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Goals: What is Analysis of Variance (ANOVA); Extending Analysis of Variance to Function Data (F-ANOVA); The role of stochastic processes in F-ANOVA; One and Two Sample Problems for F-ANOVA; One-Way F-ANOVA.
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.
This dataset contains all data and supplementary materials from "Genetics of flooding tolerance in an F2 Miscanthus sacchariflorus ssp. lutarioriparius × M. sinensis population". 1. The dataset S1 table contains the raw phenotypic data collected during the experiment. 2. The dataset S2 table contains the LSmean values for the 24 traits studied. 3. The dataset S3 table contains the TASSEL GBSv2 map, marker information, and genotype data used for mapping. 4. The dataset S4 table contains information on candidate genes found in each of the QTL intervals. 5. The dataset S5 table contains the GO annotations and KEGG enrichment analyses for those candidate genes. 6. The dataset S6 table contains information on the sequences used to classify AP2 ERF transcription factors. 7. The dataset S7 table contains information on AP2 ERF orthologs between Miscanthus and rice based on synteny. 8. Supplementary file 1 contains the ANOVA results using the raw phenotypic data collected from protocol "A". 9. Supplementary file 2 contains the ANOVA results using the raw phenotypic data collected from protocol "B". 10. Supplementary file 3 contains notes on the comparison of SNP calling methods. 11. Supplementary file 4 is a script for analyzing candidate genes found in QTL intervals.
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.
To investigate the contributing factors of variance in the measurement of an iodine 127 (127I) sample, we implement a nested random effects analysis of variance (ANOVA). Historically, the reported uncertainty on a measurement of 127I has been obtained by methods of forward uncertainty propagation because there is typically only one replicate of a given sample for which to estimate the uncertainty. When samples are processed there are several types of quality control (QC) standards analyzed along-side the unknown samples with two to five replicates for each. Assuming the variance observed in these replicate QC standards is representative of that of the unknown samples, we use these data in a nested random effects ANOVA to estimate the total uncertainty of a measurement. We demonstrate this approach with two sets of measurements from Idaho National Laboratory and compare the results with the forward uncertainty propagation approach. Variance component estimates for the coarsest level of the nesting structure were most imprecise because replicates were most limited at these levels. We find that the results largely agree between forward propagation and ANOVA, and the greatest contributors of variance are due to instrument variation and chemical processing, with human processing being among the smallest contributors. This analysis provides reassurance that the reported uncertainties using forward propagation are reasonable and the process is well controlled. We propose a future designed experiment to increase replicates at the coarsest level of the hierarchy to improve estimates of these variance components.
The safe transportation of radioactive material using appropriately designed and certified transportation packages is important to protect the public and environment. Therefore, a comprehensive and rigorous system of packaging requirements are required. The purpose of this test protocol is to determine the effects of drop testing on package performance in a Type B shipping package (DPP-3). Required physical tests for the DPP-3 package include normal conditions of transport and hypothetical accident conditions test requirements. The preparation, regulatory testing, and post-test evaluation of a Type B shipping package tested to the 10 CFR 71.71 and 10 CFR 71.73 requirements will be presented. Six packages were tested and the responses when subjected to the HAC sequence of free drop, puncture, and thermal tests according to 10 CFR 71.73 were measured. The posttest helium leak test showed a leak rate less than 1 × 10-7 He-cc/sec which means that the containment boundary was maintained after the regulatory testing, therefore maintaining a leak tight environment. To determine the amount of change in the package performance measurements, statistical analyses were conducted using SPSS version 26. The null hypothesis of the testing was that there would not be a change in the measurements from pre to post-testing large enough to find statistical significance. Therefore, a finding of statistical significance indicated too much variability in the package design and was deemed an unfavorable finding. A repeated measures t-test was used to analyze the drum lids and CV torques. A one-way ANOVA was used to analyze height and diameter packages. Results of the repeated measures t-test indicated that all six containment vessel lid torques were statistically significant. However only three out of the six drum lid torques were statistically significant. Therefore, design of the lids caused more variability than necessary when subjected to the following drop tests: 1.) horizontal and cold; 2.) vertical lid down; and 3.) corner with lid up. Results of the one-way ANOVA analysis on height indicated that four out of the six CTUs were statistically significant. Thus, design of the CTUs caused more variability then necessary when subjected to the following drop tests: 1.) horizontal hot; 2.) horizontal cold; 3.) corner lid up; and 4.) corner lid down. Results of the one-way ANOVA analysis on diameter indicated that all six CTUs were statistically significant. Thus, design of the CTUs caused more variability then necessary when subjected to all of the tests. The DPP-3 design has been shown to be an acceptable design for the transport of radioactive materials. However, results of the statistical analysis reveal a possible improvement in package and test design to reduce variability in package performance measurement before and after testing.
In the first two quarters of FY22, data acquisition continued at ORNL and LLNL using uranium sources of known enrichments. This was an FY21 task which could not be completed in FY21 because of problems encountered with the ORNL M400 CZT in Q4 of FY21, and the subsequent repairs. The detector was received back from H3D in the first of September 2021 , and the measurements resumed . Measurements using the repaired detector were completed in Q1 of FY22. The spectra were distributed by ORNL to the analyzing labs. Analysis results were received in Q2 of FY2022. The results from the various codes were intercompared and an ANOVA analysis was performed. Random and systematic uncertainties were established for each code. The ANOVA results and discussions were included in a revised version of FY21Annual Report issued in March 2022. A paper was presented at the INMM 2022Annual Conference, with the analysis results from the various isotopic codes, and the ANOVA table with random and systematic uncertainties. The Project Work Plan (PWP) for FY22 included a task to perform field testing of the M400 CZT and the analysis codes using UF 6 cylinder measurements at the Framatome Fuel Fabrication Facility in Richland, WA. PNNL was the lead for the field testing task. PNNL drafted a Field Test Plan, and refined it based on comments received from the team. PNNL coordinated with Framatome facility, the logistics of carrying out the field testing . A collimator and shield made out of TFlex (tungsten impregnated polymer) was designed and professionally manufactured. The collimators were used in the field test measurements. The measurements at Framatome were completed on April 21, 2022. A total of 34 Type 30B cylinders were measured using three M400 detectors (PNNL, LLNL, and ORNL detectors). Measurements using M400 were taken at two locations on the side of each cylinder and from the end-on bottom location. Additionally, HPGe measurements were taken at the end-on location to establish ground truth. Cylinder wall thickness measurements were also made at all three locations. To gain a better understanding of the effect of background from surrounding cylinders, the same five cylinders measured individually in low background locations were measured again in the cylinder storage yards. Due to inclement weather, manufacturer delays, shipping delays, and equipment failure, the measurement campaign spanned twice as long compared to the original timeline. Gamma-ray spectra from M400 and HPGe detectors, along with the cylinder data and photographs were organized and shared with the collaborators for further analysis. Spectra were analyzed by the participating laboratories. FY22 PWP also consists of tasks related to plutonium source measurements, adapting the codes to analyze plutonium spectra, and inter-comparison of the results from various codes. Plutonium spectra are being acquired at LANL, ORNL, and LLNL. LANL, SNL and LLNL are in the process of modifying FRAM, GADRAS, and CZTU, respectively. The plutonium related tasks will be completed in Q2 of FY23.
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.
Global sensitivity analysis (GSA) of distribution systems with respect to stochastic PV and load variations plays an important role in designing optimal voltage control schemes. This paper proposes a data-driven framework for GSA of distribution systems. In particular, two representative surrogate modeling-based approaches are developed, including the traditional Gaussian process-based and the analysis of variance (ANOVA) kernel ones. The key idea is to develop a surrogate model that captures the hidden global relationship between voltage and real and reactive power injections from the historical data. With the surrogate model, the Sobol indices can be conveniently calculated through either the sampling-based method or the analytical method to assess the global sensitivity of voltage to variations of PV and load power injections. The sampling-based method approximates the Sobol indices using Monte Carlo simulations while the analytical method calculates them by resorting to the ANOVA expansion framework. Comparison results with other model-based GSA methods on the unbalanced three-phase IEEE 37-bus and 123-bus distribution systems show that the proposed framework can achieve much higher computational efficiency with negligible loss of accuracy. The results on a real 240-node distribution system using actual smart meter data further validate the feasibility and scalability of the proposed framework.