Search NASA⌕ Search

SEARCH · Search NASA

Results for “small sample size”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Statistical Analysis Techniques for Small Sample Sizes

The small sample sizes problem which is encountered when dealing with analysis of space-flight data is examined. Because of such a amount of data available, careful analyses are essential to extract the maximum amount of information with acceptable accuracy. Statistical analysis of small samples is described. The background material necessary for understanding statistical hypothesis testing is outlined and the various tests which can be done on small samples are explained. Emphasis is on the underlying assumptions of each test and on considerations needed to choose the most appropriate test for a given type of analysis.

Navard, S. E.↗
NASA NTRSDate not supplied

Assessing Risk Due to Small Sample Size in Probability of Detection Analysis Using Tolerance Intervals

Small sample size (e.g.6-30) poses risk in results of probability of detection (POD) analysis using tolerance intervals. This method is also called as the limited sample or LS POD. The analysis is performed either during NDE procedure qualification or for assessment of reliability of an NDE procedure. The risk is primarily due to sampling error. Smaller samples are not likely to be random to the population or representative of the population. The small samples are likely to be biased. Biased samples have smaller standard deviation compared to the population. POD analysis with small biased sample can lead to overestimation of POD. Many sampling schemes are available in statistics to mitigate sampling risk. Primary objective of POD analysis is to determine a decision threshold from signal response measurements of a sample such that it is less than or equal to population decision threshold for 90% POD. Sampling error implies that this NDE reliability condition is violated. One of sampling types is called a representative sample. Representative samples reduce variance in POD estimates but also reduce magnitude of the error. Sampling sensitivity analysis for some sampling types is performed here using repetitive random sampling or Monte Carlo method. Six sampling types are considered for comparison. Some of the sampling types are similar to drawing a representative sample. LS POD model assumes random sampling. Therefore, random sampling is used as a basis for comparison with each sampling type. The sampling types used in the analysis are, A. Nominal and worst-case sampling, B. Worst-case sampling, C. Nominal case sampling, D. Random sampling, E. Random target, and sub-target sampling. F. Nominal target and sub-target sampling. Results of Monte Carlo simulation indicate that type F sampling can mitigate sampling risk and is also more practical to implement. Type A sampling may also mitigate the sampling risk, but it may be less practical to implement.

Ajay M Koshti↗
NASA NTRSDate not supplied

Small-Sample Estimator Decisions – Certainly Uncertain in Human Spaceflight at NASA

Within statistics when estimating means, we rely heavily on the Central Limit Theorem (CLT) to aid in our inference, however in cases where the CLT does not apply we begin to be strongly limited in our choices. If a violation to the CLT comes in the form of small samples and unknown population variance, yet we maintain the assumption of normality, the use of t-distributions is perfectly valid. We explore cases where population normality is not assumed, where sample sizes are small, and where some actionable estimate of the central tendency of a distribution is needed such as for spaceflight operational decisions. Here we identify different scenarios based on measures taken from spaceflight, characterizing performance of estimators of central tendency within our set of simulations. We examine bias and variability of standard estimators of central tendency as they apply to varying small sample sizes and varying population distributions. Further work in this area is needed to develop a framework or set of guidelines for individuals set in these situations. Even with limited information, decisions need to be made.

Central Tendency↗
NASA NTRS1995

Designing for Small Volume Assembly of Advanced Electronics Packages

We describe a general methodology to Design for Producibility and Reliability (DFPAR) for very small volume production runs. In cases where the entire volume for fabrication is less than five products, traditional Statistical Process Control (SPC) is inadequate due to reliance on statistics of much larger volumes and the Central Limit Theorem. Data acquisition for process parameter estimation from such a small sample size is difficult; however, it is critical to producing high reliability product.

Central Limit Theorem statistics high reliability ↗
NASA NTRS1976

On the role of dimensionality and sample size for unstructured and structured covariance matrix estimation

The experimental observation that a surprisingly small sample size vis-a-vis dimension is needed to achieve good signal-to-interference ratio (SIR) performance with an adaptive predetection filter is explained. The adaptive filter requires estimates as obtained by a recursive stochastic algorithm of the inverse of the filter input data covariance matrix. The SIR performance with sample size is compared for the situations where the covariance matrix estimates are of unstructured (generalized) form and of structured (finite Toeplitz) form; the latter case is consistent with weak stationarity of the input data stochastic process.

Morgera, S. D.↗
NASA NTRS1993

Statistical computation of tolerance limits

Based on a new theory, two computer codes were developed specifically to calculate the exact statistical tolerance limits for normal distributions within unknown means and variances for the one-sided and two-sided cases for the tolerance factor, k. The quantity k is defined equivalently in terms of the noncentral t-distribution by the probability equation. Two of the four mathematical methods employ the theory developed for the numerical simulation. Several algorithms for numerically integrating and iteratively root-solving the working equations are written to augment the program simulation. The program codes generate some tables of k's associated with the varying values of the proportion and sample size for each given probability to show accuracy obtained for small sample sizes.

Wheeler, J. T.↗
NASA NTRS2023

ChIPPS: Charged Information-storage Polymer Preparation System

Technological advances are required to support principal science objectives of missions to the solar system’s icy worlds to seek biosignatures of past/extant life. Sensitivity and reliability are key concerns due to small sample sizes (µL – mL) and the extraordinary import of the results. The preparation and processing of small samples can constrain limits of detection (LoDs); therefore, the Charged Information-storage Polymer Preparation System (ChIPPS) project is advancing the technologies of autonomous sample preparation and processing to add a new class of reliably detectable biosignatures: charged polymers and particles, which can be the information storage-and-transmission means for life. Specifically, we are developing an integrated microfluidic sample-processing unit to prepare icy-world samples to support complementary solid-state nanopore-based analyses: 1) charged-polymer analysis, to characterize variations in polymer chain size, shape, and charge vs. position along the chain; 2) polymer and nanoparticle sizing-and-counting, to characterize the relative abundance of polymer chains, as well as small (virus-sized) particles, by their dimensions and charge. Although no such autonomous system presently exists, such measurements can reveal the nature and abundance of charged polymers that could be used by biological systems to store and transfer information—as DNA and RNA are used terrestrially—without limitation to terrestrial nucleic acids, given that life elsewhere may utilize different information store-and-transfer moieties. Key system components include (a) a lysis unit for mechanical sample disruption; b) an ion-exchange column for charged macromolecule/nanoparticle purification; c) dialyzer to remove excess salt; d) concentrator to enhance signal; e) supporting pumps, valves, bubble traps, connectors, filters, etc.; f) interface to nanopore detection instruments.

Space Biology↗
NASA NTRSDate not supplied

Exploring the Relationship Between Science Funding and Science Productivity on Extended Missions

Introduction: The goal of this summer internship research project was to explore the relationship between the level of funding for science team research and science productivity for planetary spaceflight missions. The productivity and funding for the prime and extended missions were compared when possible. Determining the actual rather than anecdotal relationship between the level of science team funding and their productivity will help determine the adequacy of science team funding. Additionally, determining whether productivity increases or decreases over time (within missions, or within the years between different missions) provides insights into ongoing trends. This project was conducted using data from 11 extended missions within the Planetary Science Division. The main goals of this project were to 1) quantify the level of productivity of the science team during the extended portion of each mission, 2) compare the level of productivity between different types of missions, and 3) compare the level of productivity between the prime missions and extended missions. Methodology: The central metric enters around the “publication rate” of each mission. This rate is normalized in a variety of ways, including the number of publications per year, per Co-I, and per instruments. For the most part, this data was attainable through mission websites, team rosters, and data collected from previous projects. The publication data for this project utilized the SAO/NASA Astrophysics Data System, and it consisted of a search for any papers from the extended mission that had a co-investigator as an author. The time period for these searches also included an additional two years after the end of the extended mission to account for additional time it typically takes to finish data analysis and publish papers. Data from prime missions was collected from a previous project that measured similar metrics for the same missions. When comparing the different types of missions, three factors were used: mission size, dates of the prime and extended missions, and the type of the mission (rover, flyby, orbiter, or lander). To determine mission size, missions were compared by the number of Co-I’s on the mission, the number of instruments in the payload, and the mission class. Findings: On average, prime mission publication rates were generally higher than those of extended missions. Out of the nine missions used for this comparison, six had a higher prime mission publication rate and three had a higher extended mission publication rate. This distinction was interesting to observe, but it should be noted that the methodology for determing the number of published papers differed for the prime missions and the extended missions Discovery missions were found to be the most scientifically productive. Additionally, more recent extended missions tend to possess greater productivity. When comparing missions of different types, it was found that orbiters were much more productive than other types of missions. Future Work: There are a number of opportunities to extend and improve on this project in the future. Even though the metrics used were the same, the prime mission data could be recollected from the same sources as the extended mission data (Astrophysics Data System) to insure greater consistency. The impact level of the publications could also be accounted for, and financial data could be used to compare teams with different levels of funding. Additionally, more missions could be examined to increase the sample size of these comparisons, especially the comparison of different mission types which had an incredibly small sample size for some categories.

Cameron Maxwell Thompson↗
NASA NTRS1974

A Monte Carlo investigation of experimental data requirements for fitting polynomial functions

This report examines the extent to which sample size affects the accuracy of a low order polynomial approximation of an experimentally observed quantity and establishes a trend toward improvement in the accuracy of the approximation as a function of sample size. The task is made possible through a simulated analysis carried out by the Monte Carlo method, in which data are generated by using several transcendental or algebraic functions as models. Contaminated data of varying amounts are fitted to linear quadratic or cubic polynomials, and the behavior of the mean-squared error of the residual variance is determined as a function of sample size. Results indicate that the effect of the size of the sample is significant only for relatively small sample sizes and diminishes drastically for moderate and large amounts of experimental data.

Canavos, G. C.↗
NASA NTRS1987

A Modal-Parameter Extraction Procedure

Procedure accommodates multiple input excitations. Improved modalparameter extraction procedure applicable to linear, time-invariant systems derived in 92-page report. Algorithm allows multiple noncoherent input excitations applied to structure and generates consistent set of modal parameters. Procedure extension of simultaneous frequency-domain (SFD) techniques achieved through investigation of two automatic methods for reducing effective problem size while minimizing amount of user interaction. In several sample runs, independentcoordinate reduction method shown more accurate method for small sample size. Principle-component method used to estimate number of modes active in given frequency range.

Kurdila, A. H.↗
NASA NTRS2021

Salvaging Data Records with Missing Data: Data Imputation using the Multivariate t Distribution

When doing multivariate data analysis, one commonobstacle is the presence of incomplete observations, i.e., observationsfor which one or more key fields are blank. Missing datais often countered by deleting entire observations that containmissing data. The negative effects of deleting entire observationsare multiple: deleting observations reduces sample size andcan also result in biased inferences even if data is missing atrandom. In addition, knowledge contained within incompleteobservations is knowledge lost when they are deleted– and theeffort spent collecting that knowledge is effort wasted. Data imputationmethods, or methods of statistically “filling-in” missingdata, can help combat small sample sizes by using the existinginformation in partially complete observations with the end goalof producing less biased and higher confidence inferences. Whena sample from a multivariate normal population is only partiallycomplete, and the missing data meets appropriate assumptions(missing at random), robust data imputation of the missing datacan be implemented with monotone data augmentation (MDA)using the multivariate t distribution.Missing data imputation is applied to data from the NASA InstrumentCost Model (NICM) using the MDA algorithm underthe assumption of having a multivariate t distribution with fixeddegrees of freedom. A sensitivity analysis to the degrees offreedom parameter is presented to demonstrate robustness ofthe multivariate t distribution when dealing with small samplesas compared to the multivariate normal distribution.

DiNicola, Michael↗
NASA NTRS2022

A Closer Look at Non-Random Patterns Within Chemistry Space for a Smaller, Earlier Amino Acid Alphabet

Recent findings, in vitro and in silico, are strengthening the idea of a simpler, earlier stage of genetically encoded proteins which used amino acids produced by prebiotic chemistry. These findings motivate a re-examination of prior work which has identified unusual properties of the set of twenty amino acids found within the full genetic code, while leaving it unclear whether similar patterns also characterize the subset of prebiotically plausible amino acids. We have suggested previously that this ambiguity may result from the low number of amino acids recognized by the definition of prebiotic plausibility used for the analysis. Here, we test this hypothesis using significantly updated data for organic material detected within meteorites, which contain several coded and non-coded amino acids absent from prior studies. In addition to confirming the well-established idea that “late” arriving amino acids expanded the chemistry space encoded by genetic material, we find that a prebiotically plausible subset of coded amino acids generally emulates the patterns found in the full set of 20, namely an exceptionally broad and even distribution of volumes and an exceptionally even distribution of hydrophobicities (quantified as logP) over a narrow range. However, the strength of this pattern varies depending on both the size and composition the library used to create a background (null model) for a random alphabet, and the precise definition of exactly which amino acids were present in a simpler, earlier code. Findings support the idea that a small sample size of amino acids caused previous ambiguous results, and further improvements in meteorite analysis, and/or prebiotic simulations will further clarify the nature and extent of unusual properties. We discuss the case of sulfur-containing amino acids as a specific and clear example and conclude by reviewing the potential impact of better understanding the chemical “logic” of a smaller forerunner to the standard amino acid alphabet.

Amino acids↗
NASA NTRS2000

Assessment of Countermeasure Efficacy for Long-Term Space Missions

One of the main functions of the upcoming International Space Station (ISS) will be to provide a venue for testing proposed countermeasures for their ability to protect humans from the debilitating effects of longterm space flight. However, several limiting factors preclude an evaluation process similar to that used in clinical trials which traditionally are implemented with large sample sizes of subjects, including control groups, and with blind or double-blind application of treatments according to factorial or other balanced experimental designs. In particular, only very limited numbers of human subjects will be available for actual field testing in the ISS With no more than 125 subjects planned to fly on all ISS missions over 10 years, it is not possible to test extensive combinations of some 15-20 proposed countermeasures. Furthermore because of safety concerns and operational considerations, it is unlikely that anything other than the current best guess at the most effective countermeasure package will ever be used on ISS. In particular, control or placebos will not be allowed. In view of these limitations, historical data and groundbased or animal studies will have to be used to compensate for small sample sizes and lack of controls in the field. As a result, statistical analysis methodology will have to be developed which allows for the integration of these disparate data types into a meaningful evaluation process. The process must be sequential, providing objective rules for deciding through time whether to reject or modify an ineffective countermeasure, or whether to certify one as effective. Additional output should include performance characteristics for all relevant physiological systems, including uncertainty analyses and estimates of accept/reject decision error rates.

Feiveson, Alan H.↗
NASA NTRS2008

Test Population Selection from Weibull-Based, Monte Carlo Simulations of Fatigue Life

Fatigue life is probabilistic and not deterministic. Experimentally establishing the fatigue life of materials, components, and systems is both time consuming and costly. As a result, conclusions regarding fatigue life are often inferred from a statistically insufficient number of physical tests. A proposed methodology for comparing life results as a function of variability due to Weibull parameters, variability between successive trials, and variability due to size of the experimental population is presented. Using Monte Carlo simulation of randomly selected lives from a large Weibull distribution, the variation in the L10 fatigue life of aluminum alloy AL6061 rotating rod fatigue tests was determined as a function of population size. These results were compared to the L10 fatigue lives of small (10 each) populations from AL2024, AL7075 and AL6061. For aluminum alloy AL6061, a simple algebraic relationship was established for the upper and lower L10 fatigue life limits as a function of the number of specimens failed. For most engineering applications where less than 30 percent variability can be tolerated in the maximum and minimum values, at least 30 to 35 test samples are necessary. The variability of test results based on small sample sizes can be greater than actual differences, if any, that exists between materials and can result in erroneous conclusions. The fatigue life of AL2024 is statistically longer than AL6061 and AL7075. However, there is no statistical difference between the fatigue lives of AL6061 and AL7075 even though AL7075 had a fatigue life 30 percent greater than AL6061.

Vlcek, Brian L.↗
NASA NTRS2012

Test Population Selection from Weibull-Based, Monte Carlo Simulations of Fatigue Life

Fatigue life is probabilistic and not deterministic. Experimentally establishing the fatigue life of materials, components, and systems is both time consuming and costly. As a result, conclusions regarding fatigue life are often inferred from a statistically insufficient number of physical tests. A proposed methodology for comparing life results as a function of variability due to Weibull parameters, variability between successive trials, and variability due to size of the experimental population is presented. Using Monte Carlo simulation of randomly selected lives from a large Weibull distribution, the variation in the L10 fatigue life of aluminum alloy AL6061 rotating rod fatigue tests was determined as a function of population size. These results were compared to the L10 fatigue lives of small (10 each) populations from AL2024, AL7075 and AL6061. For aluminum alloy AL6061, a simple algebraic relationship was established for the upper and lower L10 fatigue life limits as a function of the number of specimens failed. For most engineering applications where less than 30 percent variability can be tolerated in the maximum and minimum values, at least 30 to 35 test samples are necessary. The variability of test results based on small sample sizes can be greater than actual differences, if any, that exists between materials and can result in erroneous conclusions. The fatigue life of AL2024 is statistically longer than AL6061 and AL7075. However, there is no statistical difference between the fatigue lives of AL6061 and AL7075 even though AL7075 had a fatigue life 30 percent greater than AL6061.

Vlcek, Brian L.↗
NASA NTRSDate not supplied

X-Ray Diffraction Based Phase Identification in NiTiHf Shape Memory Alloys with Variable Hf Content

NiTiHf type shape memory alloys have been studied for use in high temperature actuator applications, the most studied of which is the NiTi-20Hf atomic % composition. In this study, six samples of NiTi-Hf including 20Hf, 30Hf, 35Hf, 40Hf, 45Hf, and 50Hf were evaluated by both 1D and 2D X-ray diffraction (XRD) to elucidate what phases and crystal structures were present at room temperature. Given small sample sizes and relatively large grains, multiple cross-sections were measured to increase the sampling statistics, and 2D XRD frames were collected to corroborate the 1D XRD data. Rietveld and structureless refinements were both performed, allowing for adjustments in orientation lattice constant, and structure factor. At room temperature, the primary martensitic phase in the NiTiHf alloys with 20 at% and lower Hf is a monoclinic B19’ phase (P1121/m space group). This phase was identifiable, even in small amounts, in the higher Hf samples. The primary phase in the 30 -50 at% Hf samples is an orthorhombic B33 (Cmcm space group) phase. This work supported thermal analyses indicating the phase transition paths from the two different room temperature martensitic phases to the B2 austenitic phase.

Laura Wilson↗