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