A sample of the slides available to support the teaching of the textbook Statistics for Geography and Environmental Science by Harris & Jarvis (2011). For further information see www.social-statistics.org

1. Statistics for Geography and
Environmental Science:
an introductory lecture course
(sample)
By Richard Harris, with material
by Claire Jarvis
USA: http://amzn.to/rNBWd5
UK: http://amzn.to/tZ7fVu

2. Based on the textbook

3. Copyright notice
Statistics for Geography and Environmental Science:
an introductory lecture course, © Richard
Harris, 2011.
This course is available at www.social-statistics.org
and contains extracts from the publication Statistics
for Geography and Environmental Science by
Richard Harris and Claire Jarvis (Prentice Hall, 2011)
You are free to modify these slides for the purpose of
non-commercial teaching only, subject to the
following restrictions:
– This work, or any derivative of it, may not be stored or
redistributed in any form, paper or electronic, other than to
be available to students for their learning and
education, with access to the material restricted to the
institution to which those students belong.
– Any derivative must retain this copyright in full and at the
beginning of the work. The words ‗Based on‘ may be
inserted in the first paragraph.
– Permission to waive or modify these restrictions may be
sought from the author (Richard Harris, School of
Geographical Sciences, University of Bristol).

4. The modules
OVERVIEW

5. The modules
Module1 makes the case for knowing
about statistics as a transferable skill
and to be equipped for social and
political debate.
Module 2 is about using descriptive
statistics and simple graphical
techniques to explore and make
sense of data.
Module 3 discusses the Normal
curve, the properties of which
provide the basis for inferential

6. The modules
Module 4 is about the principles of
research design and effective data
collection.
Module 6 discusses the role of
hypothesis testing.
Module 7 is about regression
analysis.

7. The modules
Module 8 moves to modelling point
patterns, ―hotspot analysis‖ and ways
of measuring patterns of spatial
autocorrelation in data.
Module 9 looks at spatial regression
models, geographically weighted
regression and multilevel modelling.
Each module is explored more fully
in the accompanying textbook,
Statistics for Geography and
Environmental Science.

8. Module 1
(Extracts from Chapter 1 of Statistics for Geography
and Environmental Science)
DATA, STATISTICS AND
GEOGRAPHY

9. Module overview
To convince you that studying
statistics is a good idea!
Our argument is that data collection
and analysis are central to the
functioning of contemporary society
so knowledge of quantitative
methods is a necessary skill to
contribute to social and scientific
debate.

10. About statistics
Statistics are a reflective practice: a
way of approaching research that
requires a clear and manageable
research question to be formulated, a
means to answer that question,
knowledge of the assumptions of
each test used, an understanding of
the consequences of violating those
assumptions, and awareness of the
researcher‘s own prejudices when
doing the research.

11. Some reasons to study statistics
Reasons for human geographers
– Data collection and analysis are central
to the functioning of society, to systems
of governance and science.
– Knowledge of statistics is an entry into
debate, informed critique and the
possibility of creating change.

12. Some reasons to study statistics
Reasons for GI scientists
– To address the uncertainties and
ambiguities of using data analytical.
– Because of the increased integration of
mapping capabilities, data visualizations
and (geo-) statistical analysis.

13. Some reasons to study statistics
Reasons for all students
– They provide a transferable skill set
using in other areas of research, study
and employment.
– There is a recognised shortage of
students with skills in quantitative
methods, especially within the social
sciences.

14. Types of statistic
Descriptive
– Used to provide a summary of a set of
measurements, e.g. the average.
Inferential
– Use the data at hand to convey information
about the population (‗the greater
something‘) from which the data are drawn.
Relational
– Consider whether greater or lesser values
in one set of data are related to greater or
lesser values in another.

15. Geographical data
These are records of what has
happened at some location on the
Earth‘s surface and where.
For many statistical tests the where
is largely ignored.
However, it is central to geostatistics
and to spatial statistics (as their
names suggest)

16. Some problems when analysing
geographical data
Standard statistical tests assume that
each ‗bit‘ of data (each observation)
has a value that is not influenced by
any other.
However, we may often expect there
to be geographical patterns in the
data.
– Spatial autocorrelation: geographical
patterns in the measurements

17. Some problems when analysing
geographical data
Determining what causes what in a
complex and dynamic natural or
social system is extremely tricky.
Two things may be associated (e.g.
greater income inequality and more
non-recycled waste) without the one
directly causing the other.

18. Some problems when analysing
geographical data
Data and structured forms of enquiry
can only tell us so much and may not
be appropriate to some types of
research for which a more
qualitative, participatory or less
representational approach may be
better.

19. Further reading
Chapter 1 of Statistics for
Geography and Environmental
Science by Richard Harris and Claire
Jarvis (Prentice Hall / Pearson, 2011)
Includes a review of the following
key concepts: types of statistics;
why error is unavoidable;
geographical data analysis; and
spatial autocorrelation and the first
law of geography.

20. Module 2
(Extracts from Chapter 2 of Statistics for Geography
and Environmental Science)
DESCRIPTIVE STATISTICS

21. Module overview
This module is about ―everyday
statistics‖, the sort that summarise
data and describe them in simple
ways.
They include the number of home
runs this season, average male
earnings, numbers unemployed,
outside temperature, average cost of
a barrel of oil, regional variations in
crime rates, pollution statistics,
measures of the economy and other
―facts and figures‖

22. Data and variables
Data
– A collection of observations:
measurements made of something.
A variable
– Another name for a collection of data.
Variable because it is unlikely that the
data are all the same.
Data types
– These include discrete, continuous,
and categorical data.

23. Simple ways of presenting data
Discrete data Continuous data
Frequency table Summary table
Bar chart (below) Histogram (below, with a rug plot)

24. Frequency and summary tables

25. Information to include
in a summary table
Measures of central tendency
(―averages‖)
– The mean and/or median
• The ―centre‖ of the data
Measures of spread and variation
– The range (minimum to maximum)
– The interquartile range (from ‗mid-
spread‘ of the data)
– The standard deviation,s

26. More about the standard deviation
Essentially a measure of average
variation around the mean.
It is also the square root of the
variance.
The variance is the sum of squares
divided by the degrees of freedom

27. Boxplots
Are useful for
showing the
median,
interquartile
range and range
of a set of data,
for indentifying
outliers and also
for comparing
variables.

28. Other ways of classifying numeric
data
Nominal, ordinal, interval and ratio
Counts and rates
Proportions and percentages
Parametric and non—parametric
Arithmetic and geometric
Primary and secondary

29. Further reading
Chapter 2 of Statistics for Geography
and Environmental Science by Richard
Harris and Claire Jarvis (Prentice Hall /
Pearson, 2011)
Includes a review of the following key
concepts: data and variables; discrete
and continuous data; the range;
histograms, rug plots, and stem and
leaf plots; measures of central
tendency; why averages can be
misleading; quantiles; the sum of
squares; degrees of freedom; the
standard deviation and the variance;
box plots; and five and six number
summaries

30. Thank you for your interest.