Download sampling - Routledge

SAMPLING
© LOUIS COHEN, LAWRENCE MANION
& KEITH MORRISON
STRUCTURE OF THE CHAPTER
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Sample size
Sampling error
The representativeness of the sample
Access to the sample
Sampling strategy to be used
Probability samples
Non-probability samples
Sampling in qualitative research
Sampling in mixed methods research
Planning a sampling strategy
HOW LARGE MUST MY SAMPLE BE?
It all depends on:
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The research purposes, questions and design;
The population size;
The confidence level and confidence interval
required;
The likely response rate;
The accuracy required (the smallest sampling
error sought);
The kinds of variables to be used (categorical,
continuous);
The statistics to be used;
HOW LARGE MUST MY SAMPLE BE?
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The number of strata required;
The number of variables included in the study;
The variability of the factor under study;
The kind(s) of sample;
The representativeness of the sample;
The allowances to be made for attrition and
non-response;
The need to keep proportionality in a
proportionate sample;
The kind of research that is being undertaken
(qualitative/quantitative/mixed methods).
SAMPLE SIZE
N
10
15
30
100
200
300
S
10
14
28
80
132
169
N
400
500
1,000
1,500
3,000
5,000
S
196
217
278
306
346
357
N = Population; S = Sample
Note: As the population increases, the proportion
of the population in the sample decreases.
PROPORTION OF SAMPLE SIZE TO POPULATION
6000
5000
4000
SA M PLE
3000
POPU LA T ION
2000
1000
0
Note: As the population increases, the proportion of the
population in the sample decreases.
SAMPLE SIZE
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Ensure a sufficiently large sample for each
variable.
 Samples in qualitative research must be large
enough to generate ‘thick descriptions’.
 A large sample does not guarantee
representativeness; representativeness
depends on the sampling strategy.
 Sample size also depends on the
heterogeneity or homogeneity of the
population: if it is highly homogeneous then a
smaller sample may be possible.
SAMPLE SIZE
Large samples are preferable when:
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there are many variables;
only small differences or small relationships are
expected or predicted;
the sample will be broken down into subgroups;
the sample is heterogeneous in terms of the
variables under study;
reliable measures of the dependent variable are
unavailable.
SAMPLE SIZE
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A weighted sample may be required if there
are small sub-groups of populations.
 A weighted sample: where a higher
proportion of the sub-group is sampled, and
then the results are subsequently scaled
down to be fairer in relation to the whole
sample.
SAMPLE SIZE
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Sample size depends on the style of research
(e.g. surveys may require large samples,
ethnographies may require smaller samples).
 Sample size depends on the numbers of
variables to be used, the kinds of variables, and
the statistics to be calculated.
 Sample size depends on the scales being used in
measurement (the larger the scale, the larger the
sample).
STANDARD ERROR OF THE SAMPLE
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If many samples are taken from the same
population, it is unlikely that they will all have
characteristics identical with each other or with the
population; their means will be different.
 Sampling error is the difference between the
sample mean and the population mean, due to the
chance selection of individuals.
 Sampling error reduces as the sample size
increases.
 Samples of >25 usually yield a normal sampling
distribution of the mean.
SAMPLING ERROR
Sample size
depends on the
margin of error
and the
confidence
levels that the
researcher is
prepared to
tolerate.
CALCULATING THE STANDARD
ERROR OF THE SAMPLE
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Stage One: Draw several number of samples of
equal size from a population, to create a sampling
distribution.
 Stage Two: Calculate the Standard Error (SE) of
the mean:
s
SD
SE 
N
SDs = standard deviation of the sample (a measure
of dispersal around the mean)
N = the number in the sample
EXAMPLE OF STANDARD ERROR
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If SDs = 13.76 and N = 120
Then
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SE 
SDs
13
.
96

 1.27
120
N
The Standard Error (SE) is 1.27.
SAMPLE SIZE, CONFIDENCE
LEVELS AND SAMPLING ERROR
N
S (95%)
S (99%)
50
44
50
100
79
99
200
132
196
500
217
476
1,000
278
907
2,000
322
1,661
5,000
357
3,311
THE REPRESENTATIVENESS OF THE
SAMPLE
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What is being represented (e.g. groups,
variables, spread of population).
 If the sample has unequal sub-groups, then it
may be necessary equalize the sample by
weighting, to represent more fairly the
population.
ACCESS TO THE SAMPLE
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Is access to the sample permitted,
practicable, realistic?
 Who will give/withhold/deny permission to
access the sample?
 Who are the ‘gatekeepers’?
SAMPLING STRATEGIES
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Probability sample
 Non-probability sample
PROBABILITY SAMPLE
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Every member of the wider population has an
equal chance to be included; choice is made on
chance alone. The aim is for generalizability
and wide representation.
 Less risk of bias in the sample.
RANDOM SAMPLE
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Drawing randomly from a list of the
population (e.g.: names from a hat, using a
matrix of random numbers).
 The probability of a member of the population
being selected is unaffected by the selection
of other members of the population, i.e. each
selection is entirely independent of the next.
SYSTEMATIC SAMPLING
Every nth person (e.g. every 4th person).
To find the frequency use the formula:
N
f 
sn
where f = frequency interval;
N = the total number of the wider population;
sn = the required number in the sample.
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In a company of 1,500 employees a sample
size of 306 is required (from tables of sample
size for random samples). The formula is:
This rounds to 5, i.e. every 5th person.
RANDOM STRATIFED SAMPLE
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Stage 1: Identify those characteristics which
appear in the wider population which must also
appear in the sample, i.e. divide the wider
population into mutually exclusive homogeneous
groups.
 Stage 2: Randomly sample within these groups,
the size of each group being determined by
judgement or tables of sample size.
THE PROBLEM OF STRATA
Whole company
English employees
Scottish employees
Welsh employees
American employees
N
1,000
S
278
Total
278
800
100
50
50
260
80
44
44
428
SCHOOLING
No schooling
Pre-primary
Primary incomplete
Primary complete
Junior secondary
Senior secondary
Tertiary, non-degree
Tertiary, degree
Special
Total
SUB-TOTAL
35,020
6,811
80,285
109,561
94,491
66,250
7,481
23,944
360
424,203
BUT . . . Total without strata
SAMPLE SIZE
380
364
384
384
384
382
367
379
186
3,210
384
PROBLEMS OF STRATA
The greater the number of strata, the larger the
sample will be.
Therefore, keep to as few strata as s necessary.
CLUSTER SAMPLE
Sampling within a particular cluster (e.g.
geographical cluster);
 Useful where population is large and
widely dispersed.
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STAGED (MULTI-STAGED) SAMPLE
1.
2.
3.
4.
5.
If the target population is 1,000 employees in
nine organizations, then the sample size is 278
from the nine organizations.
Put the names of the nine organizations on a
card each and give each organization a number,
then place all the cards in a box.
Draw out the first card and put a tally mark by the
appropriate organizations on the list.
Return the card to the box.
Do this 278 times and then total the number of
employees required from each organization (the
number of tally marks for each organization).
Organization
1
2
3
4
5
6
7
8
9
Total
Required
number of
employees
30
21
45
12
54
23
16
43
34
278
Go to each organization and ask for the required
random number from each.
MULTI-PHASE SAMPLE
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Change the sampling strategy at each phase
of the research, different samples for different
stages of the research, e.g.:
 Junior employees at stage one, middle
management at stage two, senior
management at stage 3 (determined by the
purposes of the research).
NON-PROBABILITY SAMPLE
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Members of the wider population are
deliberately excluded. The aim is for the
sample to represent itself rather than to seek
generalizability.
 Non-probability sampling can be of issues as
well as people.
CONVENIENCE SAMPLE
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Opportunity sample (often those to whom
there is easy access).
QUOTA SAMPLE
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The non-probability equivalent of stratified
sampling.
 Seeks to represent significant characteristics
(strata) of the wider population and to
represent these in the proportions in which
they can be found in the wider population.
EXAMPLE OF A PROPORTIONATE/QUOTA
SAMPLE FROM A UNIVERSITY
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Performing arts:
 Natural sciences:
 Humanities:
 Business & social sciences:
300 students
300 students
600 students
500 students
Proportions: 3: 3: 6: 5
 Minimum required is 3 + 3 + 6 + 5 = 17
HOW TO OBTAIN A PROPORTIONATE
(QUOTA) SAMPLE
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Stage 1: Identify those characteristics which
appear in the wider population which must
also appear in the sample, i.e. divide the
wider population into mutually exclusive
homogeneous groups, one row for each
characteristic.
 Stage 2: Identify the frequencies and
proportions in which the selected
characteristics appear in the wider population
(as a percentage).
HOW TO OBTAIN A PROPORTIONATE
(QUOTA) SAMPLE
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Stage 3: Ensure that the same percentages
of characteristics appear in the sample.
 Stage 4: Calculate the totalled percentage
and divide it by the highest common factor of
the cells in that column.
 Stage 5: Add together the totals for the
column to find out the total.
PURPOSIVE SAMPLE
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Deliberately chosen for specific purposes.
KINDS OF PURPOSIVE SAMPLING
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Critical case sampling
Extreme case sampling
Deviant case sampling
Boosted sample
Negative case sampling
Maximum variation sampling
Typical case sampling
Intensity sampling
KINDS OF PURPOSIVE SAMPLING
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Homogeneous sampling
Reputational case sampling
Revelatory case sampling
Politically important case sampling
Complete collection sampling
Theoretical sampling
Confirming and disconfirming case sampling
DIMENSIONAL SAMPLING
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Identify the group of factors (dimensions) to
be sampled, and obtain one respondent (or
more) for each group, i.e. a respondent who
carries more than one factor, e.g. a junior
employee who is a not-native English
speaker.
SNOWBALL SAMPLING
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One sample leads on to more of the same
kind of sample.
SNOWBALL SAMPLING
Person
1
RESEARCHER
Friend/contact 1
contacts his/her
own
friends/contacts/
4
5
RESEARCHER
HAS 3 CONTACTS
Friend/contact 2
contacts his/her
own
friends/contacts/
6
7
8
Friend/contact 3
contacts his/her
own
friends/contacts/
9
10
11
12
THE 3 CONTACTS EACH HAVE 3 CONTACTS
VOLUNTEER SAMPLING
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Volunteers may be well intentioned, but they
do not necessarily represent the wider
population.
 Caution: people volunteer for different
motives, e.g.:
– wanting to help a friend
– interest in the research
– wanting to benefit society
– revenge on a particular
school or headteacher.
THEORETICAL SAMPLING
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The researcher must have sufficient data to
be able to generate and ‘ground’ the theory in
the research context, i.e. to create theoretical
explanation of what is happening in the
situation, without having any data that do not
fit the theory.
 The researcher proceeds in gathering more
and more data until the theory remains
unchanged, until no modifications to the
grounded theory are made in light of the
constant comparison method.
MIXED METHOD SAMPLING DESIGNS
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Parallel mixed methods sampling
Sequential mixed methods sampling
Multilevel mixed methods sampling
Stratified purposive sampling
Purposeful random sampling
Nested sampling designs
PLANNING A SAMPLING STRATEGY
Stage One: Decide whether you need a sample, or
whether it is possible to have the whole population.
Stage Two: Identify the population, its important
features (the sampling frame) and its size.
Stage Three: Identify the kind of sampling strategy
you require (e.g. which variant of probability, nonprobability, or mixed methods sample you require).
Stage Four: Ensure that access to the sample is
guaranteed. If not, be prepared to modify the
sampling strategy.
PLANNING A SAMPLING STRATEGY
Stage Five: For probability sampling, identify the
confidence level and confidence intervals that you
require. For non-probability sampling, identify the
people whom you require in the sample.
Stage Six: Calculate the numbers required in the
sample, allowing for non-response, incomplete or
spoiled responses, attrition and sample mortality.
Stage Seven: Decide how to gain and manage
access and contact.
Stage Eight: Be prepared to weight (adjust) the
data, once collected.