Download Introduction to Basic Statistical Methods

Introduction to Basic Statistical Methods
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0. Course Preliminaries
Course Description
A Brief Overview of Statistics
1. Introduction
1.1 Motivation: Examples and Applications
1.2 The Classical Scientific Method and Statistical Inference
1.3 Definitions and Examples
1.4 Some Important Study Designs in Medical Research
1.5 Problems
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2. Exploratory Data Analysis and Descriptive Statistics
2.1 Examples of Random Variables and Associated Data Types
2.2 Graphical Displays of Sample Data
• Dotplots, Stemplots,…
• Histograms: Absolute Frequency, Relative Frequency, Density
2.3 Summary Statistics
• Measures of Center: Mode, Median, Mean,... (+ Shapes of Distributions)
• Measures of Spread: Range, Quartiles, Variance, Standard Deviation…
2.4 Summary: Parameters vs. Statistics, Expected Values, Bias, Chebyshev’s Inequality
2.5 Problems
3. Theory of Probability
3.1 Basic Ideas, Definitions, and Properties
3.2 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 Distributions
4.1 Discrete Models: Binomial Distribution, Poisson Distribution,…
4.2 Continuous Models: Normal Distribution,…
4.3 Problems
5. Sampling Distributions and the Central Limit Theorem
5.1 Motivation
5.2 Formal Statement and Examples
5.3 Problems
6. Statistical Inference and Hypothesis Testing
6.1 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 Samples
6.2.1 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 Association
and Test of Homogeneity of Odds Ratios, Mantel-Haenszel
Estimate of Summary Odds Ratio
6.3 Several Samples
6.3.1 Proportions (Chi-squared Test)
6.3.2 Variances (Bartlett’s Test, etc.)
6.3.3 Means (ANOVA, F-test, Multiple Comparisons)
6.4 Problems
7. Correlation and Regression
7.1 Motivation
7.2 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
8. Survival Analysis
8.1 Survival Functions and Hazard Functions
8.2 Estimation: Kaplan-Meier Product-Limit Formula
8.3 Statistical Inference: Log-Rank Test
8.4 Linear Regression: Cox Proportional Hazards Model
8.5 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: Newton’s 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 such
differences be in order to reject random chance as their sole
cause, and accept that an alternative mechanism is responsible?
Source: Nature Genetics, November 2, 1999.