Basic statistical concepts and techniques

• Mean and variance• Probability distribution, and statistical

significance• Harmonic analysis and power spectrum• White and red noise

How to compute the mean and variance of a time series

X1

n--- X

i

i 1=

n

∑=

σ S Q R T1

n 1–------------ X

iX–( )

2

i 1=

n

∑⎝ ⎠⎜ ⎟⎛ ⎞

=

mean is given by

The variance is given by

Time series are given by X1, X2-----------Xn, then the

Probability distribution

• The normal distribution--the bell curve

Probability distribution• An non-normal distribution

Statistical significance

• The significance of a climate anomaly

38%

95%

The statistical significance of the warming of the last 20 years

Statistical significance

• The significance of a trend

Harmonic analysis

• A time-series may be decomposed into a set of harmonics

Harmonic analysis

• Power spectrum of a time series

Changes in the distribution