Statistics

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Statistics

• If I had only one day left to live, I would live
  it in my statistics class the day would seem so
  much longer

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Aims of the Course

• introduction to basic statistics
• minimise underlying maths, BUT
• understand underlying principles
• demonstrate geographical context
• learn to use analysis tools in EXCEL
• make you an intelligent user of data
• make you an intelligent user of statistics

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Statistics

• Its not the figures themselves,its what you
  do with them that matters
• The undoing of Lamia Gurdleneck
• KAC Manderville

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Course Structure

• lectures on Mondays
• in main lecture theatre (Hall)
• practicals on Wednesday afternoons
• in class room (computer lab)

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Practicals
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How the course works

• Cover the statistical principles in lecture
• course lecture notes
• Go through lecture notes in own time before
  practical
• use textbooks to supplement lecture notes
• Attend practical
• work through practical handouts
• ask demonstrators for help
• Take online assessments
• theory any time after lecture
• practical any time after finishing prac

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Course Information

• ALL INFORMATION IS ON THE WEB
• http//techniques.geog.ox.ac.uk
• lecture notes and glossary
• practical notes
• EXCEL files
• internet resources
• recommended textbooks
• tests

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Course Outline

• Week 1 Describing data - central tendency
• Week 2 Describing data - dispersion
• Week 3 Normal distribution and probability
• Week 4 Confidence intervals for the mean
• Week 5 Testing for the difference between means
• Week 6 The Chi-square test
• Week 7 Correlation
• Week 8 Regression

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Some things you should find out before the
practical

• Normal and non-normal distributions
• Parametric and non-parametric statistical tests
• Nominal, ordinal and interval scales of
  measurement
• Discrete and continuous data
• Variables, samples and populations
• Dependent and independent samples
• Parameters and statistics

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Types of Data

• Interval
• can tell exactly how far any measurement is from
  any other
• examples height, age, size
• Ordinal
• a set of observation is ordered according to some
  criterion
• cannot tell how far one measurement is from the
  next
• examples horses positions in race, the ten
  highest mountains in the world
• interval data can be converted into ordinal form

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Types of Data

• Interval
• Ordinal

• Nominal (categorical)
• data are grouped into categories
• example land use, ethnicity, rock type
• note that interval data can be converted into
  nominal form

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Week 1 - Central Tendency

• why statistics?
• samples
• descriptive statistics
• frequency distribution
• measures of central tendency
• mode
• median
• arithmetic mean
• precision and accuracy

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Why statistics?

• make quantified statements about a phenomenon we
  are interested in
• frequently this phenomenon is too large to go out
  and measure exhaustively
• so we collect samples as proxies of the greater
  population of individuals or items that make up
  the phenomenon we are interested in.

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Samples

• A subset of the target population
• Random
• the individuals in the samples are randomly
  selected
• each member of the population has a known, but
  possibly non-equal, chance of being included in
  the sample
• Independent
• a sample should have no effect and are not
  affected by other samples selected from the same
  population, or different populations.

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Descriptive Statistics

• Describe the overall characteristics of a sample
  (and hence the population?)
• Transform raw data into more easily understood
  forms
• Central tendency average character of the
  data.

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Frequency Distribution

• the spread of data along its range
• either mathematical description
• or (and) visual description
• a frequency histogram
• define categories or intervals or classes
• count the number of measurements that fall into
  each class
• plot classes along x-axis
• plot counts (frequencies) on y-axis

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Frequency Distribution
Grades for 1st Stats Practical (1991-2002)
Grade (in percent)
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Mode

• most commonly occurring value
• for nominal data we refer to the modal class
• not appropriate for ordinal or (usually) interval
  data

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Mode

• most commonly occurring value
• for nominal data we refer to the modal class
• not appropriate for ordinal or (usually) interval
  data
• multi-modal distribution

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Median

• central value in an ordered set of data

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Median

• even number of values

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Arithmetic Mean
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Arithmetic Mean
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Arithmetic Mean
data 4, 2, 5, 1, 7, 10, 6
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The average

• average central tendency
• the mean, mode and median are all measures of
  average
• average ? mean

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Precision and accuracy

• Precision
• The degree of refinement with which an operation
  is performed or a measurement stated
• Accuracy
• Freedom from mistake or error

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Precision and accuracy