A note on the interpretation of the statistical analysis of the $M_{\bullet}-M_{G}\sigma ^{2}$ scaling relation

If we make a set of measurements, such as narrow-band or multicolour photo-electric measurements, which are designed to improve a scheme of classification, and in particular if they are designed to extend the number of dimensions of classification, i.e. the number of classification parameters, then some important problems of analytical procedure arise. First, it is important not to reproduce the errors of the classification scheme which we are trying to improve. Second, when trying to extend the number of dimensions of classification we have little or nothing with which to test the validity of the new parameters.Problems similar to these have occurred in other areas of scientific research (notably psychology and education) and the branch of Statistics called Multivariate Analysis has been developed to deal with them. The techniques of this subject are largely unknown to astronomers, but, if carefully applied, they should at the very least ensure that the astronomer gets the maximum amount of information out of his data and does not waste his time looking for information which is not there. More optimistically, these techniques are potentially capable of indicating the number of classification parameters necessary and giving specific formulas for computing them, as well as pinpointing those particular measurements which are most crucial for determining the classification parameters.

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Quantitative parallel EELS spectrum imaging developed as a new tool in AEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010013064x ◽

1992 ◽

Vol 50 (2) ◽

pp. 1202-1203

Author(s):

Gianluigi Botton ◽

Gilles L'espérance

Keyword(s):

Statistical Analysis ◽

Spatial Resolution ◽

Personal Computer ◽

Systematic Study ◽

Present Author ◽

Chemical Elements ◽

Detection Limits ◽

Research Groups ◽

Quantitative Performance ◽

Spectrum Imaging

As interest for parallel EELS spectrum imaging grows in laboratories equipped with commercial spectrometers, different approaches were used in recent years by a few research groups in the development of the technique of spectrum imaging as reported in the literature. Either by controlling, with a personal computer both the microsope and the spectrometer or using more powerful workstations interfaced to conventional multichannel analysers with commercially available programs to control the microscope and the spectrometer, spectrum images can now be obtained. Work on the limits of the technique, in terms of the quantitative performance was reported, however, by the present author where a systematic study of artifacts detection limits, statistical errors as a function of desired spatial resolution and range of chemical elements to be studied in a map was carried out The aim of the present paper is to show an application of quantitative parallel EELS spectrum imaging where statistical analysis is performed at each pixel and interpretation is carried out using criteria established from the statistical analysis and variations in composition are analyzed with the help of information retreived from t/γ maps so that artifacts are avoided.

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Statistical analysis related to fetal heart rate patterns

American Journal of Obstetrics and Gynecology ◽

10.1016/s0002-9378(79)80052-6 ◽

1979 ◽

Vol 135 (1) ◽

pp. 168

Author(s):

H. William Perlis ◽

John F. Huddleston

Keyword(s):

Heart Rate ◽

Statistical Analysis ◽

Fetal Heart Rate ◽

Fetal Heart

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Mass spectroscopic measurements in the plasma edge of the W7-AS stellarator and their statistical analysis

Journal of Nuclear Materials ◽

10.1016/s0022-3115(96)00632-0 ◽

1997 ◽

Vol 241-243 (1) ◽

pp. 919-924

Author(s):

P Zebisch

Keyword(s):

Statistical Analysis ◽

Plasma Edge ◽

Spectroscopic Measurements

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248 Effects of compression on second order myocardial texture statistical analysis of digitally stored 2-D echocardiographic images

European Journal of Echocardiography ◽

10.1016/s1525-2167(99)80149-8 ◽

1999 ◽

Vol 1 ◽

pp. S43-S43

Author(s):

E FERDEGHNINI ◽

M MORALES ◽

M PIACENTI

Keyword(s):

Statistical Analysis ◽

Second Order ◽

Echocardiographic Images

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Statistical Analysis of Stochastic Processes in Time

10.1017/cbo9780511617164 ◽

2004 ◽

Cited By ~ 33

Author(s):

J. K. Lindsey

Keyword(s):

Statistical Analysis ◽

Stochastic Processes

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Intraindividual Variability in Development Within and Between Individuals

European Psychologist ◽

10.1027//1016-9040.6.3.187 ◽

2001 ◽

Vol 6 (3) ◽

pp. 187-193 ◽

Cited By ~ 47

Author(s):

John R. Nesselroade

Keyword(s):

Statistical Analysis ◽

Research Design ◽

Intraindividual Variability ◽

Factor Analytic

A focus on the study of development and other kinds of changes in the whole individual has been one of the hallmarks of research by Magnusson and his colleagues. A number of different approaches emphasize this individual focus in their respective ways. This presentation focuses on intraindividual variability stemming from Cattell's P-technique factor analytic proposals, making several refinements to make it more tractable from a research design standpoint and more appropriate from a statistical analysis perspective. The associated methods make it possible to study intraindividual variability both within and between individuals. An empirical example is used to illustrate the procedure.

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