GEOG 1230 Lecture 4 Sampling and Inference. October 24 th, 2003 GEOG1230 - Week 4 A model for research A model for research Quantitative/Qualitative Quantitative/Qualitative

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


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


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


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


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


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


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.


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


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?



Guardian, Oct. 22nd, 2003


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


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




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


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


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


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



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


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



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



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




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


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)


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.


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



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.


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!

Documents

GEOG 1230 Lecture 4 Sampling and Inference. October 24 th, 2003 GEOG1230 - Week 4 A model for research A model for research Quantitative/Qualitative Quantitative/Qualitative