Topics Overview
Topics Overview
MIT 18.443
Statistics for Applications
Dr. Kempthorne
Spring 2015
MIT 18.433Statistics for Applications
Topics Overview
1
Topics Overview
Classic Derived Distributions
Fitting Probability Distributions
Testing Hypotheses and Assessing Goodness of Fit
Summarizing Data
Linear Least Squares
Analysis of Categorical Data
Comparing Two Samples
Text and References
Classic Derived Distributions (from Gaussian)
Chi-square distribution
Student’s t distribution
Fisher F distribution
Distributions of sample statistics
Note: Distribution theory pervasive in motivating/interpretting
statistical methods
MIT 18.433Statistics for Applications
Topics Overview
2
Topics Overview
Classic Derived Distributions
Fitting Probability Distributions
Testing Hypotheses and Assessing Goodness of Fit
Summarizing Data
Linear Least Squares
Analysis of Categorical Data
Comparing Two Samples
Text and References
Probability Distributions
Poisson
Exponential/Gamma
Gaussian/Normal
Binomial/Multinomial
Parameter Estimation Methods
Method of Moments (MOM)
Method of Maximum Likelihood (MLE)
Bayesian approach
Estimation Theory
Large-sample (asymptotic) distributions of estimates
Point estimates vs interval estimates
Confidence intervals
Bayesian credible intervals
Bootstrap methodology
MIT 18.433Statistics for Applications
Topics Overview
3
Topics Overview
Classic Derived Distributions
Fitting Probability Distributions
Testing Hypotheses and Assessing Goodness of Fit
Summarizing Data
Linear Least Squares
Analysis of Categorical Data
Comparing Two Samples
Text and References
Hypothesis Testing
The Neyman-Pearson Paradigm
Duality of hypothesis tests and confidence intervals
Generalized likelihood ratio tests
Assessing Goodness of Fit
Likelihood ratio tests for multinomial distributions
Probability plots
MIT 18.433Statistics for Applications
Topics Overview
4
Topics Overview
Classic Derived Distributions
Fitting Probability Distributions
Testing Hypotheses and Assessing Goodness of Fit
Summarizing Data
Linear Least Squares
Analysis of Categorical Data
Comparing Two Samples
Text and References
Summarizing Data
Methods based on cumulative distribution function
(empirical cdf; quantile-quantile plots)
Histograms, density curves, Stem-and-Leaf Plots
Measures of location
(mean, median, M-estimates, trimmed mean)
Measures of dispersion
Box plots
Scatterplots of bivariate data
MIT 18.433Statistics for Applications
Topics Overview
5
Topics Overview
Classic Derived Distributions
Fitting Probability Distributions
Testing Hypotheses and Assessing Goodness of Fit
Summarizing Data
Linear Least Squares
Analysis of Categorical Data
Comparing Two Samples
Text and References
Linear Least Squares
Simple linear regression
Matrix approach to linear least squares
Distribution theory of least-squares estimates
Multiple linear regression
MIT 18.433Statistics for Applications
Topics Overview
6
Topics Overview
Classic Derived Distributions
Fitting Probability Distributions
Testing Hypotheses and Assessing Goodness of Fit
Summarizing Data
Linear Least Squares
Analysis of Categorical Data
Comparing Two Samples
Text and References
Analysis of Categorical Data
Fisher’s Exact Test
Chi-Square test of Homogeneity
Chi-Square Test of Independence
Odds ratios
MIT 18.433Statistics for Applications
Topics Overview
7
Topics Overview
Classic Derived Distributions
Fitting Probability Distributions
Testing Hypotheses and Assessing Goodness of Fit
Summarizing Data
Linear Least Squares
Analysis of Categorical Data
Comparing Two Samples
Text and References
Comparing Two Samples
Comparing two independent samples
Comparing paired samples
Principles of Experimental Design
(placebos, randomization)
MIT 18.433Statistics for Applications
Topics Overview
8
Topics Overview
Classic Derived Distributions
Fitting Probability Distributions
Testing Hypotheses and Assessing Goodness of Fit
Summarizing Data
Linear Least Squares
Analysis of Categorical Data
Comparing Two Samples
Text and References
Text Book: Mathematical Statistics and Data Analysis, Third
Edition, John A. Rice
Statistics Package: R and RStudio Desktop.
See:
http://www.rstudio.com/products/rstudio/download/
http://cran.rstudio.com/
MIT 18.433Statistics for Applications
Topics Overview
9
MIT OpenCourseWare
http://ocw.mit.edu
18.443 Statistics for Applications
Spring 2015
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