Cosmic Membrane Theory of Gravitation

Cosmic Membrane Theory of Gravitation

Welcome at the Homepage of

Stefan von Weber

Physicist Dr. rer. nat. Dr. sc. techn.

University of Applied Sciences HS Furtwangen

Department of Mechanical and Environmental Engineering

(First web-version September 24, 2002 / last update Oct 17, 2008)

The Content of this Page

1 Physical Research: Cosmic Membrane Theory of Gravitation Part 1 (Please click here)

1 Introduction

2 Newtons Law and the Cosmic Membrane

3 Differential Approach and Numerical Calculations to Curvature

4 Special Relativity

4.1 Longitudinal and Transversal Contraction

4.2 Coordinate and Time Transformation

Part 2 (Please click here)

4.3 Momentum, Mass and Energy

4.4 Membrane Theory and Basic Physical Phenomenons

4.5 Experiments Concerning Special Relativity

4.6 Apparent Constancy of Velocity of Light

4.7 Tidal and Frequency Effects

5 Classical Proofs of General Relativity

5.1 Shapiro Effekt, Light Bending and Depth of Space

5.2 Perihelion Advance of Mercury

Part 3 (Please click here)

6 Novel Proofs of General Relativity

6.1 Electron and Space Torsion

6.2 Gravitational Waves

6.3 Anomalous Acceleration of Pioneer 10 and 11

7 Cosmology

7.1 The Cosmological Constant and the Expansion of the Universe

7.2 Dark Matter and Frame Dragging

7.3 Quintessence or Dark Energy and the Expansion of the Universe

7.4 Dark Matter and Space Drilling,Geodetic Precession (de Sitter Precession)

Part 4 (Please click here)

8 Analysis and Conclusions

References

Additional papers concerning Membrane Theory:

Kosmische Membrantheorie - ein didaktisches Modell

Newtons absoluter Raum (printed 1995)

Membrane Theory of Gravitation (printed 1998)

Proofs of the Cosmic Membrane Theory (printed 2002)

Source Codes of used calculations in membrane theory

Gravitation – die Kraft aus der vierten Dimension (Deutsch)

Gravity – the force from the fourth dimension (English)

Gravitation - la force de la quatrième dimension (Française)

2 Statistical Research

2.1 CWA - a Robust Regression Algorithm

2.2 CFA/KFA - Configural Frequency Analysis

2.3 DASY - Daten Analyse System

3. Ausbildung von Ingenieuren / Education of Engineers

Biotechnologie (Biotechnology), Verfahrenstechnik (Process engineering), Biomedical Engineering (Master Course)

1. Skript zur Automatisierungstechnik für UV4 (MS-WORD-Document)

2. Script of the lecture Biomedical Statistics (MS-WORD-Document)

3. Skript zu Biomedizinische Statistik (MS-WORD-Document)

4. Skript Informationsverarbeitung (Programmierung, Anwendung) (MS-WORD-Document)

5. Skript Mathematik 2

4. Publications / Veröffentlichungen

If you have a question or an advice or you like to discuss with me or you want to get the original MS-Word documents or the source code of the used calculating programs, please then click here at CONTACT

Part 1: Physics

A short description of the

COSMIC MEMBRANE THEORY

OF GRAVITATION

ABSTRACT

The proposed membrane theory of gravitation is of type Kaluza-Klein with non-compactified fourth spatial dimension and delivers Newton's law of gravitation in a direct way and explains light bending, Shapiro effect and perihelion advance of Mercury with the same accuracy as the General Relativity (GR). The basic idea is that the 3D-membrane (the quantum vacuum, soliton, brane, supermembrane or superbrane, expanding shell) expands as a balloon in an ether-filled 4D-space. Matter within the membrane resists the ether wind and causes so the curvature of the membrane. There is no reason to believe that the speed of gravity is greater than the speed of light. From the point of view of the proposed Cosmic Membrane Theory (CMT) the GR of Albert Einstein is a projection of the 4-dimensional space into the 4-dimensional spacetime.

There exists a direct line from Einstein's 4D-spacetime, Kaluza's idea of a fourth spatial dimension over Ponce de Leon, Price & Thorne, Wesson & Liu and Haisch & Rueda, Polchinski, Witten and Duff to the cosmic membrane. The theory is easy to understand since it is a geometrical theory. Both, the geometrical and the differential approach deliver the same differential equation of space curvature.

The computation of the energy flow of longitudinal gravitational waves yields the same value as calculated by the GR. The Lense-Thirring effect (frame dragging effect) does not exist in the context of Cosmic Membrane Theory, but another effect of space torsion or frame dragging is thinkable. The calculation of the de Sitter precession (or geodetic precession) of gravity probe B (gpb) yields the same value of 6.6 arcseconds precession, as the GR does. The calculation of the Compton wavelength of the electron is using the estimated density of the membrane. Both, the velocity of light c and the rest mass of a body depend on the strength of gravity. An investigation of the Gravitational Red-shift of Photons shows that Planck's constant must change its value with field strength of the gravitational field. Spontaneous creation of new matter seems to be possible, because the resistance of the existing matter inside the membrane is delivering great amounts of energy.

The depth of space W_o at the edge of sun is a central value of the Cosmic Membrane Theory. From its value one can calculate the ether-acceleration A_e (equivalent to the force caused by the ether wind acting on a mass) and the tension F_o of the membrane. Higher terms of the formulas of signal retardation and light bending yield values of W_o, but with great error bars. A similar value of the depth of space W_o we find, and thus anew the connection back to the GR, if we take Feynman's radius of excess of the sun r_Ex=491[m] as the geometrical path lengthening dS_R from the edge of Sun to its centre.

There is a significant difference between GR based cosmology and membrane Theory. In all GR based models, e.g. the Einstein-Friedmann models or the Friedmann-Lemaitre models, the expansion of space depends on mass or energy parameters. The Friedmann equations suggest that baryonic mass, dark matter or a cosmological constant (vacuum energy) can influence the expansion rate of our universe. The Membrane Theory denies this imagination. The mass and the speed of the membrane is so overwhelmingly greater than all baryonic mass, dark matter and other forms of matter or energy inside our three spatial dimensions that this forms of matter can not influence the speed of expansion in any way. The Friedmann equations describe a three-dimensional cosmos, Membrane Theory a four-dimensional one. In this context questions became obsolete concerning the critical mass, W, e.g., or the signature of the metric. The metric of our universe is spherical, but nearly flat in the visible part because of the vast radius.

The Cosmological Constant is given by the action of the membrane tension F_o in opposite direction to the expansion direction of the Universe. It has a small value only. Quintessence or Dark Energy is the kinetic energy of the Virial Mass of the membrane in direction of the expansion. The expansion does not accelerate, but speed of light and the eigen-time of the Universe. Reversely, the membrane density decreases. The inflation of the Universe at the first milliseconds follows from the special behaviour of the eigentime. The first time ticks had been very long, i.e., in a short eigentime the Universe stretched over many orders of magnitude. The Universe seems to us to be flat, i.e., to have an Euclidean metric. This follows from the vast radius of the Universe. The expansion speed V_E is assumed here to be much greater than the speed of light. The Cosmic Membrane Theory yields two new candidates of Cold Dark Matter (CDM). Both candidates are not real matter, but a violation of the law of gravitation in the environment of real matter. The first cold dark matter effect is caused by the ether wind, the second effect is caused by frame dragging.

The anomalous acceleration of the spacecrafts Pioneer 10 and 11 is caused by the neglection of a small sun-near potential which plays a role, e.g., by the perihelion advance of the planet Mercury.

The Special Relativity remains nearly unchanged. With the Lorentz transformation we can describe all effects of Special Relativity without any change of the formulas, although the author describes still another similar transformation which one could use. Vladimir V. Onoochin has found independently the same transformation with length and cross contraction. The conservation laws of energy and momentum, Maxwell's equations, the experiments of Michelson-Morley and Kennedy-Thorndike (interferometer), Fizeau (Fresnel's drag coefficient), Airy (aberration), Haefele-Keating (clocks), Trouton-Noble (plate capacitor), Sagnac (rotating interferometer) and, as well as the Thomas precision of the electron or the apparent constancy of light - they all do not harm.

Two technical exploitations could become interesting some day - in a far future - the ether sail and the ether mill (ether engine). The ether sail is a body deflecting the ether wind from fourth dimension so that the ether wind gets a component in our common three dimensions, and in this way it causes a repulson force. It could be a way to reach with a space craft speeds near the speed of light. The ether engine is consisting of two or more ether sails placed on a wheel and making it rotate. The energy is coming from the vast and inexhaustible virial energy of the expanding membrane (called dark energy or quintessence).

Acknowledgements

First of all I thank Burkhardt Seifert (Zuerich) for his critical reading and helpful discussions of a lot of my papers.

In our university this work was supported by the Membrane Research Group of the Fachhochschule Furtwangen University. Especially, Manfred Raff (Schwenningen) gave me helpful aid concerning the properties of technical membranes. I thank also Friedrich Engelke (Furtwangen), Uwe Klemm and Walter Zahradnik (both Schwenningen) for their interest and helpful discussions.

Hans-Joachim Blome (Aachen) and Wolfgang Priester (Bonn) helped me with papers and aid. Furthermore, I thank Robert J. Bradbury (Washington) for a dark-matter discussion, Carlos Calvet (Barcelona) for the discussion concerning the Background Field and the Primordial Star, Tom Van Flandern for a discussion concerning the speed of gravity, Ronald Hatch (Redondo Beach) concerning aether discussion and clocks, Thomas Naumann (Berlin) concerning speed of light.

Patricio Valdés Marin I thank for a discussion concerning gravity and the shape of the universe.

Jeffrey O'Callaghan, Juan Echaurren and Christian Mills I thank for a discussion concerning four spatial dimensions,cosmology and gravitation and for the title "collaborator" One can reach their theory "the shadows of four spatial dimensions" at http://home.comcast.net/~jeffocal/shadows.htm. I thank Terry Matilsky from the State University of New Jersey for a fine discussion concerning Dark Matter and the properties of particles.

Tuomo Suntola at www.sci.fi/~suntola I thank for a good discussion concerning the 4-sphere, energy balance in the Universe and varying speed of light. I thank Vladimir Onoochin, Moscow, who discussed cross and longidudinal contraction and other questions concerning the resting ether model with me. In 2004/2005 we wrote a joint paper.

Interesting questions will be answered by L3xicon.com - a web thesaurus and lexicon listing fh-furtwangen.de/~webers/index.htm under Newton, gravitation and curvature .

Hamed Vahidi of Juno.com I thank for an interesting discussion concerning expansion of space and its physical meaning. I thank Dieter Kolpert (Braunschweig) for an interesting discussion concerning space, curvature of space and matter. Alexandar Balevsky I thank for a good discussion concerning the spiral arms of galaxies with surprisingly nice ideas.

Cited Authors

(Full list of references in Part 4 of Membrane Theory)

A. Abramovici, P. A. R. Ade, A. Albrecht, F. Aldabe, G. Aldering, G. Allen, W. E. Althouse, R. A. Alpher, J. D. Anderson, N. Andersson, G. Antoni, T. B. Andrews, M. E. Ash, J. G. Assis, P. Astier, A. Babul, N. A. Bahcall, D. Barnaby, J. D. Barrow, U. Bartocci, R. A. Battye, K. G. Begeman, J. D. Bekenstein, A. Berera, P. de Bernadis, O. Bertolami, B. Bertotti, H. A. Bethe, V. B. Bezerra, A. Billyard, S. Bize, H. J. Blome, J. J. Bock, C. Boehm, J. R. Bond, J. Borrill, A. Boscaleri, G. D. Bothun, C. H. Brans, L. de Broglie, J. C. Breidenthal, J. P. Brenkle, D. Brill, W. Bruckman, G. Burbidge, F. Burgbacher, R. T. Cahill, D. L. Cain, C. Calvet, D. B. Campbell, B. Carter, R. Ciardullo, S. Carlip, S. Capozziello, S. M. Carroll, W. E. Jr. Carter, M. Casse, E. Chachoua, P. Challis, F. H. Cheng, J. N. Chengalur, C. W. Churchill, I. Ciufolini, A. Clairon, M. A. Clayton, A. Clocchiatti, K. Coble, R. L. Collins, H. C. Corben, S. Cornbleet, T. E. Cranshaw, B. P. Crill, W. F. Cuddihy, F. Darabi, E. W. Davies, C. Deffayet, R. Deustua, R. H. Dicke, A. Diercks, Y. Dobyns, D. Dogosyan, C. Doran, A. Dressler, R. W. P. Drever, M. J. Drinkwater, I. T. Durham, M. J. Duff, G. Dvali, R. B. Dyce, J. Echaurren, P. A. Egelstaff, A. Einstein, J. Ellis, R. Ellis, E. P. Esteban, C. W. E. Everitt, S. Fabbro, K. Farakos, P. C. Farese, L. Ferrarese, P. G. Ferreira, R. P. Feynman, A. V. Filippenko, V. V. Flambaum, T. Fliessbach, E. B. Fomalont, M. J. Fomerth, H. C. Ford, A. Friedmann, W. L. Freedman, J. A. Frieman, A. S. Fruchter, W. H. Furry, C. Furtado, T. Futamase, G. Gabadadze, B. Gaensicke, G. Gamov, K. Ganga, P. M. Garnavich, G. de Gasperis, R. Gass, P. Gerber, M. Giacometti, B. K. Gibson, R. Gilliland, M. L. Giroux, G. Goldhaber, R. B. Goldstein, A. Goobar, M. Grady, J. A. Graham, B. Greene, D. E. Groom, Y. Gürsel, A. Guth, J. C. Haefele, B. Haisch, T. Hamana, M. Hamuy, A. T. Jr. Harley, R. R. Hatch, S. W. Hawking, F. W. Hehl, R. A. Herrmann, P. Heyde, E. Hivon, J. Hoell, C. Hogan, I. M. Hook, D. Hooper, P. Horava, F. Hoyle, V. V. Hristov, M. Huang, J. P. Huchra, G. Huey, S. M. G. Hughes, A. Iacoangeli, L. Iess, G. D. Illingworth, C. Impey, R. I. Ingalls, M. Irwin, A. V. Ivanchik, H. E. Ives, A. H. Jaffe, B. Jimerson, G. Joos, S. Kachru, C. Kacser, D. Kalligas, Th. Kaluza, H. S. Kang, T. M. Kaufman, S. Kawamura, R. Keating, C. R. Keeton, D. D. Kelson, R. J. Kennedy, R. C. Kennicutt Jr., G. D. Kerlick, M. Keyl, J. Khoury, A. Kim, M. Y. Kim, R. P. Kirshner, O. Klein, R. A. Knop, I. I. Kogan, K. D. Kokkotas, E. W. Kolb, T. A. Komarek, S. M. Kopeikin, V. Krasnoholovets, L. M. Krauss, C. Laemmerzahl, P. A. Laing, S. J. Landau, A. E. Lange, T. N. LaRosa, A. L. Larsen, A. Lasenby, E. L. Lau, A. Laurence, J. H. L. Lawler, B. Leibundgut, A. Lewis, J. E. Lidsey, D. E. Liebscher, O. Q. Lim, H. Liu, J. T. Liu, H. A. Lorentz, J. Louko, C. Maccone, A. Macias, P. E. MacNeil, L. M. Macri, B. F. Madore, L. Magnani, J. Magueijo, C. Mandache, A. G. Markowitz, P. Marmet, H. Martel, L. Martinis, B. Mashhoon, P. Mason, T. Matilsky, J. Mattei, W. Mattig, R. Matzner, P. D. Mauskopf, N. E. Mavromatos, J. Maza, S. S. Gaugh, A. Melchiorri, F. Melia, F. M. Meno, K. Meyl, W. H. Jr. Michael, A. A. Michelson, L. Miglio, M. Milgrom, Ch. Mills, V. A. Mitsou, J. W. Moffat, T. Montroy, F. Moraes, E. W. Morley, A. Moss, J. R. Mould, M. Mukherjee, D. V. Nanopoulos, J. V. Narlikar, J. M. Nester, C. B. Netterfield, G. Neugebauer, M. M. Nieto, K. Nordtvedt, P. Nugent, J. O'Callaghan, K. O'Neil, Y. N. Obukhov, K. Olive, V. V. Onoochin, R. Opher, J. P. Ostriker, D. Overbye, J. M. Overduin, B. Ovrut, N. Pailer, R. Pain, N. Panagia, E. Pascale, J. J. Paul, M. Pavsic, K. Pennicott, C. R. Pennypacker, A. A. Penzias, S. Perlmutter, M. J. Perry, P. Petitjean, G. H. Pettengill, A. O. Petters, M. M. Phillips, F. Piacentini, J. Polchinski, J. Ponce de Leon, M. Porrati, R. V. Pound, P. Premadi, R. H. Price, W. Priester, S. J. Prokhovnik, S. Prunet, H. E. Puthoff, R. Quimby, F. J. Raab, G. G. Raffelt, A. F. Ranada, L. Randall, S. Rao, J. Raux, R. D. Reasenberg, D. Reiss, A. G. Riess, D. S. Robertson, E. Rodriguez, G. Romeo, A. Rueda, M. L. Ruggiero, J. E. Ruhl, P. Ruiz-Lapuente, W. A. Sabra, W. N. Sajko, S. Sakai, C. Salomon, E. E. Salpeter, R. H. Sanders, M. S. Santos, M. Sati, F. Scaramuzzi, B. E. Schaefer, J. P. Schiffer, I. Schmelzer, B. P. Schmidt, H. K. Schmidt, E. Schmutzer, R. A. Schommer, D. Schramm, B. F. Schutz, N. Seiberg, F. Selleri, R. Sexl, D. Sforna, B. Shahid-Saless, I. I. Shapiro, P. R. Shapiro, D. Shoemaker, S. N. Shore, E. R. Siegel, L. Sievers, J. Silk, E. Silverstein, A. K. Singal, E. M. Sion, W. de Sitter, T. Sleator, R. Smith, J. L. Snider, Y. Sortais, W. Sparks, R. E. W. Spero, J. H. Spurk, J. Spyromilio, A. A. Starobinsky, G. Steigman, P. J. Steinhardt, P. B. Stetson, G. R. Stilwell, H. Stoecker, C. Stubbs, R. Sundrum, T. Suntola, N. B. Suntzeff, P. Szkody, A. Tartaglia, A. N. Taylor, Y. Terzian, E. M. Thorndike, K. S. Thorne, W. G. Tifft, J. L. Tonry, P. Tortora, H. J. Treder, M. Trodden, M. S. Turner, N. Turok, S. G. Turyshev, J. A. Tyson, J. K. Webb, P. S. Wesson, T. Van Flandern, P. Valdés Marin, D. A. Varshalovich, N. Vittorio, R. E. Vogt, M. I. Vuletic, T. P. Walker, J. Walsh, N. Walton, A. Watson, S. Weinberg, R. Weiss, J. A. Wheeler, S. E. Whitcomb, M. White, C. M. Will, R. W. Wilson, D. L. Wiltshire, E. Witten, D. K. Yeomans, M. Zaldarriaga, M. E. Zucker, A. Zygielbaum

Part 2: Statistics

2.1 THE CW-ALGORITHM

(mit freundlicher Genehmigung von Thomas Carl Cierzynski, WIAS Berlin)

Der CW-Algorithmus zur Merkmalsselektion in der multiplen Regressionsanalyse ist besonders effektiv in Fällen, wo mehr Merkmale zur Auswahl stehen, als Messpunkte vorhanden sind, und zusätzlich ein hoher Restfehler in der Vorhersage der Zielvariablen zu erwarten ist. Von gleichartig wirkenden Merkmalen wird nicht unbedingt eines selektiert und die anderen verworfen, sondern es findet automatisch eine Mittelung statt. Die zukünftige Forschung an diesem Algorithmus betrifft das Abbruchkriterium der Iteration. Unendliche Iteration liefert die Gauß-Markov-Lösung mit ihren bekannten Nachteilen im Falle realer Daten.

The CW-Algorithm is used in the selection of variables in the multiple regression analysis. The algorithm works especially effectively in cases where more variables exist than measuring points, and one expects additionally a high amount of residual error. If there is a group of similar variables, the algorithm averages them instead to select one of them. We will concentrate the future research on the stop criterion of the algorithm. Infinite iteration yields the Gauss-Markov solution, which has known disadvantages in the case of real data.

Many investigations had been carried out to find stable algorithms for the use in statistical applications (Bai 1988, Cook/ Weisberg 1994, Läuter 1994, Wegscheider 1984). The CW-algorithm (Cierzynski/ v.Weber 1990) was originally developed for the use in regression analysis. There it reduces about 10% of the mean quadratic error of prediction compared with the best stepwise algorithm. The use of the CW-algorithm is practicable if data are prone to relatively great errors, if more variables exist than individuals and the variables are highly correlated (Cierzynski/v.Weber 1992). On the other hand, for theoretical reasons, the use of the CW-algorithm in the discriminant analysis e.g. cannot deliver results as good as those for the regression analysis. The reason is the lack of the dominating effect of CWA, the inherent variable selection. However the positive effect, that similar variables are averaged instead of subtracted, results in a more stable solution in this case also.

Cited Authors

Bai, Zhao Jun , Cierzynski, T. C, Cook, R. D., Fahrmeir, L., Hamerle, A. , Läuter, J. , Wegscheider, K. ,Weisberg, S.

2.2 Configuration Frequency Analysis (CFA/KFA)

Die Konfigurations-Frequenz-Analyse (KFA) ist eine Methode zur Auswertung von Kontingenztafeln. Kontingenztafeln entstehen z.B. bei der Auszählung von Fragebögen. Der Begründer der KFA war G.A.Lienert.

The Configural-Frequency-Analysis (CFA) is a method to analyse contingency tables. Contingency tables, e.g., one uses handling questionnaires. The method was founded by G.A.Lienert.

Ein Vergleich in der KFA verwendeter Tests mittels Simulationsrechnungen

Das Ziel des Autors bei seinen Untersuchungen war die Herausgabe einer Empfehlung für den Praktiker, welcher Test und welche Testprozedur für seine Daten die sichersten Ergebnisse liefert. Es wurden Kontingenztafeln der Dimension (Merkmalszahl) d=2, 3 und 4 simuliert. Verwendete Testprozeduren waren Holms Prozedur und die zweistufige Suche. Alle Tests wurden einseitig mit H_o:kein Typ oder Antityp und H_A: Typ durchgeführt. Die in diesem Papier untersuchten 5 Tests waren: Der X-Komponententest von G.A.Lienert, der Binomialtest von Krauth, der hypergeometrische Residualtest von Lehmacher mit Stetigkeitskorrektur nach Küchenhoff, derr asymptotische Test nach Perli, Hommel und Lehmacher, der Test nach Victor, Dunkl und v.Eye. Neu dürfte die Einbeziehung von Kombinationstesten nach einer Idee von Erwin Lautsch sein Die Resultattabellen liefern a und b in Abhängigkeit von der Zellenzahl und mittleren Zellenbelegung der Tafel, des vorgegebenen a und dem Gewicht der Kontingenztypen.

A Comparison of Tests used in the CFA by Simulation

by Stefan von Weber, 2000

Comparison (by simulation) of 5 tests and 2 test procedures used in the CFA to explore and confirm types. The comparison is based on the observed a and b ( error type 1 and type 2). In the simulation was varied the demanded a, the number of cells, the mean cell frequency of the contingency table and the ratio of weight of the type to mean cell frequency. As a result of this study the author gives recommendations which test one uses best for a given table. Combined tests proposed by E.Lautsch are new.

Key words: contingency table, configural frequencies analysis, CFA, type exploration, test, test procedure, simulation, combined tests

Table-specific continuity corrections for Configural Frequency Analysis

submitted

Stefan von Weber, Erwin Lautsch, Alexander von Eye

Für sechs verschiedene KFA-Tests werden neue Stetigkeitskorrekturen vorgestellt. Die Korrektur ist eine Konstante für eine Tafel. Sie hängt von den Eigenschaften der Tafel (Freiheitsgrade, Dimension, mittlere Zellbelegung, Typgewicht) und vom vorgegebenen Fehler 1. Art ab. Das Typgewicht ist eine quantitative Bewertung von Typen. Simulationsrechnungen zeigen, dass drei Tests (der Test von Perli et al., die Neue Prozedur von Lautsch/v.Weber, der CHI-Quadrat-Komponententest von Lienert) 90% der besten Lösungen abdecken.

This article presents new continuity corrections for six tests in Configural Frequency Analysis (CFA). For each table, the correction is a constant. The magnitude of this constant depends on characteristics of the table such as degrees of freedom, size, cell frequency, strength of type, and on the nominal level α. Strength of type is a quantitative descriptor of types. Simulation results suggest that, three tests, specifically the test proposed by Perli et al., the new test proposed by Lautsch and von Weber, and the CHI-square-component test, cover over 90% of the best solutions.

On the limits of Configural Frequency Analysis:

Analyzing small tables, in preparation

by Stefan von Weber, Alexander von Eye, Erwin Lautsch

Abstract

Configural Frequency Analysis (CFA) is known to be a useful tool for the exploration of contingency tables. Typical applications of CFA use tables of moderate size, that is, tables that are spanned by 3 to 5 variables, each having about 3 categories. In this article, we ask whether CFA can be meaningfully applied to 2 x 2 tables. We present analytical and simulation results that suggest that, because of the dependency of tests, first order CFA which takes the main effects into account is not a suitable candidate for 2 x 2 table analysis. Zero order CFA of 2 x 2 tables is more promising because three degrees of freedom are available instead of only one for first order CFA of 2 x 2 tables.

A New Test Procedure in the CFA

E. Lautsch, S. von Weber

Summary, Zusammenfassung

One of the aims of the Configural Frequency Analysis (CFA) is the identification of symptom configurations as types or anti-types. Following the pattern of an efficient regression algorithm of Cierzynski and v. Weber the authors developed a gradient method, which minimizes iteratively the total c² of a contingency table, reducing by a small amount the frequency of the most suspicious cell in the step of iteration (in the case of an anti-type the frequency will be increased). The final result is a table, which fulfills perfectly the hypothesis of independence. The expectation values one can calculate from this table are known as Victor-expectation values in the literature. With this values and the original cell frequencies the trustworthy small-group test of Dunkl and v.Eye is performed and then confirmed by Holm's procedure. With a Bayesian ansatz (types are hidden by preference in highly frequented cells) a further improvement of the results has been reached. Numerical simulations are showing the correctness of the method. A comparison with the results of the "new approach" of Kieser and Victor is showing a large measure of conformity.

Independency or Association in 2x2 contingency tables

in preparation

by Alexander von Eye, Erwin Lautsch, Stefan von Weber

abstract

The results of a simulation study on the performance of measures for the analysis of 2 x 2 tables are reported. The simulations included 11 measures for 2 x 2 tables: Pearson's χ, the standard normal z, the log-odds ratio, the log-linear interaction, Goodman's (1991) weighted log-linear interaction, Vogel's z, the binomial test, Lehmacher's (1981) asymptotic hypergeometric test, Perli, Hommel, and Lehmacher's (1985) asymptotic test, Lindner's (1984) exact hypergeometric test, and Lausch and von Weber's (2002) adaptation of Dunkl and von Eye's (1990) test. The factors varied in the simulations were (1) type of sampling distribution, (2) sample size, (3) strength of association in the 2 x 2 table, (4) the symmetry of the distribution in the 2 x 2 table, and (5) the nominal α. Results suggest that the distribution of these 11 tests is very near the normal under all conditions. Of the five factors, only the type of the sampling distribution has no strong effects on the β-curves of the 11 measures. Finally, it was found that the 11 measures respond differently to the five factors such that the rank order of performance varies with the simulated conditions.

Combinatoric Search for Types and Antitypes

Stefan von Weber, Alexander von Eye, Erwin Lautsch

Zusammenfassung

Die von Kieser und Victor 1991 vorgeschlagene kombinatorische Typensuche wurde im Rahmen der üblichen KFA-Methodik realisiert. Ein Teil der Verbesserungen gegenüber früheren Such- und Testverfahren ergibt sich durch zusätzliche Terme in der Suchstatistik, die über die Vorschläge von Kieser und Victor hinausgehen. Vergleiche der kombinatorischen Typensuche mit vier anderen Verfahren zeigt die Power des neuen Verfahrens: Es ist in allen Vergleichen besser als die betrachteten Konkurrenzverfahren.

Abstract

The authors realised a Combinatoric Search Procedure for types, proposed by Kieser and Victor in 1991, within the frame of the CFA methodology. One part of the improvements, compared with former search and test procedures, is a result of additional terms of the search statistic. This terms are new. A comparison of the combinatoric search with four other test procedures shows the power of the new algorithm. It is better in all cases than the considered competitive methods.

In 1999 Kieser and Victor published the paper "Configural Frequency Analysis (CFA) Revisited - a New Look at an old Approach". Here the conception was transformed to a log-linear model. The use of a log-linear base model has the advantage that one can change it with a simple change of the design matrix. Types are found as residuals with a positive deviation, antitypes as residuals with a negative deviation. A multiplicity issue arises from the fact that the proof of types requires both testing the null-hypothesis of the non-type/antitype cells and the alternative hypothesis for the type/antitype cells.

The authors decided in 2002 to make some afford to establish the originally intended combinatoric CFA-procedure, i.e. to remain in the frame of classical CFA. Since 1991 the speed and memory capacity of PCs have dramatically increased. So we have had a good chance to overcome the time issue.×

Cited Authors

Cierzynski, T. C., Diaconis, P., DuMouchel, W., Dunkl, E., Efron, B., von Eye, A., Feige, K.-D., Goodman, L. A., Guiard, V., Guiterrez-Pena, E., Herrendoerfer, G., Holm, S., Hommel, G., Indurkhya, A., Kareev, Y., Kieser, M., Koehler, K. J., Krauth, J., Kuechenhoff, H., Larntz,K., Lautsch, E., Lehmacher, W., Lienert, G. A., Lin, C.-D., Lindner, K., Liu, K.-J., Mun, E.-Y., Perli, H.-G., Preece, P. F., Rosenthal, R., Rovine, Rubin, D. B., M. J., Schmacker, R. E., Schuster, Thompson, K. N., C., Spiel, C.,Victor, N., Vogel, F.

2.3 DASY - Daten Analyse System

Boxplots

Scatterplots und Korrelation

Das Daten Analyse System DASY der HS Furtwangen University ist Freeware. Es ist ein kleines Statistik-Paket mit einigen Besonderheiten. Unter anderem enthält DASY eine:

- Konfigurationsfrequenzanalyse (KFA) mit Alpha- und Beta-Kontrolle und der effektiven Typensuche nach der neuen Combinatoric Search Prozedur von von Eye, Lautsch, von Weber nach einer Idee von N. Victor. Die KFA in DASY ist eine Weiterentwicklung des kleinen Pakets SICFA aus dem KFA-Buch von Lautsch/vonWeber.

- Multivariate kategoriale Merkmalsauswahl über das Chi-Quadrat der Kontingenztafel bis 20 Startmerkmale

- Analyse von 2x2-Kontingenztafeln mit der Berechnung von 6 Assoziations- bzw. Zusammenhangsmassen mit Signifikanz und Betaschaetzung, Typensuche nach dem Zero-Order-Modell von A. v. Eye, Vergleich von relativen Häufigkeiten

- Bootstrap-Simulation zur Bestimmung des zellspezifischen Beta-Fehlers

einer Kontingenztafel

- Auto- und Kreuzkorrelationsfunktionen, Produkt-Momenten Korrelation

mit Scatterplots und Histogrammen

- Lineare und nichtlineare einfache Regressionsmodelle

- Multiple Regressionsanalyse mit dem CW-Algorithmus oder dem Stepwise-Algorithmus, Wichtung, nichtlineare Modelle, Prognosefehlerschätzung mit Jackknife-Methoden

- Einfache Varianzanalyse mit 3 Mittelwertvergleichen und Boxplots

- Diskriminanzanalyse nach H. Ahrens und J. Laeuter mit multiplem

Mittelwertvergleich und Schätzung des Klassifikationsfehlers mittels Jack-knife

- Clusteranalyse mit Merkmalsranking nach einem Kontingenztafel-Informationsmass, 3 Methoden zur Bestimmung der Kernobjekte, 3 Linkage-Methoden und Reklassifikation mit den Mitteln der Diskriminanzanalyse

- Verschiedene Dateneingaben (z.B. auch für den PREMA-Messcomputer oder den micromec-Datenlogger oder für Kontingenztafeln)

- Datenprüfungen, z.B. Minimum, Maximum, Ausreißerkontrolle, Quantile,

Test auf Normalverteilung, Boxplots

- Umfangreiche Möglichkeiten der Datentransformation zur Modellbildung

- Umfangreiche Online-Hilfe auf Deutsch

- Alle Ausgaben auf Deutsch, Graphiken als Bitmap

- DASY kann mit der Tastatur allein oder aber mit Maus und Tastatur gemeinsam bedient werden

- DASY ist ein DOS-Programm, das den VGA Modus der Graphikkarte benötigt

Externe Nutzer von DASY außerhalb der Hochschule Furtwangen / External Users of DASY :

Liat Hasenfratz, Erwin Lautsch, Manfred Schaerfke, Dirk Groneberg, T. Schandert, Herta Pohl, Dennis Pfisterer, Hubert Gerspacher, Christoph Koerber, Roman Richter, Norbert Schinko, Kai-Uwe Hildebrandt, Manuel Kobelt

3. Vorlesungen / Lectures

Mathematik 2. Semester
Informationsverarbeitung, unterteilt in Prozedurale Programmierung und Computeranwendungen, 3. Semester
Automatisierungstechnik (Automation Technique) 4. Semester Verfahrenstechnik
Biomedizinische Statistik (Wahlfach alle Semester)

Praktika / Practical Courses

Übungen zur Mathematik, 2. Semester
Praktika zur Informationsverarbeitung

4. Publications / Veröffentlichungen

(Choice / Auswahl)

G. Becherer, S. v. Weber: Der Abbrucheffekt eines isolierten Maximums in der Röntgenstrukturanalyse einatomiger Flüssigkeiten, Annalen der Physik, 7. Folge, Bd. 20 (1967) 5/6, 313-320

I.O. Kerner, H. Kiesewetter, S. v. Weber: Numerische Resultate zu den Eigenwerten und Eigenfunktionen der Neutronentransportgleichung für eine Platte, Kernenergie 10, (1967) 10, 299-306

J. Einfeldt, K.H. Kutschke, S. v. Weber: Zur Berechnung der Gestalt freier Flüssigkeitsoberflächen in rotationssymmetrischen Gefäßen, Monatsberichte der Deutschen Akademie der Wissenschaften zu Berlin, Bd. 11 (1969) 8/9, 610-615

G. Becherer, S. v. Weber: Der Abbrucheffekt in der Röntgenstrukturanalyse einatomiger Flüssigkeiten, Annalen der Physik, 7. Folge, Bd. 25 (1970) 4, 368-374

G. Reichart, D. Timm, S. v. Weber: R 300-FORTRAN (Manual), Ministerium für Hoch- und Fachschulwesen (1974)

S. v. Weber: A shortened Method for the Calculation of Ranks, Biom. J. vol. 19 (1977), no 4, 275-281

S. v. Weber: Zur Fehlerbehandlung in einer Rahmenstruktur für Spezialsprachen, EIK 15 (1979) 1/2, 105-110

H.-D. Matthes, G. Herrendörfer, S. v. Weber: Die Bedeutung der Varianz des Zuchtwertes für die Bestimmung des Relativzeitraumes und der Genauigkeit der Zuchtwertschätzung von Bullen bei verschiedenen Methoden der Nachkommensprüfung auf Mast- und Schlachtleistung, Arch. Tierzucht, Berlin 26 (1983) 3, 239-249

T.C. Cierzynski, S. v. Weber: Canonical Sequences and Simulation, Syst. Anal. Model. Simul. 5 (1988) 2, 165-170

T.C. Cierzynski, S. v. Weber: Simualtion Experiments with a Stable Regression Algorithm, Syst. Anal. Model. Simul. 7 (1990) 2, 155-160

F. Bornholdt, K. Hermann, S. v. Weber: Anwendung der Diskriminanzanalyse in der Bildauswertung, Z. Klin. Med. 45 (1990) 15, 1347-1348

E. Lautsch, S. v. Weber: Die Konfigurationsfrequenzanalyse (KFA) - Methoden und Anwendungen, Volk und Wissen Verlag GmbH, Berlin 1990

T.C. Cierzynski, S. v. Weber: Simulation experiments with CWA, a new stable regression algorithm, and comparisons with two other stable regression algorithms, Statistical Software Newsletter, vol. 13 (1992) 4, 485-491

S. v. Weber: Newtons absoluter Raum, Forschungsbericht 1995 der Fachhochschule Furtwangen, 55-57

E. Lautsch, S. v. Weber: Methoden und Anwendungen der Konfigurationsfrequenzanalyse (KFA), Beltz Psychologie Verlags Union, Weinheim 1995

S. v. Weber: Membrane Theory of Gravity, Forschungsbericht 1998 der Fachhochschule Furtwangen, 59-62

von Weber, St.: A comparison of tests used in the CFA by simulation, Psychologische Beiträge, Bd. 42, 3, (2000), Pabst Science Publishers

S. v. Weber: Proofs of the Cosmic Membrane Theory, Forschungsbericht 2002 der Fachhochschule Furtwangen, 78-80

Lautsch, E., von Weber, S.: A new test procedure in the CFA, Psychology Sciences, 45 (2003), p. 389-399

Alexander von Eye, Erwin Lautsch, Stefan von Weber: Table specific Continuity Corrections for Configural Frequency Analysis, Psychology Sciences, 45 (2003), p. 355-368

Erwin Lautsch, Alexander von Eye, Stefan von Weber: CFA-Software - an Overview, Psychologische Beiträge, Psychology Sciences, 45 (2003), p. 437-441

Stefan von Weber, Alexander von Eye, Erwin Lautsch: On the limits of Configural Frequency Analysis: Analyzing small tables, , Psychology Sciences, 45 (2003), p. 339-354

Alexander von Eye, Erwin Lautsch, Stefan von Weber: The Type II error of measures for the analysis of 2x2 tables, Understanding Statistics 3 (4), p. 259-282 (2004)

Alexander von Eye, Stefan von Weber: Simulation Methods for Categorial Variables, in Encyclopedia of Statistics in Behavioral Science, Eds. Brian S. Everitt & David C. Howell, Wiley 2005

S. von Weber, A. von Eye, E. Lautsch: Combinatoric search for types and antitypes, Psychology Science, 47 (2005) p. 401-423

(Mit freundlicher Genehmigung von Alexander von Eye,

Michigan State University)