Transcript GEOG 1230 Lecture 4 - University of Leeds

GEOG 1230
Lecture 4
Sampling and Inference
Lecture Structure
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A model for research
Quantitative/Qualitative
A taste of statistics
Sampling in a geographical context
Sampling strategies
Sampling exercise
Worksheet on sampling
Reading
Next time
October 24th, 2003
GEOG1230 - Week 4
A Model for Research
a) Identify topic and hypotheses
b) Design data collection strategy
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that allows testing of these hypotheses
c) Data collection and analysis
d) Use analysed data to:
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try to falsify these hypotheses; and
perhaps consider new hypotheses
e) Conclusions
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Quantitative/Qualitative
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Remember these two categories of
data:
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Quantitative data are
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measured on a numerical scale
height (in cm) or weight (in kg)
represents a quantity or amount of
something
Qualitative data are
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non-numerical and can only be classified
into categories
i.e. colour, education level, male/female
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Quantitative
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Four types of measurements:
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Nominal: categorical identity info
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e.g. colour, yes/no, species, region
Ordinal: identity + relationship info
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Categories with relationship information
between categories
e.g. ranked data (income bands), age
classes, roundness, hardness, brightness
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Quantitative
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Interval: identity + relationship info +
additivity of differences
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additivity means you can add/subtract the
values (unlike colour )
e.g. normal numbers, date, temperature
Ratio: identity + relative categories +
additivity of differences + independence
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e.g. weight, length, age, area, brightness
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Qualitative
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Important in physical and human
geography
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Many things cannot be quantified replace measurement with observation
Sometimes things change as we
measure them
What we measure is defined by what we
are trying to ask
Thus, quantitative methods are as
objective or independent as we think
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Project Context
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For your projects
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BAs – will be working with a mix of
quantitative and qualitative.
BSc - will be working largely with
quantitative data BUT remember that
you still need to unearth a much more
complicated reality - description is still
required - e.g. soil profiles and setting
Quantitative and qualitative data
support each other.
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A Taste of Statistics
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There are three kinds of lies:
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lies, damned lies and statistics
(rumoured to have been said by
Benjamin Disraeli, British Prime Minister
1868)
But he was a politician. I’ve also
heard:
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lies, damned lies and statistics quoted
by politicians
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A Taste of Statistics
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This raises an important point
Statistics themselves are not lies but
the way they are mis-used
(accidentally or intentionally) that
can to mislead the public
This is why we need to understand
stats! Are you convinced?
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Guardian, Oct. 22nd, 2003
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Sampling
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biggest problem faced in data
collection - quantitative or qualitative
rarely can we measure a whole
‘population’
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Thus we must sample the population
e.g. sand grains on a beach, people in a
region, stones in a river
statements about the population
based on samples is INFERENCE
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The Sampling Problem
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Important question:
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How do we choose a sample from the
population?
Use a sampling strategy
Defining a sampling strategy is a
complex problem that plagues
scientists
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How do we sample?
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How do we know that the sample
characteristics reflects those of the
population? Do we have enough?
Usually, it can never be known!
BUT… we can estimate the probability
of the sample being a good reflection
of the population
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Probability
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If probability is high then we can
make inferences for the population
as a whole
In statistics, a high probability is
more than 95% confident – but the
closer to 100% the better
Can never be 100% confident
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Inference
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So, this is why we use inferential
statistics:
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enables the geographer to make
statements about the characteristics of
the population based on the sample
but only within certain limits
These are discussed in more detail
after Xmas
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Types of Sampling Strategies
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Accessibility sample
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Sampling determined by what is
available
Judgmental sample
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Person tries to choose a random
selection
Person tries to choose a
representative sample
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Must Reduce Bias
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Probability sampling
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The three main techniques are:
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The most important
Simple random
Stratified random
Systematic
You will be using all of these on the
fieldtrip in Week 7
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Simple Random
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With simple random:
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each ‘individual’ must have equal
chance of inclusion in the sample
the selection of one should not affect
the chance of selecting another
the probabilities of inclusion in the
sample should be equal and
independent of one another
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Simple Random
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Main problem with random sampling
is making sure that you have a
representative set of samples
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Systematic
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Where data is selected in a regular
way
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i.e. selecting every 4th address from a
list, a grid of soil cores
quicker and easier than random
sampling
but does not necessarily produce a
representative sample
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Other Practices
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Sub-sampling
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Sampling from a sample
Allows estimation of characteristics of
larger sampling unit without measuring
the whole unit - e.g. soil core - take
small samples from the core, not the
whole core
Reduced cost/time, but decreases
precision
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Other Practices
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Composite sampling
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Reduced cost
But assumes a valid mean from a single
analysis
This may not occur in reality as it
assumes that all the samples in the
composite contribute the same amount
to the composite
No estimate of variability (e.g. pH 3-11
but mean 7)
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Sampling Exercise
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This is easy and optional!
In Ebdon (1985) Exercise 3.1
illustrates some sampling issues
Will help you with your worksheet
Give this exercise a try. All relevant
information is on the Nathan
Boddington so you don’t need the
text.
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Worksheet 1
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A sampling exercise
Due by 12pm on Friday October 31th
Submitted to labelled box in the
basement of the Main Geography
building
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Readings
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Some more reading you might find
useful
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Hodgson J.M 1978. Soil sampling and soil
description. Oxford Clarendon Press.
Rowell, D.L., 1997. Soil Science Methods
and Applications. Longman.
Williams, R.B.G. and Rendel B.G. 1984.
Introduction to Statistics for Geographers
and Earth Scientists. Macmillan, London.
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Next Time
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Review material from this week
Go through the worksheet exercise
and answer questions
Don’t forget:
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Due by 12pm on Friday October 31th at
the beginning of the lecture or in the
GEOG box in reception.
Also, late submissions will require a
lengthy and humiliating explanation!
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