Univariate and Bivariate Statistics | ||
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Measurements systems Random variables Parametric vs. non parametric methods Central tendencies, mean, and variance Accuracy vs. Precision |
Kachigan; Preface and Chapters 1 - 5 |
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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 |
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Introduction to bivariate statistics Bivariate Association Some Terms Variance and Covariance The linear correlation coefficient, r |
Kachigan; Chapter 9, 10 |
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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 |
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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