Research Methods in Education 6th Edition

1. © LOUIS COHEN, LAWRENCE
MANION & KEITH MORRISON
SAMPLING

2.  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
STRUCTURE OF THE CHAPTER

3. It all depends on:
 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?

4.  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).
HOW LARGE MUST MY SAMPLE BE?

5. N S N S
10 10 400 196
15 14 500 217
30 28 1,000 278
100 80 1,500 306
200 132 3,000 346
300 169 5,000 357
N = Population; S = Sample
Note: As the population increases, the proportion
of the population in the sample decreases.
SAMPLE SIZE

6. 0
1000
2000
3000
4000
5000
6000
SA M PLE
PO PU LA TIO N
Note: As the population increases, the proportion of the
population in the sample decreases.
PROPORTION OF SAMPLE SIZE TO POPULATION

7. SAMPLE SIZE
 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.

8. SAMPLE SIZE
Large samples are preferable when:
 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.

9. SAMPLE SIZE
 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.

10. SAMPLE SIZE
 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).

11.  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.
STANDARD ERROR OF THE SAMPLE

12. SAMPLING ERROR
Sample size
depends on the
margin of error
and the
confidence
levels that the
researcher is
prepared to
tolerate.

13.  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:
SDs = standard deviation of the sample (a measure
of dispersal around the mean)
N = the number in the sample
N
SD
SE
s
=
CALCULATING THE STANDARD
ERROR OF THE SAMPLE

14. If SDs = 13.76 and N = 120
Then
The Standard Error (SE) is 1.27.
27.1
120
96.13 ===
N
SD
SE
s
EXAMPLE OF STANDARD ERROR

15. 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
SAMPLE SIZE, CONFIDENCE
LEVELS AND SAMPLING ERROR

16.  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.
THE REPRESENTATIVENESS OF THE
SAMPLE

17.  Is access to the sample permitted,
practicable, realistic?
 Who will give/withhold/deny permission to
access the sample?
 Who are the ‘gatekeepers’?
ACCESS TO THE SAMPLE

18.  Probability sample
 Non-probability sample
SAMPLING STRATEGIES

19.  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.
PROBABILITY SAMPLE

20.  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.
RANDOM SAMPLE

21. sn
N
f =
where f = frequency interval;
N = the total number of the wider population;
sn = the required number in the sample.
Every nth
person (e.g. every 4th
person).
To find the frequency use the formula:
SYSTEMATIC SAMPLING

22.  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.
9.4
306
500,1
==f

23.  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.
RANDOM STRATIFED SAMPLE

24. N S Total
Whole company 1,000 278 278
English employees 800 260
Scottish employees 100 80
Welsh employees 50 44
American employees 50 44
428
THE PROBLEM OF
STRATA

25. SCHOOLING SUB-TOTAL SAMPLE SIZE
No schooling 35,020 380
Pre-primary 6,811 364
Primary incomplete 80,285 384
Primary complete 109,561 384
Junior secondary 94,491 384
Senior secondary 66,250 382
Tertiary, non-degree 7,481 367
Tertiary, degree 23,944 379
Special 360 186
Total 424,203 3,210
BUT . . . Total without strata 384

26. The greater the number of strata, the larger the
sample will be.
Therefore, keep to as few strata as s necessary.
PROBLEMS OF STRATA

27. Sampling within a particular cluster (e.g.
geographical cluster);
Useful where population is large and
widely dispersed.
CLUSTER SAMPLE

28. 1. If the target population is 1,000 employees in
nine organizations, then the sample size is 278
from the nine organizations.
2. 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.
3. Draw out the first card and put a tally mark by the
appropriate organizations on the list.
4. Return the card to the box.
5. Do this 278 times and then total the number of
employees required from each organization (the
number of tally marks for each organization).
STAGED (MULTI-STAGED)
SAMPLE

29. 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.

30.  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).
MULTI-PHASE SAMPLE

31.  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.
NON-PROBABILITY SAMPLE

32.  Opportunity sample (often those to whom
there is easy access).
CONVENIENCE SAMPLE

33.  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.
QUOTA SAMPLE

34.  Performing arts: 300 students
 Natural sciences: 300 students
 Humanities: 600 students
 Business & social sciences: 500 students
Proportions: 3: 3: 6: 5
∴ Minimum required is 3 + 3 + 6 + 5 = 17
EXAMPLE OF A
PROPORTIONATE/QUOTA SAMPLE
FROM A UNIVERSITY

35.  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

36.  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.
HOW TO OBTAIN A PROPORTIONATE
(QUOTA) SAMPLE

37.  Deliberately chosen for specific purposes.
PURPOSIVE SAMPLE

38. ● 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

39. ● Homogeneous sampling
● Reputational case sampling
● Revelatory case sampling
● Politically important case sampling
● Complete collection sampling
● Theoretical sampling
● Confirming and disconfirming case sampling
KINDS OF PURPOSIVE SAMPLING

40.  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.
DIMENSIONAL SAMPLING

41.  One sample leads on to more of the same
kind of sample.
SNOWBALL SAMPLING

42. Person
1
Friend/contact 1
contacts his/her
own
friends/contacts/
Friend/contact 2
contacts his/her
own
friends/contacts/
Friend/contact 3
contacts his/her
own
friends/contacts/
4 5 6 7 8 9 10 11 12
RESEARCHER RESEARCHER
HAS 3 CONTACTS
THE 3 CONTACTS EACH HAVE 3 CONTACTS
SNOWBALL SAMPLING

43.  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.
VOLUNTEER SAMPLING

44.  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.
THEORETICAL SAMPLING

45.  Parallel mixed methods sampling
 Sequential mixed methods sampling
 Multilevel mixed methods sampling
 Stratified purposive sampling
 Purposeful random sampling
 Nested sampling designs
MIXED METHOD SAMPLING DESIGNS

46. 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, non-
probability, 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

47. 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.
PLANNING A SAMPLING STRATEGY