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1

Quantitative approaches

Lesson 3:

Sampling

2

Quantitative approaches

Plan

1. Introduction to quantitative sampling

2. Sampling error and sampling bias

3. Response rate

4. Types of "probability samples"

5. The size of the sample

6. Types of "non-probability samples"

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Quantitative approaches

1. Introduction to quantitative sampling

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Quantitative approaches

Sampling: Definition

Sampling = choosing the unities (e.g. individuals,

famililies, countries, texts, activities) to beinvestigated

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Quantitative approaches

Sampling: quantitative and qualitative"First, the term "sampling" is problematic for qualitative research,because it implies the purpose of "representing" the population sampled.

Quantitative methods texts typically recognize only two main types ofsampling: probability sampling (such as random sampling) andconvenience sampling."

(...) any nonprobability sampling strategy is seen as "conveniencesampling" and is strongly discouraged."

This view ignores the fact that, in qualitative research, the typical way ofselecting settings and individuals is neither probability sampling norconvenience sampling."

It falls into a third category, which I will call purposeful selection; otherterms are purposeful sampling and criterion-based selection."

This is a strategy in which particular settings, persons, or activieties areselected deliberately in order to provide information that can't be gottenas well from other choices."Maxwell , Joseph A. , Qualitative research design..., 2005 , 88

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Quantitative approaches

Population and Sample

Population

Sample

SamplingIIIIIIIIIIIIIIII

IIIIIIIIIIIIIIII

IIIIIIIIIIIIIIII

IIIIIIIIIIIIIIII

IIIIIIIIIIIIIIII

IIIII

IIIII

(= !Miniature population!)

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Quantitative approaches

Population, Sample, Sampling frame

Population = ensemble of unities from which the sample istaken

Sample = part of the population that is chosen for investigation. The choice may be based onrandomness or not.

Sampling

frame = list of all the unities from which the choice ismade.

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Quantitative approaches

Representative sample, probability sample

Representative sample = Sample that reflects the populationin a reliable way: the sample is a!miniature population!

Probability sample = Sample that has been randomlychosen. Therefore, every unity hasa known probability to be chosen.

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Quantitative approaches

Representativity: an empirical question

The representativity of the sample cannot be assured byfollowing a given method. If we use the correct methods(random choice, stratification etc.) we can only maximize theprobability of producing a representative sample.

It is an empirical question (and should be tested) if thesample is really representative of the population.

For example: we would investigate if the percentage ofwomen in the sample are not significantly different fromthose of the population (==> the sample is representativeconcerning gender).

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Quantitative approaches

2. Sampling error, sampling bias

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Quantitative approaches

Errors: different types

1. Sampling error due to chance, size of sample

2. Sampling bias not due to chance or size of sample. E.g. non-response linkedto the specific theme of the research

3. Data collection error e.g. bad question wording; bad interviewing

4. Data processing error e.g. wrong coding

5. Data analysis error e.g. wrong statistical model;erroneous data analysis

6. Data interpretation error e.g. wrong interpretation of results

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Quantitative approaches

Sampling error, sampling bias

Sampling error = Differences between the sample and thepopulation that are due to the sampling(the randomness). Sampling error can bediminished by increasing the size of thesample

Sampling bias = Differences between the sample and thepopulation that are not due to sampling(the randomness); the sampling biasdoes not diminish with increased samplesize.

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Quantitative approaches

Sampling error/bias: example (I)

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

smokers non-smokers

Population : N = 200

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

smokers non-smokers

Population : N = 200

Sample : N = 32

no error/bias

P(s) = 0.5; p(s) = 0.5

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Quantitative approaches

Sampling error/bias: example (II)

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

smokers non-smokers

Population : N = 200

Sample : N = 32

a bit of error/bias

P(s) = 0.5; p(s) = 0.47

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O

smokers non-smokers

Population : N = 200

Sample : N = 32

a lot of error/bias

P(s) = 0.5; p(s) = 0.33

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Quantitative approaches

Sampling error: decreases

with increasing sample sizeExperiment with a coin

Probability of throwing !heads!?

P !in reality! = 0.5

We do 5 tries with N =1,2,5,20

With growing N, the p is approaching the P

N = 1 -> p = 0, 1, 0, 1, 1

N = 2 -> p = 0, 0.5, 0.5, 1, 0

N = 5 -> p = 0.6, 0.2, 0.4, 0.8, 0.1

N = 20 -> p = 0.4, 0.35, 0.45, 0.35, 0.55

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Quantitative approaches

Possible reasons for sampling bias

The sampling frame does not include all the elements of thepopulation (example: telephone directory)

The choice is not really random (example: open telephonedirectory at a random page and choose the next 600 names)

Certain groups of respondents have a higher (lower) responserate (example: the very poor, the very rich, ther very active,the people with an active interest in the question, the peoplecritical of surveys)

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Quantitative approaches

Sampling error vs. sampling bias: Citation

Sampling error is random. Every time you select an individual, a text, asituation, or any "unit of observation," that unit of observation will bedifferent from the population of such units. Hence you always have anerror (we hope a small one) in generalizing to the population of units."

"Unlike sampling error, "sampling bias" is systematic (nonrandom). Forexample, if for a focus group study you "randomly" select one of everyfive students who happen to be in the library on a Friday afternonnon,you might have a bia