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Introduction
About this book
How to use this book
What are statistics good for?
Statistics is the grammar of science…
Lies, damned lies and statistics…
Descriptive Statistics
Summary Statistics: Part I
Example: Sensitivity of Standard Deviation to Sampling
What is a distribution?
Summary Statistics: Part II
Statistical Hypothesis Testing
Basic Probability
The Standard Normal Distribution
What is ENSO?
The
z
-Statistic
Signal-to-Noise
The Central Limit Theorem
Estimating Statistical Significance with a
z
-test
The
t
-Statistic
Resampling Techniques
Linear Regression
Introduction to Linear Regression
Confidence Intervals
Goodness of Fit
Assumptions of Linear Regression
Compositing
Filtering or Detrending using Regression
Correlation
Review of Correlation
Statistical Significance of Correlation Coefficients
Non-parametric Correlations
Autocorrelation
Persistence in Time Series
Autocorrelation in Climate and Geophysical Data
Introduction to Red Noise
Example: Correlation with Memory
Accounting for Autocorrelation: Effective Sample Size
Time Series Analysis
Filtering in the Time Domain: Part I
Filtering in the Time Domain: Part II
Filtering in the Frequency Domain: Discrete Fourier Transform
Fast Fourier Transform
Continuous Power Spectrum and the Significance of Spectral Peaks
Spectral Leakage
Convolution and Filtering in the Time Domain
Patterns in Multivariate Data
Introduction to Principal Component Analysis
Review of Linear Algebra
Eigenanalysis
EOFs via Eigenanalysis
EOFs with Real Data
Epilogue
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