Statistische Methoden I: Grundlagen Und Versuchsplanung
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Einführung in die Mathematik.- I. Mengen.- II. Funktionen.- III. Folgen.- IV. Reihen.- V. Stetigkeit, Differenzierbarkeit und Integration.- VI. Permutation und Kombination.- VII. Funktionen zweier Variablen.- H Matrizenrechnung.- Matrizen.- Determinanten.- Rang einer Matrix.- Quadratische Formen.- Matrizen-Inversion.- Auflösung linearer Gleichungssyteme.- Eigenwerte und Eigenvektoren.- Beschreibende Statistik.- Häufigkeitsverteilung, Mittelwert und Varianz.- Darstellung zweivariabler Beobachtungen.- Regression und Korrelation.- Wahrscheinlichkeitsrechnung.- Grundbegriffe.- Spezielle diskrete Verteilungen.- * Grenzwertsätze.- Wichtige Prüfverteilungen.- Zweivariable Verteilungen.- * Anwendungen der Bayesschen Formel.- H* Markoffsche Ketten.- H* Verzweigungsprozesse.- * Drei Beispiele für die Anwendung stochastischer Prozesse in der Medizin.- * Monte-Carlo-Methoden.- Statistische Methoden.- Stichproben (Pfander).- Statistische Schlußweisen.- ?2-Anpassungstest.- Vierfeldertest.- Kontingenztafeln.- Nichtparametrische Tests.- Wahrscheinlichkeitspapier.- * Zusammenstellung verschiedener Methoden für den Einstichprobenfall.- H* Die Maximum-LikeIihood-Methode.- * Grundbegriffe der Entscheidungstheorie.- * Sequentialanalyse.- * Stichprobenpläne.- * ED5o-Schätzung.- * Sterbetafelmethode.- Varianzanalyse und Versuchsplanung.- Einführung in die Versuchsplanung.- Varianzanalyse: Einfachklassifikation.- Total hierarchische Klassifikation.- * Teilausgewogene total hierarchische Versuchspläne.- Zweifachklassifikation.- Dreifachklassifikation.- Partiell hierarchische Klassifikation.- Anhang zu partiell hierarchischen Klassifikationen.- Auswertung von Blockversuchen.- * Versuche in ausgewogenen unvollständigen Blöcken.- Lateinische Quadrate.- * Graecolateinische undhypergraecolateinische Quadrate.- Cross-Over-Versuche.- * Wechselversuche.- Versuchspläne zur Schätzung von Nachwirkungen.- Signifikanztests bei Vergleichen zwischen mehr als zwei Mittelwerten.- Transformationen.- Nichtparametrische Methoden für die Versuchsplanung.- Fehlende Beobachtungen.- Regression und Korrelation.- Einfache lineare Regression (Pfander).- H Multiple und partielle Regression (Jesdinsky und Pfander).- Nichtlineare Regression (Pfander).- * Orthogonalpolynome (Jesdinsky).- Einfache Kovarianzanalyse.- Mehrfache Kovarianzanalyse.- H* Nichtorthogonale Varianzanalyse.
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