mathscr{B}(H → c\bar{c}$) is 0.94 (0.50$^{+0.22}_{– 0.15}$)pb at 95% confidence level (C.L.), corresponding to 14 (7.6$^{+3.4}_{–2.3}$) times the standard model prediction. For the Higgs-charm Yukawa coupling modifier, $κ_c$, the observed (expected) 95% C.L. interval is 1.1 < |$κ_c$| < 5.5 (|$κ_c$| < 3.4), the most stringent constraint to date.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

SST-TG-P1F4R3200: Decaying Stably-Stratified Turbulence (SST), Initialized Using Taylor-Green Vortices (TG) at Prandtl Number Pr=1, Froude Number Fr=4, Reynolds Number Re=3200

This dataset comprises direct numerical simulations (DNS) of decaying stably-stratified turbulence influenced by a linear background density gradient, initialized using an array of Taylor-Green vortices, as described in [Riley & de Bruyn Kops (2003)](https://doi.org/10.1063/1.1578077). The initial Prandtl, Froude, and Reynolds numbers are (Pr, Fr, Re) = (1, 4, 3200). A total of 15,000 snapshots are recorded at uniform time intervals, each with a spatial resolution of 512x512x256 grid points. Four flow variables are associated with each snapshot: the three velocity components (u,v,w) and the perturbed density field (rho) away from the background gradient. All fields are stored in binary format (32-bit little-endian), each with a size of 255 MB, yielding a total dataset size of 15.3 TB. Further details are referenced in the attached README file, and a current list of publications and associated analysis tools are provided at https://stratified-turbulence.github.io/web/.

42 ENGINEERING↗

DOE OSTI2025

SST-TG-P50F4R3200: Decaying Stably-Stratified Turbulence (SST), Initialized Using Taylor-Green Vortices (TG) at Prandtl Number Pr=50, Froude Number Fr=4, Reynolds Number Re=3200

This dataset comprises direct numerical simulations (DNS) of decaying stably-stratified turbulence influenced by a linear background density gradient, initialized using an array of Taylor-Green vortices, extending the Pr=1 simulations performed in [Riley and de Bruyn Kops (2003)](https://doi.org/10.1063/1.1578077). The initial Prandtl, Froude, and Reynolds numbers are (Pr, Fr, Re) = (50, 4, 3200). A total of 1,680 snapshots are recorded at uniform time intervals, each with a spatial resolution of 3584x3584x1792 grid points. Four flow variables are associated with each snapshot: the three velocity components (u,v,w) and the perturbed density field (rho) away from the background gradient. All fields are stored in binary format (32-bit little-endian), each with a size of 85.8 GB, yielding a total dataset size of 577 TB. Further details are referenced in the attached README file, and a current list of publications and associated analysis tools are provided at https://stratified-turbulence.github.io/web/.

42 ENGINEERING↗

DOE OSTI2025

SST-TG-P7F4R3200: Decaying Stably-Stratified Turbulence (SST), Initialized Using Taylor-Green Vortices (TG) at Prandtl Number Pr=7, Froude Number Fr=4, Reynolds Number Re=3200

This dataset comprises direct numerical simulations (DNS) of decaying stably-stratified turbulence influenced by a linear background density gradient, initialized using an array of Taylor-Green vortices, extending the Pr=1 simulations performed in [Riley and de Bruyn Kops (2003)](https://doi.org/10.1063/1.1578077). The initial Prandtl, Froude, and Reynolds numbers are (Pr, Fr, Re) = (7, 4, 3200). A total of 15,250 snapshots are recorded at uniform time intervals, each with a spatial resolution of 1280x1280x640 grid points. Four flow variables are associated with each snapshot: the three velocity components (u,v,w) and the perturbed density field (rho) away from the background gradient. All fields are stored in binary format (32-bit little-endian), each with a size of 4 GB, yielding a total dataset size of 244 TB. Further details are referenced in the attached README file, and a current list of publications and associated analysis tools are provided at https://stratified-turbulence.github.io/web/.

42 ENGINEERING↗

DOE OSTI2024

Experimental Soil Warming Impacts Soil Moisture and Plant Water Stress and Thereby Ecosystem Carbon Dynamics (Blodgett, CA)

This dataset contains data on daily soil temperature, moisture and flux, and soil carbon stock and root biomass across a soil profile down to 100 cm depth at Blodgett Forest Research Station, CA, USA. These data were generated to determine if modeling of an experimental soil warming of 4C showed increased soil CO2 emissions and changes in bulk soil carbon stocks with depth consistent with field observations, as part of the study: Riley et al. (2025) Experimental Soil Warming Impacts Soil Moisture and Plant Water Stress and Thereby Ecosystem Carbon Dynamics in Journal of Advances in Modeling Earth Systems. This research was performed within the framework of the TES Belowground Biogeochemistry SFA project, in particular association with a 1 m-deep experimental soil heating experiment at the University of California Blodgett Forest Research Station, California (120 ° 39′40′′W; 38 ° 54′43′′N). Continuous data were collected at the plot level, and bulk soil carbon and root biomass were sampled once a year from each plot from 0-100 cm, in 10 cm intervals. Measurements relevant to the current study include soil temperature and soil volumetric water content measured continuously at multiple depths in the top meter; fine root biomass and SOC stocks measured from annual soil cores. Soil flux was continuously monitored using a LI-8100 Automated CO2 Flux System in conjunction with the LI-8150 Multiplexer (Licor, Nebraska, USA). Soil flux was determined using SoilFluxPro software, with flux values showing an R² fit of less than 0.9 being excluded from the analysis. Data were collected from each paired plot (1-3): one control (C) and one heated (H).

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Synthetic Atmospheric River Ensembles Generated by Deep-AR

This dataset contains 35,850 synthetic landfalling atmospheric river (AR) realizations generated by the Deep-AR two-stage deep-learning framework over the Northeast Pacific and U.S. West Coast. The archive contains 25 stochastic ensemble members for each of 1,434 held-out observed seed events. Each synthetic realization is initialized from conditions 48 hours before the corresponding observed AR landfall and is generated autoregressively at 6-hour intervals over a 144-hour period. Deep-AR combines a deterministic residual network (ResNet) that advances the large-scale atmospheric state with a Wasserstein generative adversarial network (WGAN) that produces stochastic, high-resolution fields. Each HDF5 file contains 0.25° gridded synthetic integrated vapor transport components (qu, qv), 10 m wind components (u10, v10), and 6-hour accumulated precipitation on a common 200 × 480 grid. The files also include coordinate and datetime arrays. This dataset supports AR hazard analysis, ensemble-based uncertainty characterization, precipitation-extremes research, and regional stress testing. Synthetic files follow the naming convention deepar.model.YYYYMMDD.HHMMSS.vNN.h5. YYYYMMDD.HHMMSS identifies the UTC initial-condition timestamp, which occurs 48 hours before the diagnosed observed landfall, and vNN identifies the zero-padded ensemble member, ranging from v01 through v25. Each synthetic file can be paired with its corresponding observed file by matching the initial-condition timestamp. The paired observed file follows the naming convention deepar.obs.YYYYMMDD.HHMMSS.h5 and is available in the separately registered oracle/deepar.obs dataset at https://wdh.energy.gov/ds/oracle/deepar.obs (DOI: https://doi.org/10.21947/3377671).

17 WIND ENERGY↗

NASA NTRS1990

Nonlinear feedback control for high alpha flight

Analytical aerodynamic models are derived from a high alpha 6 DOF wind tunnel model. One detail model requires some interpolation between nonlinear functions of alpha. One analytical model requires no interpolation and as such is a completely continuous model. Flight path optimization is conducted on the basic maneuvers: half-loop, 90 degree pitch-up, and level turn. The optimal control analysis uses the derived analytical model in the equations of motion and is based on both moment and force equations. The maximum principle solution for the half-loop is poststall trajectory performing the half-loop in 13.6 seconds. The agility induced by thrust vectoring capability provided a minimum effect on reducing the maneuver time. By means of thrust vectoring control the 90 degrees pitch-up maneuver can be executed in a small place over a short time interval. The agility capability of thrust vectoring is quite beneficial for pitch-up maneuvers. The level turn results are based currently on only outer layer solutions of singular perturbation. Poststall solutions provide high turn rates but generate higher losses of energy than that of classical sustained solutions.

Stalford, Harold↗

NASA NTRS1997

Archiving of Wideband Plasma Wave Data

Beginning with the third year of funding, we began a more ambitious archiving production effort, minimizing work on new software and concentrating on building representative archives of the missions mentioned above, recognizing that only a small percentage of the data from any one mission can be archived with reasonable effort. We concentrated on data from Dynamics Explorer and ISEE 1, archiving orbits or significant fractions of orbits which attempt to capture the essence of the mission and provide data which will hopefully be sufficient for ongoing and new research as well as to provide a reference to upcoming and current ISTP missions which will not fly in the same regions of space as the older missions and which will not have continuous wideband data. We archived approximately 181 Gigabytes of data, accounting for some 1582 hours of data. Included in these data are all of the AMPTE chemical releases, all of the Spacelab 2/PDP data obtained during the free-flight portion of its mission, as well as significant portions of the S3, DE-1, Imp-6, Hawkeye, Injun 5, and ISEE 1 and 2 data sets. Table 1 summarizes these data. All of the data archived are summarized in gif-formatted images of frequency-time spectrograms which are directly accessible via the internet. Each of the gif files are identified by year, day, and time as described in the Web page. This provides a user with a specific date/time in mind a way of determining very quickly if there is data for the interval in question and, by clicking on the file name, browsing the data. Alternately, a user can browse the data for interesting features and events simply by viewing each of the gif files. When a user finds data of interest, he/she can notify us by email of the time period involved. Based on the user's needs, we can provide data on a convenient medium or by ftp, or we can mount the appropriate data and provide access to our analysis tools via the network. We can even produce products such as plots or spectrograms in hardcopy form based on the specific request of the user.

Kurth, William S.↗

NASA NTRS1995

Flux of Millimetric Space Debris

In 21.4 hr of zenith radar observations on 4 days at 8510 MHz, we found 831 particles with altitudes between 177 and 1662 km. From the duration of the echoes and the angular size (0.030 deg) of the antenna beam 157 particles were identified as passing through the side lobes and not through the main beam. Our analysis is based on the 674 particles that did not broaden the beam. On the assumptions that these particles went through the main beam, their radar cross sections vary between 0.02 and 260 sq mm , and their radial velocities vary between +/- 700 m/s. If they are conducting spheres, their diameters lie between 2 and 18 mm. If not, they must be larger. The flux of these particles, that is the number per sq km day, was determined in 100 km intervals. The maximum flux, 3.3 particles per sq km day, occurs at 950 km altitude. The small and large particles are not well mixed. The largest particles occur beyond 1000 km and middle-sized particles are missing below 300 km. If the earth's atmosphere caused the smallest particles to lose energy from initial orbits identical to those of the large particles, the orbits would have lower eccentricity at low altitudes. We find a larger eccentricity for the inner particles, and conclude that two or more populations are present.

Goldstein, R. M.↗

NASA NTRS1999

Global Geometric Properties of Martian Impact Craters: A Preliminary Assessment Using Mars Orbiter Laser Altimeter (MOLA)

Impact craters on Mars have been used to provide fundamental insights into the properties of the martian crust, the role of volatiles, the relative age of the surface, and on the physics of impact cratering in the Solar System. Before the three-dimensional information provided by the Mars Orbiter Laser Altimeter (MOLA) instrument which is currently operating in Mars orbit aboard the Mars Global Surveyor (MGS), impact features were characterized morphologically using orbital images from Mariner 9 and Viking. Fresh-appearing craters were identified and measurements of their geometric properties were derived from various image-based methods. MOLA measurements can now provide a global sample of topographic cross-sections of martian impact features as small as approx. 2 km in diameter, to basin-scale features. We have previously examined MOLA cross-sections of Northern Hemisphere and North Polar Region impact features, but were unable to consider the global characteristics of these ubiquitous landforms. Here we present our preliminary assessment of the geometric properties of a globally-distributed sample of martian impact craters, most of which were sampled during the initial stages of the MGS mapping mission (i.e., the first 600 orbits). Our aim is to develop a framework for reconsidering theories concerning impact cratering in the martian environment. This first global analysis is focused upon topographically-fresh impact craters, defined here on the basis of MOLA topographic profiles that cross the central cavities of craters that can be observed in Viking-based MDIM global image mosaics. We have considered crater depths, rim heights, ejecta topologies, cross-sectional "shapes", and simple physical models for ejecta emplacement. To date (May, 1999), we have measured the geometric properties of over 1300 impact craters in the 2 to 350 km diameter size interval. A large fraction of these measured craters were sampled with cavity-center cross-sections during the first two months of MGS mapping. Many of these craters are included in Nadine Barlow's Catalogue of Martian Impact Craters, although we have treated simple craters smaller than about 7 km in greater detail than all previous investigations. Additional information is contained in the original extended abstract.

Garvin, J. B.↗

NASA NTRS1998

Examination of two methods for statistical analysis of data with magnitude and direction emphasizing vestibular research applications

When the dependent (or response) variable response variable in an experiment has direction and magnitude, one approach that has been used for statistical analysis involves splitting magnitude and direction and applying univariate statistical techniques to the components. However, such treatment of quantities with direction and magnitude is not justifiable mathematically and can lead to incorrect conclusions about relationships among variables and, as a result, to flawed interpretations. This note discusses a problem with that practice and recommends mathematically correct procedures to be used with dependent variables that have direction and magnitude for 1) computation of mean values, 2) statistical contrasts of and confidence intervals for means, and 3) correlation methods.

Vestibule↗