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Monte Carlo computations of decision error probabilities for chain pooling and variations for fractional factorial experiments
Chain pooling analysis of error variance with real effects for two level factorial replication free experiments
Chain pooling tests for two level factorial replication-free experiments using Monte Carlo methods
Statistical mechanics of always usable, limited length, permutation tests for two way analysis of variance and applications in quality control
Statistical mechanics of sequential randomization tests for two way variance emphasizing most recently acquired data and applications in quality control
Statistical mechanics of sequential randomization tests for one way variance emphasizing most recently acquired data and applications in quality control
An analysis of variance (ANOVA) study was conducted for historical hurricane data dating back to 1851 that was obtained from the U. S. Department of Commerce National Oceanic and Atmospheric Administration (NOAA). The data set was chosen because it is a large, publicly available collection of information, exhibiting great variability which has made the forecasting of future states, from current and previous states, difficult. The availability of substantial, high-fidelity validation data, however, made for an excellent uncertainty assessment study. Several factors (independent variables) were identified from the data set, which could potentially influence the track and intensity of the storms. The values of these factors, along with the values of responses of interest (dependent variables) were extracted from the data base, and provided to a commercial software package for processing via the ANOVA technique. The primary goal of the study was to document the ANOVA modeling uncertainty and predictive errors in making predictions about hurricane location and intensity 24 to 120 hours beyond known conditions, as reported by the data set. A secondary goal was to expose the ANOVA technique to a broader community within NASA. The independent factors considered to have an influence on the hurricane track included the current and starting longitudes and latitudes (measured in degrees), and current and starting maximum sustained wind speeds (measured in knots), and the storm starting date, its current duration from its first appearance, and the current year fraction of each reading, all measured in years. The year fraction and starting date were included in order to attempt to account for long duration cyclic behaviors, such as seasonal weather patterns, and years in which the sea or atmosphere were unusually warm or cold. The effect of short duration weather patterns and ocean conditions could not be examined with the current data set. The responses analyzed were the storm latitude, longitude and intensity, as recorded in the data set, 24 or 120 hours beyond the current state. Several ANOVA modeling schemes were examined. Two forms of validation were used: 1) comparison with official hurricane prediction performance metrics and 2) cases studies conducted on hurricanes from the 2005 season, which were not included within the model construction and ANOVA assessment. In general, the ANOVA technique did not perform as well as the established official prediction performance metrics published by NOAA; still, the technique did remarkably well in this demonstration with a difficult data set and could probably be made to perform better with more knowledge of hurricane development and dynamics applied to the problem. The technique provides a repeatable prediction process that eliminates the need for judgment in the forecast.
Statistical Analysis Toolset is a collection of eight Microsoft Excel spreadsheet programs, each of which performs calculations pertaining to an aspect of statistical analysis. These programs present input and output data in user-friendly, menu-driven formats, with automatic execution. The following types of calculations are performed: Descriptive statistics are computed for a set of data x(i) (i = 1, 2, 3 . . . ) entered by the user. Normal Distribution Estimates will calculate the statistical value that corresponds to cumulative probability values, given a sample mean and standard deviation of the normal distribution. Normal Distribution from two Data Points will extend and generate a cumulative normal distribution for the user, given two data points and their associated probability values. Two programs perform two-way analysis of variance (ANOVA) with no replication or generalized ANOVA for two factors with four levels and three repetitions. Linear Regression-ANOVA will curvefit data to the linear equation y=f(x) and will do an ANOVA to check its significance.
An analysis of variance (ANOVA) study was performed to quantify the potential uncertainties of lift and pitching moment coefficient calculations from a computational fluid dynamics code, relative to an experiment, for a jet flap airfoil configuration. Uncertainties due to a number of factors including grid density, angle of attack and jet flap blowing coefficient were examined. The ANOVA software produced a numerical model of the input coefficient data, as functions of the selected factors, to a user-specified order (linear, 2-factor interference, quadratic, or cubic). Residuals between the model and actual data were also produced at each of the input conditions, and uncertainty confidence intervals (in the form of Least Significant Differences or LSD) for experimental, computational, and combined experimental / computational data sets were computed. The LSD bars indicate the smallest resolvable differences in the functional values (lift or pitching moment coefficient) attributable solely to changes in independent variable, given just the input data points from selected data sets. The software also provided a collection of diagnostics which evaluate the suitability of the input data set for use within the ANOVA process, and which examine the behavior of the resultant data, possibly suggesting transformations which should be applied to the data to reduce the LSD. The results illustrate some of the key features of, and results from, the uncertainty analysis studies, including the use of both numerical (continuous) and categorical (discrete) factors, the effects of the number and range of the input data points, and the effects of the number of factors considered simultaneously.
This paper is a tutorial introduction to the analysis of variance (ANOVA), intended as a reference for aerospace researchers who are being introduced to the analytical methods of the Modern Design of Experiments (MDOE), or who may have other opportunities to apply this method. One-way and two-way fixed-effects ANOVA, as well as random effects ANOVA, are illustrated in practical terms that will be familiar to most practicing aerospace researchers.
The goal of this work is, through computational simulations, to provide statistically-based evidence to convince the testing community that a distributed testing approach is superior to a clustered testing approach for most situations. For clustered testing, numerous, repeated test points are acquired at a limited number of test conditions. For distributed testing, only one or a few test points are requested at many different conditions. The statistical techniques of Analysis of Variance (ANOVA), Design of Experiments (DOE) and Response Surface Methods (RSM) are applied to enable distributed test planning, data analysis and test augmentation. The D-Optimal class of DOE is used to plan an optimally efficient single- and multi-factor test. The resulting simulated test data are analyzed via ANOVA and a parametric model is constructed using RSM. Finally, ANOVA can be used to plan a second round of testing to augment the existing data set with new data points. The use of these techniques is demonstrated through several illustrative examples. To date, many thousands of comparisons have been performed and the results strongly support the conclusion that the distributed testing approach outperforms the clustered testing approach.
A common problem in the design of expert systems is the definition of rules from data obtained in system operation or simulation. While it is relatively easy to collect data and to log the comments of human operators engaged in experiments, generalizing such information to a set of rules has not previously been a direct task. A statistical method is presented for generating rule bases from numerical data, motivated by an example based on aircraft navigation with multiple sensors. The specific objective is to design an expert system that selects a satisfactory suite of measurements from a dissimilar, redundant set, given an arbitrary navigation geometry and possible sensor failures. The systematic development is described of a Navigation Sensor Management (NSM) Expert System from Kalman Filter convariance data. The method invokes two statistical techniques: Analysis of Variance (ANOVA) and the ID3 Algorithm. The ANOVA technique indicates whether variations of problem parameters give statistically different covariance results, and the ID3 algorithms identifies the relationships between the problem parameters using probabilistic knowledge extracted from a simulation example set. Both are detailed.
A common problem in the design of expert systems is the definition of rules from data obtained in system operation or simulation. A statistical method for generating rule bases from numerical data, motivated by an example based on aircraft navigation with multiple sensors is presented. The specific objective is to design an expert system that selects a satisfactory suite of measurements from a dissimilar, redundant set, given an arbitrary navigation geometry and possible sensor failures. The systematic development of a Navigation Sensor Management (NSM) Expert System from Kalman Filter covariance data is described. The development method invokes two statistical techniques: Analysis-of-Variance (ANOVA) and the ID3 algorithm. The ANOVA technique indicates whether variations of problem parameters give statistically different covariance results, and the ID3 algorithm identifies the relationships between the problem parameters using probabilistic knowledge extracted from a simulation example set.
Nine cooperating rule-based systems, collectively called AUTOCREW which were designed to automate functions and decisions associated with a combat aircraft's subsystems, are discussed. The organization of tasks within each system is described; performance metrics were developed to evaluate the workload of each rule base and to assess the cooperation between the rule bases. Simulation and comparative workload results for two mission scenarios are given. The scenarios are inbound surface-to-air-missile attack on the aircraft and pilot incapacitation. The methodology used to develop the AUTOCREW knowledge bases is summarized. Issues involved in designing the navigation sensor selection expert in AUTOCREW's NAVIGATOR knowledge base are discussed in detail. The performance of seven navigation systems aiding a medium-accuracy INS was investigated using Kalman filter covariance analyses. A navigation sensor management (NSM) expert system was formulated from covariance simulation data using the analysis of variance (ANOVA) method and the ID3 algorithm. ANOVA results show that statistically different position accuracies are obtained when different navaids are used, the number of navaids aiding the INS is varied, the aircraft's trajectory is varied, and the performance history is varied. The ID3 algorithm determines the NSM expert's classification rules in the form of decision trees. The performance of these decision trees was assessed on two arbitrary trajectories, and the results demonstrate that the NSM expert adapts to new situations and provides reasonable estimates of the expected hybrid performance.
1. The notion that small, 'non-hypotensive' reductions of effective blood volume alter neither arterial pressure nor arterial baroreceptor activity is pervasive in the experimental literature. We tested two hypotheses: (a) that minute arterial pressure and cardiac autonomic outflow changes during hypovolaemia induced by lower body suction in humans are masked by alterations in breathing, and (b) that evidence for arterial baroreflex engagement might be obtained from measurements of thoracic aorta dimensions. 2. In two studies, responses to graded lower body suction at 0 (control), 5, 10, 15, 20 and 40 mmHg were examined in twelve and ten healthy young men, respectively. In the first, arterial pressure (photoplethysmograph), R-R interval, and respiratory sinus arrhythmia amplitude (complex demodulation) were measured during uncontrolled and controlled breathing (constant breathing frequency and tidal volume). In the second, cross-sectional areas of the ascending thoracic aorta were calculated from nuclear magnetic resonance images. 3. Lower body suction with controlled breathing resulted in an increased arterial pulse pressure at mild levels (5-20 mmHg; ANOVA, P < 0.05) and a decreased arterial pulse pressure at moderate levels (40 mmHg; ANOVA, P < 0.05). Both R-R intervals and respiratory sinus arrhythmia were negatively related to lower body suction level, whether group averages (general linear regression, r > 0.92) or individual subjects (orthogonal polynomials, 12 of 12 subjects) were assessed. 4. Aortic pulse area decreased progressively and significantly during mild lower body suction, with 47% of the total decline occurring by 5 mmHg. 5. These results suggest that small reductions of effective blood volume reduce aortic baroreceptive areas and trigger haemodynamic adjustments which are so efficient that alterations in arterial pressure escape detection by conventional means.
The use of Post-Flight Feedback (PFFB) and Above Real-Time Training (ARTT) while training novice pilots to perform a coordinated level turn on a PC-based flight simulator was investigated. One group trained at 1.5 ARTT followed by an equal number of flights at 2.0 ARTT; the second group experienced Real Time Training (RTT). The total number of flights for both groups was equal. Each group was further subdivided into two groups one of which was provided PFFB while the other was not. Then, all participants experienced two challenging evaluation missions in real time. Performance was assessed by comparing root-mean-square error in bank-angle and altitude. Participants in the 1.512.0 ARTT No-PFFB sequence did not show improvement in performance across training sessions. An ANOVA on performance in evaluation flights found that the PFFB groups performed significantly better than those with No-PFFB. Also, the RTT groups performed significantly better than the ARTT groups. Data from two additional groups trained under a 2.011.5 ARTT PFFB and No-PFFB regimes were collected and combined with data from the previously Trainers, Real-time simulation, Personal studied groups and reanalyzed to study the computers, Man-in-the-loop simulation influence of sequence. An ANOVA on test trials found no significant effects between groups. Under training situations involving ARTT we recommend that appropriate PFFB be provided.
VO2max is associated with many factors, including age, gender, physical activity, and body composition. It is popularly believed that habitual smoking lowers aerobic fitness. PURPOSE: to determine the effect of habitual smoking on VO2max after controlling for age, gender, activity and BMI. METHODS: 2374 men and 375 women employed at the NASA/Johnson Space Center were measured for VO2max by indirect calorimetry (RER>=1.1), activity by the 11 point (0-10) NASA Physical Activity Status Scale (PASS), BMI and smoking pack-yrs (packs day*y of smoking). Age was recorded in years and gender was coded as M=1, W=0. Pack.y was made a categorical variable consisting of four levels as follows: Never Smoked (0), Light (1-10), Regular (11-20), Heavy (>20). Group differences were verified by ANOVA. A General Linear Models (GLM) was used to develop two models to examine the relationship of smoking behavior on VO2max. GLM #1(without smoking) determined the combined effects of age, gender, PASS and BMI on VO2max. GLM #2 (with smoking) determined the added effects of smoking (pack.y groupings) on VO2max after controlling for age, gender, PASS and BMI. Constant errors (CE) were calculated to compare the accuracy of the two models for estimating the VO2max of the smoking subgroups. RESULTS: ANOVA affirmed the mean VO2max of each pack.y grouping decreased significantly (p<0.01) as the level of smoking exposure increased. GLM #1 showed that age, gender, PASS and BMI were independently related with VO2max (R2 = 0.642, SEE = 4.90, p<0.001). The added pack.y variables in GLM #2 were statistically significant (R2 change = 0.7%, p<0.01). Post hoc analysis showed that compared to Never Smoked, the effects on VO2max from Light and Regular smoking habits were -0.83 and -0.85 ml.kg- 1.min-1 respectively (p<0.05). The effect of Heavy smoking on VO2max was -2.56 ml.kg- 1.min-1 (p<0.001). The CE s of each smoking group in GLM #2 was smaller than the CE s of the smoking group counterparts in GLM #1. CONCLUSIONS: After accounting for the effects of gender, age, PASS and BMI the effect of habitual smoking on reducing VO2max is minimal, about 0.85 ml/kg/min, until the habit exceeds 20 pack.y at which point an additional decrease of 1.71 ml/kg/min is noted. Adding pack.y data improves the accuracy of predicting the VO2max of smokers.
Post-spaceflight orthostatic intolerance is characterized by hypotension and presyncope in 20-30% of returning astronauts. Previous data from our laboratory suggests that this is largely a result of decreased venous return. Currently, NASA astronauts wear an anti-gravity suit (AGS) which consists of inflatable air bladders over the calves, thighs and abdomen, which are typically pressurized from 0.5 to 1.5 PSI (~27 to 78 mmHg). ISS crew members sometimes wear Russian Kentavr suits which consist of laced compression shorts and gaiters, providing ~30 mmHg nominally. While these garments are effective during reentry, there are a number of drawbacks that make them impractical for postflight use. We studied the ability of commercially available, custom fit, graded compression stockings (Jobst, 55 mmHg at ankle to 6 mmHg at top of thigh, 25 mmHg mean compression) to prevent postflight orthostatic intolerance, hypothesizing that these garments would prevent orthostatic intolerance following short duration space flight. Crew members from a single Space Shuttle flight were tilted to 80 degrees for 10 min while wearing the stockings (n=5 males) upon arrival at the clinic (~2 hrs after landing). Hemodynamic data were compared to data from all crewmembers tilted (without countermeasures) since return to flight (n=9). Two-way, repeated measures ANOVA, using the entire tilt time curve (0-10 min) show that systolic blood pressure (SBP, group effect p=0.008), stroke volume (SV, group effect p=0.003), and cardiac output (CO, group effect p=0.004) were higher in crewmembers who wore the Jobst stockings. A one-way ANOVA comparing the last minute standing also showed that SV (p=0.001) and CO (p less than 0.001) were higher and SBP tended to be higher (p=0.06) in Jobst subjects compared to controls. Control subjects had a higher rate of presyncope than Jobst subjects (3/9 vs 0/5) during the tilt on landing day. Orthostatic hypotension continues to present following spaceflight, despite fluid loading and other countermeasures. This preliminary study shows that commercially available compression stockings may ameliorate this problem. These stockings are readily available, inexpensive, and can be worn for days following landing. We have observed similar protection against orthostatic intolerance in ground-based studies of hypovolemic test subjects. Further refinements to the design and compression of the stockings are in progress.