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Results for “Chi-square test”

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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Multivariate normality

Sets of experimentally determined or routinely observed data provide information about the past, present and, hopefully, future sets of similarly produced data. An infinite set of statistical models exists which may be used to describe the data sets. The normal distribution is one model. If it serves at all, it serves well. If a data set, or a transformation of the set, representative of a larger population can be described by the normal distribution, then valid statistical inferences can be drawn. There are several tests which may be applied to a data set to determine whether the univariate normal model adequately describes the set. The chi-square test based on Pearson's work in the late nineteenth and early twentieth centuries is often used. Like all tests, it has some weaknesses which are discussed in elementary texts. Extension of the chi-square test to the multivariate normal model is provided. Tables and graphs permit easier application of the test in the higher dimensions. Several examples, using recorded data, illustrate the procedures. Tests of maximum absolute differences, mean sum of squares of residuals, runs and changes of sign are included in these tests. Dimensions one through five with selected sample sizes 11 to 101 are used to illustrate the statistical tests developed.

Crutcher, H. L.↗
NASA NTRS1983

LANDSAT 4 investigation of thematic mapper and multispectral scanner applications

Six different band combinations of TM data were selected for evaluation by four experienced photointerpreters who were asked to rank the band combinations according to the ease with which the category of image feature designated for each set of combinations could be distinguished. There were four sets of combinations selected for each category of image feature. Scenes of Oklahoma City, Oklahoma and of the Sacramento Valley, California area were enlarged to 1:250,000 and 2 cm circular chips were cut from each print. A nonparametric rank order test was carried out on the data to determine if the interpreters found no difference among the band combinations in ranking for the designated categories. Kendall's coefficient of concordance (W) was calculated and the significance of the W value was determined by a chi-square test. A table summarizes the results of the evaluation and shows the rank order of band combinations indicated as valid by rejection of the null hypothesis.

Lauer, D. T.↗
NASA NTRS1975

Tables of critical values for examining compositional non-randomness in proteins and nucleic acids

A binomially distributed statistic is defined to show whether or not the proportion of a particular amino acid in a protein deviates from random expectation. An analogous statistic is derived for nucleotides in nucleic acids. These new statistics are simply related to the classical chi-squared test. They explicitly account for the compositional fluctuations imposed by the finite length of proteins, and they are more accurate than previous tables.

Laird, M.↗
NASA NTRS1976

X-ray spectra of the Puppis A and the Vela supernova remnants

Low-energy X-ray spectra are presented for the entire Vela supernova remnant (SNR), the two most intense subregions of the Vela SNR, and the Puppis A SNR. Acceptable chi-squared fits are obtained from the model of a high-temperature low-density plasma with Allen cosmic abundances when thermal bremsstrahlung, radiative recombination, line emission, and interstellar absorption are included. A suggested increase of 45-fold in the Si abundance for the entire Vela SNR is found unacceptable by chi-squared tests of the present spectra. The two enhanced regions of Vela are found to have different temperatures. A deficiency of at least a factor of 3 is seen in the O VII and O VIII emission from the entire Vela SNR. Because ultraviolet observations indicate a normal abundance of oxygen, this is interpreted as evidence for the existence of nonequilibrium conditions in the emitting plasma.

Moore, W. E.↗
NASA NTRS1979

Soft X-ray structure of the Coma cluster of galaxies

Results are reported for an observation of the Coma cluster with an imaging X-ray telescope system aboard a sounding rocket. A two-dimensional X-ray map of the cluster in the energy range from 0.15 to 2.0 keV is presented. The radial distribution, granularity, and ellipticity of the X-ray surface brightness are investigated, and the spectrum and flux within the field of view are analyzed. These properties are then examined quantitatively by comparing the observations with models through the use of a chi-squared test. It is found that: (1) no single galaxy contributes more than a few percent of the total X-ray flux of the Coma cluster; (2) the X-ray source is diffuse but granular on a scale of several arcmin, particularly in the central region; (3) the centroid of the X-ray source is at a local intensity minimum; and (4) the data are most consistent with an isothermal hydrostatic model.

Gorentstein, P.↗
NASA NTRS1978

Comparison of high energy gamma rays from absolute value of b greater than 30 deg with the galactic neutral hydrogen distribution

High-energy gamma-ray (energy above 35 MeV) data from the SAS 2 satellite have been used to compare the intensity distribution of gamma rays with that of neutral hydrogen (H I) density along the line of sight, at high galactic latitudes (absolute values greater than 30 deg). A model has been constructed for the case where the observed gamma-ray intensity has been assumed to be the sum of a galactic component proportional to the H I distribution plus an isotropic extragalactic emission. A chi-squared test of the model parameters indicates that about 30% of the total high-latitude emission may originate within the Galaxy.

Ozel, M. E.↗
NASA NTRS1981

A planetary nebula with high oxygen abundance in the galactic bulge

Extensive photoelectric spectra of the planetary nebula H1-55 in the galactic bulge are obtained, and indicate that the object is overabundant in oxygen and nitrogen. Temperature and density are estimated, and chi-square tests are used to place confidence limits on the result. The logarithmic oxygen abundance is found to be 9.50, and the abundance of other heavy elements are also enhanced, such as N = 8.87, S = 7.4, and Ar = 7.4. Helium, sulfur, and argon abundances are affected by uncertainties in the corrections for unobserved ions, which remains consistent with the exceptionally low electron temperature of less than 5600 K. Results agree with the usual models of planetary nebula formation; and therefore, if H1-55 is formed like most planetary nebulae, there must be some very metal-rich stars in the galactic bulge.

Price, C. M.↗
NASA NTRS1980

The Apollo 16 regolith - A petrographically-constrained chemical mixing model

A mixing model for Apollo 16 regolith samples has been developed, which differs from other A-16 mixing models in that it is both petrographically constrained and statistically sound. The model was developed using three components representative of rock types present at the A-16 site, plus a representative mare basalt. A linear least-squares fitting program employing the chi-squared test and sum of components was used to determine goodness of fit. Results for surface soils indicate that either there are no significant differences between Cayley and Descartes material at the A-16 site or, if differences do exist, they have been obscured by meteoritic reworking and mixing of the lithologies.

Kempa, M. J.↗
NASA NTRS1982

The Apollo 15 regolith - Chemical modeling and mare/highland mixing

The chemical compositions of thirty-one A-15 soils from nine sampling stations were studied. Mixing models were calculated using five components: 'representative A-15 mare basalt', anorthosite, low-K Fra Mauro basalt, green glass, and medium-K KREEP (Laul and Papike, 1980). A linear-least-squares mixing model (Boynton et al., 1975) was used with sum check and chi-square tests of the fit of components to soil composition. The soils show significant compositional variability, in some instances over relatively small distances within a sampling station. The models indicate that green-glass abundance does not vary systematically with location and that a significant KREEP component is found in all Apennine Front soils. The models also show the soils from the rim of Hadley Rille to be the most mare-enriched, and soils from Station 2 to be the most highland-enriched. The regolith from Station 8-LM is anomalously high in KREEP component relative to the other mare soils, possibly because of ray material.

Walker, R. J.↗
NASA NTRS1984

Statistical analysis of Thematic Mapper Simulator data for the geobotanical discrimination of rock types in southwest Oregon

An evaluation of Thematic Mapper Simulator (TMS) data for the geobotanical discrimination of rock types based on vegetative cover characteristics is addressed in this research. A methodology for accomplishing this evaluation utilizing univariate and multivariate techniques is presented. TMS data acquired with a Daedalus DEI-1260 multispectral scanner were integrated with vegetation and geologic information for subsequent statistical analyses, which included a chi-square test, an analysis of variance, stepwise discriminant analysis, and Duncan's multiple range test. Results indicate that ultramafic rock types are spectrally separable from nonultramafics based on vegetative cover through the use of statistical analyses.

Morrissey, L. A.↗
NASA NTRS1984

The distribution of hot spots

Statistical analyses are compared for two published hot spot data sets, one minimal set of 42 and another larger set of 117, using three different approaches. First, the earths surface is divided into 16 equal-area fractions and the observed distribution of hot spots among them is analyzed using chi-square tests. Second, cumulative distributions about the principal axes of the hot spot inertia tensor are used to describe hot spot distribution. Finally, a hot spot density function is constructed for each of the two hot spot data sets. The methods all indicate that hot spots have a nonuniform distribution, even when statistical fluctuations are considered. To the first order, hot spots are concentrated on one half of of the earth's surface area; within that portion, the distribution is consistent with a uniform distribution. The observed hot spot densities for neither data set are explained solely by plate speed.

Stefanick, M.↗
NASA NTRS1977

Multivariate-normality goodness-of-fit tests

Computer program applies chi-square Pearson test to multivariate statistics for application in any field in which data of two or more variables (dimensions) are sampled for statistical purposes. Program handles dimensions two through five, with up to thousand data sets.

Falls, L. W.↗
NASA NTRS1979

Statistical analysis of multivariate atmospheric variables

Topics covered include: (1) estimation in discrete multivariate distributions; (2) a procedure to predict cloud cover frequencies in the bivariate case; (3) a program to compute conditional bivariate normal parameters; (4) the transformation of nonnormal multivariate to near-normal; (5) test of fit for the extreme value distribution based upon the generalized minimum chi-square; (6) test of fit for continuous distributions based upon the generalized minimum chi-square; (7) effect of correlated observations on confidence sets based upon chi-square statistics; and (8) generation of random variates from specified distributions.

Tubbs, J. D.↗
NASA NTRS1974

Channel simulation for direct detection optical communication systems

A technique is described for simulating the random modulation imposed by atmospheric scintillation and transmitter pointing jitter on a direct detection optical communication system. The system is capable of providing signal fading statistics which obey log normal, beta, Rayleigh, Ricean or chi-squared density functions. Experimental tests of the performance of the Channel Simulator are presented.

Tycz, M.↗
NASA NTRS1974

Channel simulation for direct-detection optical communication systems

A technique is described for simulating the random modulation imposed by atmospheric scintillation and transmitter pointing jitter on a direct-detection optical communication system. The system is capable of providing signal fading statistics which obey log-normal, beta, Rayleigh, Ricean, or chi-square density functions. Experimental tests of the performance of the channel simulator are presented.

Tycz, M.↗
NASA NTRS1984

Specular reflectance of optical-black coatings in the far infrared

Far-infrared specular reflectance spectra of seven optically black coatings near normal incidence are presented. Seven photometric spectra were obtained using eleven bandpass transmission filters in the wavelength range between 12 and 500 microns, and three interferometric spectra were obtained for corroboration. Data on the construction, thickness, and rms surface roughness of the coatings are also presented. The chemical composition of three coatings can be distinguished from that of the others by a strong absorption feature between 20 and 40 microns, which can be largely attributed to amorphous silicate material. At 100 microns, the most and least reflective coatings differ by nearly 3 orders of magnitude. Inverse relationships observed between the spectra and the roughness and thickness of the coatings led to development of a reflecting-layer model for the measured reflectance. The model successfully describes the spectra at wavelengths outside the silicate absorption, and optical constants are deduced from a nonlinear least squares fit to the data. Parametric errors are estimated by chi-square analysis, and sensitivity tests are performed to determine which parameters control reflectance in different spectral regions.

Smith, S. M.↗
NASA NTRS1974

Chain pooling to minimize prediction errors in subset regression

The existing theory of subset regression is examined, taking into account optimality criteria, small experiments, nonlinear models, colinearities, and special techniques. Approaches based on chain pooling coupled with principal components regression are discussed, giving attention to a comparison of half-normal plotting with chain pooling, a procedure based on prior ordering, deletion under the F-test, the largest of a set of chi-square variates, and principal components regression and model deletion. The choice of a true (population) model for simulations is considered along with the evaluation of the decision procedure and suitable computer programs.

Holms, A. G.↗