8/11/2019 Introduction to Basic Statistical Methods

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Introduction to Basic Statistical MethodsNote: Underlined headings are active webpage links!

0. Course Preliminaries

Course Description

A Brief Overview of Statistics

1. Introduction1.1 Motivation: Examples and Applications1.2 The Classical Scientific Method and Statistical Inference1.3 Definitions and Examples1.4 Some Important Study Designs in Medical Research1.5 Problems

2. Exploratory Data Analysis and Descriptive Statistics2.1 Examples of Random Variables and Associated Data Types2.2 Graphical Displays of Sample Data

Dotplots, Stemplots,

Histograms: Absolute Frequency, Relative Frequency, Density2.3 Summary Statistics

Measures of Center: Mode, Median, Mean,... (+ Shapes of Distributions)

Measures of Spread: Range, Quartiles, Variance, Standard Deviation2.4 Summary: Parameters vs. Statistics, Expected Values, Bias, Chebyshevs Inequality

2.5 Problems

3. Theory of Probability3.1 Basic Ideas, Definitions, and Properties3.2 Conditional Probability and Independent Events (with Applications)3.3 Bayes Formula

3.4 Applications

Diagnostic: Sensitivity, Specificity, Predictive Power, ROC curves

Epidemiological: Odds Ratios, Relative Risk

3.5 Problems

4. Classical Probability Distributions4.1 Discrete Models: Binomial Distribution, Poisson Distribution,

4.2 Continuous Models: Normal Distribution,4.3 Problems

5. Sampling Distributions and the Central Limit Theorem5.1 Motivation5.2 Formal Statement and Examples5.3 Problems

6. Statistical Inference and Hypothesis Testing6.1 One Sample

6.1.1 Mean (Z- and t-tests, Type I and II Error, Power & Sample Size)6.1.2 Variance (Chi-squared Test)

6.1.3 Proportion (Z-test)

6.2 Two Samples6.2.1 Means (Independent vs. Paired Samples, Nonparametric tests)6.2.2 Variances (F-test, Levene Test)6.2.3 Proportions (Z-test, Chi-squared Test, McNemar Test)

Applications: Case-Control Studies, Test of Associationand Test of Homogeneity of Odds Ratios, Mantel-HaenszelEstimate of Summary Odds Ratio

6.3 Several Samples6.3.1 Proportions (Chi-squared Test)

6.3.2 Variances (Bartletts Test, etc.)6.3.3 Means (ANOVA, F-test, Multiple Comparisons)

6.4 Problems

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http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/0_-_Preliminaries/http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/1_-_Introductionhttp://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/2_-_Exploratory_Data_Analysis/http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/3_-_Probability_Theory/http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/4_-_Classical_Probability_Distributionshttp://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/5_-_Central_Limit_Theoremhttp://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/6_-_Statistical_Inference/http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/6_-_Statistical_Inference/http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/5_-_Central_Limit_Theoremhttp://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/4_-_Classical_Probability_Distributionshttp://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/3_-_Probability_Theory/http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/2_-_Exploratory_Data_Analysis/http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/1_-_Introductionhttp://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/0_-_Preliminaries/

8/11/2019 Introduction to Basic Statistical Methods

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7. Correlation and Regression7.1 Motivation7.2 Linear Correlation and Regression (+ Least Squares Approximation)

7.3 Extensions of Simple Linear Regression

Transformations (Power, Logarithmic,)

Multilinear Regression (ANOVA, Model Selection, Drug-Drug Interaction)

Logistic Regression (Dose-Response Curves)7.4 Problems

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Survival Analysis8.1 Survival Functions and Hazard Functions8.2 Estimation: Kaplan-Meier Product-Limit Formula

8.3 Statistical Inference: Log-Rank Test8.4 Linear Regression: Cox Proportional Hazards Model8.5 Problems

APPENDIX

A1. Basic Reviews

Logarithms

Perms & Combos

A2. Geometric Viewpoint

Mean and Variance

ANOVA

Least Squares Approximation

A3. Statistical Inference

Mean, One Sample

Means & Proportions, One & Two Samples

General Parameters & FORMULA TABLES

A4. Regression Models

Power Law Growth

Exponential Growth

Multilinear Regression Logistic Regression

Example: Newtons Law of Cooling

A5. Statistical Tables

Z-distribution

t-distribution

Chi-squared distribution

F-distribution (in progress...)

Even genetically identical organisms, such as these inbred mice,can exhibit a considerable amount of variation in physical and/or

behavioral characteristics, due to random epigenetic differences

in their development. But statistically, how large must suchdifferences be in order to reject random chance as their solecause, and accept that an alternative mechanism is responsible?Source:Nature Genetics, November 2, 1999.

http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/7_-_Correlation_and_Regressionhttp://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/8_-_Survival_Analysishttp://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/8_-_Survival_Analysishttp://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/APPENDIX/http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/APPENDIX/A1._Basic_Reviews/http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/APPENDIX/A2._Geometric_Viewpoint/http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/APPENDIX/A3._Statistical_Inference/http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/APPENDIX/A4._Regression_Modelshttp://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/APPENDIX/A5._Statistical_Tableshttp://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/APPENDIX/A5._Statistical_Tableshttp://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/APPENDIX/A4._Regression_Modelshttp://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/APPENDIX/A3._Statistical_Inference/http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/APPENDIX/A2._Geometric_Viewpoint/http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/APPENDIX/A1._Basic_Reviews/http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/APPENDIX/http://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/8_-_Survival_Analysishttp://www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/7_-_Correlation_and_Regression