introduction to basic statistical methods
Post on 03-Jun-2018
217 Views
Preview:
TRANSCRIPT
-
8/11/2019 Introduction to Basic Statistical Methods
1/2
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
S
A
M
P
L
E
P
O
P
U
L
A
T
I
O
N
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
2/2
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
8.
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
top related