GEOF 301 Statistikkpakken

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GEOF 301Statistikkpakken

• Dag Johan Steinskog
• Ph.D. student
• NERSC/BCCR

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The plan for Statistikkpakken

• 1st hour Talk and discussion about statistics
  and software
• 2nd and 3rd hour You do three exercises working
  with statistically software
• Please ask a lot of questions!!!!

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This is only a teaser.

• These courses should be considered
• Pure statistics
• STAT 110,STAT 111, STAT 200, STAT201 etc.
• Geofysics and statistics
• GEOF 210

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After three hours you should expect to

• Know something about simple statistics
• Know something about R, and know where to look
  for help in statistical routines
• Have seen the some of the purpose of statistics
• However, not be an expert even trained
  statistians meet new challenges every day (I do
  so ?)!

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What is statistics?

• Major activities in statistics include
• design of experiments and surveys to collect
  data (e.g. meteorological observation networks)
• exploration and visualization of sample data
  (e.g. graphs, maps, tables)
• summary description of sample data (e.g.
  climatology)
• modelling relationships between variables (e.g.
  predictability studies)
• stochastic modelling of uncertainty (e.g.
  stochastic parameterisations)
• forecasting based on suitable models (e.g.
  seasonal forecasting)
• hypothesis testing and statistical inference
  (e.g. detection and attribution of climate change)

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Further.

• Statistics is neither really a science nor a
  branch of mathematics. It is perhaps best
  considered as a meta-science (or language) for
  dealing with data collection, analysis, and
  interpretation. As such its scope is enormous and
  it provides much guiding insight in many branches
  of science, business, etc.
• Critical statistical reasoning can be extremely
  useful for making sense of the ever increasing
  amount of information becoming available (e.g.
  via the web).
• Knowledge of statistics is a very useful
  transferable skill!

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Literature

• Statistics and meteorology/oceanography
• Statistical Analysis in Climate Research, by Hans
  von Storch and Francis W. Zwiers
• Statistical Methods in the Atmospheric Sciences,
  Second Edition by Daniel S. Wilks
• Basic Introduction
• Introduction to Probability and Statistics for
  Engineers and Scientists, Third Edition, by
  Sheldon M. Ross

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Some simple statistics

• Centre/Location
• Mean (m or x)
• Median (x )
• Scale/Spread
• Standard deviation (s)
• Interquartile range (IQR)
• Shape
• Skewness (e.g. b1)
• Kurtosis (e.g. b2)

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Shape
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Statistical Software

• Powerful language-based packages
• S-PLUS, R, and SAS
• Interactive packages
• MINITAB and SPSS
• Packages with statistical libraries
• MATLAB and PV-Wave/IDL
• Home made subroutines
• Many climate researchers have a bad habit of
  doing statistics using subroutines in Fortran
  that they have either written by themselves,
  obtained from a friend, or copied from numerical
  recipes. This Do-It-Yourself cookbook approach
  has several disadvantages that include time being
  wasted reinventing the wheel programming routines
  rather than timebeing spent thinking about the
  appropriate choice of method etc., and lack of
  any input or contact with professional
  statisticians.

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R

• R is a free statistical software based on R.
• R can be used in several OS (Mac, Windows og
  Linux)
• It can be downloaded from
• www.r-project.org
• Lots of packages are available for you on the web!

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RClim

• A joint effort has been made to make R more
  suitable for climate researchers.
• The initiative includes NERSC/BCCR and
  UCAR/Reading.
• It will be launched in February 2006.
• For more information, see
• http//www.met.reading.ac.uk/cag/rclim/
• http//www.nersc.no/dagjs/R.htm

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Examples of RClim I
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Examples from Rclim II
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Examples from Rclim III
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How to start up R?

• Windows Simple click and run!
• Linux Open a terminal window, and type the
  following
• mkdir R/work
• cd R/work
• R
• q() to quit

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Helpful commands

• To get up the help-page
• help.start()
• To achieve the documentation of a commando
• ?solve eller help(solve)
• NB R is case-sensitive
• ls() to achieve an overview of objects.
• Objects are variables, matrices, strings,
  functions or more generel structures build up by
  such components
• rm() to delete obejcts
• read.table() to read a dataset

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A simple example

• testlt-rnorm(100,3,4)
• mean(test)
• var(test)
• sd(test)
• summary(test)
• median(test)
• t.test(test,alternative"two.sided",mu7)
• plot(test,typel,colred,lwd2)
• We then end up with a figure looking like this
  one

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Continuing the example

• hist(test,col2)
• ?hist
• Does this indicate a normal distribution?
• hist(test,col4,br40)
• library(nortest)
• shapiro.test(test)
• Shapiro-Wilk normality test
• data test
• W 0.9918, p-value 0.8079

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qq-plot

• x11()
• qqnorm(test)
• qqline(test)
• Library(fBasics)
• skewness(test)
• 1 0.1364627
• kurtosis(test)
• 1 -0.4187804

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And finally

• boxplot(test,maintest)
• what is a boxplot?
• acf(test)
• What is auto-correlation function?

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Quotations concerning statistics

• There are three kinds of lies lies, damned lies,
  and statistics. (Benjamin Disrali)
• Statistician A man who believes figures dont
  lie, but admits that under analysis some of them
  wont stand up either. (Evan Esar)
• Statistics The only science that enables
  different experts using the same figures to draw
  different conclusions. (Evan Esar)