Lecture notes on Statistical Methods

Univariate and Bivariate Statistics
Lecture Notes
Topics
Optional Further Readings
1. Measurements and Stats
 Measurements systems
Random variables
Parametric vs. non parametric methods
Central tendencies, mean, and variance
Accuracy vs. Precision		 Kachigan; 
Preface and Chapters 1 - 5
2. Distributions and Sampling
 Central Limit Theorem
Degrees of Freedom
Z-test (large sample mean test)
Student's t-test (small sample mean test)
Type I and Type II errors in hypothesis testing		 Kachigan; 
Chapter 6, Sections 1-4, 6, 12, 14
Chapter 7
Chapter 8, Section 5
3. Covariance and correlation
 Introduction to bivariate statistics
Bivariate Association
Some Terms
Variance and Covariance
The linear correlation coefficient, r
Kachigan; 
Chapter 9, 10
4. Simple Linear Regression
 Predictive Methods
Defining the Linear Regression Model
Assumptions of the method
Evaluating the Fit
    A measure of the model error
    How much variance is explained?
    Determining statistical significance
    Confidence Interval for future predictions		 Kachigan; 
Chapter 11 sections 1-7
Multivariate Statistics
5. Analysis of Variance Introduction to Analysis of Variance (ANOVA)
Single-factor ANOVA with equal sample size, n
The ANOVA table
Evaluating the model: The F-distribution and F-test
Multiple comparisons
    Orthogonal contrasts
    Confidence intervals
    Partial F-tests
    Variance explained		 Kachigan; 
Chapter 12
6. Multivariate Regression
 		Prediction revisited
The multiple linear regression model
Assumptions
Generating a multiple regression
Potential problems
Evaluating the fit
    The Regression ANOVA Table
    Determining statistical significance
    A measure of the model error
    How much variance is explained?		 Kachigan; 
Chapter 11 sections 8-17
7. Discriminant Functions
 		Determining group membership
The discriminant function model
Assumptions
Finding the discriminant function(s)
Potential problems
Determining statistical significance		 Kachigan; 
Chapter 14
8. Factor Analysis
 		Introduction to Factor Analysis
    R-mode Factor Analysis
    Q-Mode Factor Analysis
Assumptions and Limitations		 Kachigan; 
Chapter 15
Davis; Chapter 3
handouts and journal articles
Time Series Analysis
9. Times Series Sampler
 		Introduction to wave and frequency domain processes
Serial correlation and the decorrelation length scale
Properties of a wave: period, amplitude, frequency
Spectral decomposition of variance: Fourier Transform
Fourier frequencies, sample interval, Nyquist frequency, etc.
Spectral Shapes		 Online lecture notes
10. Sampling issues
and Power Spectra
 Sampling Issues (Aliasing, leakage and smearing)
Data windowing (tapering): dealing with leakage and smearing
Autospectral methods
    Single Taper Methods
         Blackman-Tukey Method
        Maximum Entropy Method
    Multi-Taper Method		 Kachigan; Chapter 18
11. Time Series Significance and related methods
 		Extensions to Spectral Analysis
Confidence intervals
Significance Tests
Related Methods
    Singular Spectrum analysis (SSA)
    Cross-spectral analysis
        Coherence
        Phase		 StatSoft  Electronic Textbook (Time Series Analysis)
handouts

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