MODULE R7 - SAMPLING
Randomization
Random sampling as suggested by Van Dalen (1979) often means chance
or a haphazard method of assignment to many people, but in reality it is a
carefully controlled process. Randomization is used to eliminate bias, both
conscious and unconscious, that researchers might introduce while
selecting a sample. Kerlinger (1986) described randomization as the
assignment of objects (subjects, treatments, groups, etc.) of a population to
subsets (sample) of the population in such a way that, for any given
assignment to a subset (sample), every member of the population has an
equal probability of being chosen for that assignment. Randomization is
essential for probability samples which are the only samples that can
generalize results back to the population. Kerlinger (1986) reported that
random sampling is important because it is required by inferential
statistics. If the researcher desires to make inferences about populations
based on the behavior of samples, then random sampling must be used.
Stratification
Stratified sampling is a procedure for selecting a sample that includes
identified subgroups from the population in the proportion that they exist
in the population. This method can be used to select equal numbers from
each of the identified subgroups if comparisons between subgroups is
important. A good example of stratified sampling would be to divide the
population into men and women. The different strata to use for each study
would be determined in part by the review of literature of previous
research. The purpose of stratified sampling is to guarantee the desired
distribution among the selected subgroups of the population.
Proportional
Proportional sampling (Van Dalen, 1979) provides the researcher a way to
achieve even greater representativeness in the sample of the population.
This is accomplished by selecting individuals at random from the
subgroup in proportion to the actual size of the group in the total
population. Proportional sampling is used in combination with stratified
and cluster sampling.
Clusters
The most used method in educational research according to Kerlinger
(1986) is cluster sampling. Groups of elements (clusters) instead of
individuals from the population are used for the sample. Cluster sampling
often is more convenient when the population is very large. It often isn’t
possible to randomly select from the entire population but is more
manageable when using clusters because of time, expense, and
convenience. A cluster sampling is using schools as clusters and randomly
selecting from the list of schools instead of randomly selecting individuals
from a list that includes all schools. This can help the researcher cut down
on travel expense, time, etc. One problem with cluster sampling is that it
usually produces a larger sampling error than a simple random sample of
the same size because the clusters tend to be more similar within the
cluster, reducing the representativeness of the sample (Van Dalen, 1979).
Systematic
In some cases when the population of a study is available as a list, a
sample is drawn from certain intervals on the list. The starting point is
randomly chosen and then every so many numbers another individual is
chosen from the list and added to the sample. This method can be equal to
random selection only if the names were randomized at the beginning.
Van Dalen (1979) cautions us to be wary of departure from randomness of
the list because of structure, some trend, or cyclical fluctuation.
Purposive
Kerlinger (1986) explained purposive sampling as another type of nonprobability sampling, which is characterized by the use of judgment and a
deliberate effort to obtain representative samples by including typical
areas or groups in the sample. In other words, the researcher attempts to
do what proportional clustering with randomization accomplishes by using
human judgment and logic. As a result, there are many opportunities for
error. In addition, nonprobability samples do not use random sampling
which makes them unacceptable for generalizing back to the population.
In random sampling each object has an equal and independent
opportunity of being chosen. Stratified sampling involves the identification
of the variable and subgroups (strata) for which you want to guarantee
appropriate representation (either proportional or equal). To use cluster
sampling, you must list and identify all clusters that comprise the
population and estimate the average number of population members per
cluster to determine the number of clusters needed for the sample.
Proportional sampling determines the ratio of individuals in subgroups for
which you want proportional representation. Once the strata, cluster, or
ratio has been determined, individual objects, clusters, or individuals in a
subgroup are randomly selected. Systematic sampling takes every nth
name (n=size of population divided by desired sample size) on a list of the
population until the desired sample size is reached.
Determination of Sample Size
The first thing that is needed is to identify or define the population.
Jaccard (1983) defined population as the aggregate of all cases to which
one wishes to generalize. At this time, it is necessary to determine if your
research requires the identification of subgroups and if so define the
subgroups within the population. To have a sample that is of use it needs
to be as close as possible to being representative of the complete
population. Popham and Sirotnik (1973) contend that in order to draw
legitimate inferences about populations from samples that the sample has
to be representative of the population and randomly selected.
Van Dalen (1979) lists three factors that he considers to determine the
size of an adequate sample as (l) the nature of the population, (2) the type
of investigation, and (3) the degree of precision desired. The formula for
estimating the sample size and a table for determining the sample size
based on confidence level needed from a given population was provided by
Krejcie and Morgan (1970).
where
S = required sample size
N = the given population size
P = population proportion that for table construction has been assumed to
be .50, as this magnitude yields the maximum possible sample size
required
d = the degree of accuracy as reflected by the amount of error that can be
tolerated in the fluctuation of a sample proportion p about the population
proportion P - the value for d being .05 in the calculations for entries in
the table, a quantity equal to
X2 = table value of chi square for one degree of freedom relative to the
desired level of confidence, which was 3.841 for the .95 confidence level
represented by entries in the table
TABLE FOR DETERMINING NEEDED SIZE S OF A RANDOMLY
CHOSEN SAMPLE FROM A GIVEN FINITE POPULATION OF N
CASES SUCH THAT THE SAMPLE PROPORTION p WILL BE WITHIN
± .05 OF THE POPULATION PROPORTION P WITH A 95 PERCENT
LEVEL OF CONFIDENCE
Population
Size
Sample
Size
Population
Size
Sample
Size
Population
Size
Sample
Size
10
10
220
140
1200
291
15
14
230
144
1300
297
20
19
240
148
1400
302
25
24
250
152
1500
306
30
28
260
155
1600
310
35
32
270
159
1700
313
40
36
280
162
1800
317
45
40
290
165
1900
320
50
44
300
169
2000
322
55
48
320
175
2200
327
60
52
340
181
2400
331
65
56
360
186
2600
335
70
59
380
191
2800
338
75
63
400
196
3000
341
80
66
420
201
3500
346
85
70
440
205
4000
351
90
73
460
210
4500
354
95
76
480
214
5000
357
100
80
500
217
6000
361
110
86
550
226
7000
364
120
92
600
234
8000
367
130
97
650
242
9000
368
140
103
700
248
10000
370
150
108
750
254
15000
375
160
113
800
260
20000
377
170
118
850
265
30000
379
180
123
900
269
40000
380
190
127
950
274
50000
381
200
132
1000
278
75000
382
210
136
1100
285
100000
384
Survey Design Notes by Dr. Don Dillman;
A Survey Can: "Provide the distribution of a characteristic in a population
by collecting information from only a few of its members."
Rules of Thumb:
Sample randomly
Doubling sample size reduces sampling error by half
Sampling can be far more complex than described.
Measurement Error:
Occurs when respondent answers to questions are inaccurate.
A result of question wording, the questionnaire, the interviewer, the
survey method, and/or the respondent.
Sampling Error
Occurs because only a subset of the population is surveyed.
n
97
Precision
385
+/- 5%
1068
+/- 3%
2175
+/- 2%
+/- 10%
Coverage Error
Occurs because samples list does not include all elements of the population that
one wishes to survey.
Each member of the entire population needs to have a known (non-zero) chance of
being included in the sample.
Non-response Error
Occurs when some of the sampled individuals do not respond and they are
different from those who do in a way that is relevant to study.
This is more important than response rate!
For a survey to be accurate, each of the four sources of data collection error
must be attended to .
sampling error
Coverage error
measurement error
Non-response error
Perspective for Improving Response
Increase rewards
Decrease costs
Promote trust
This is a social exchange, not and economic exchange.
Requirements for Maximizing Mail Survey Response
Respondent-friendly questionnaire
Personalized correspondence
Prepaid financial incentive - $ 2 - 5
First Class mail
Four contacts - pre-notice, questionnaire, reminder, replacement questionnaire
Fifth contact - 2 day priority mail or telephone
Why Mail Surveys Usually Fail
Inadequate sample frames and respondent selection
Poor Questions
Selective non-response
How to Improve Responce
A List
Multiple contacts
Stamped return envelope
$ Pre-incentive
Respondent-friendly questionnaire
B List
No labels
Real signature
Green paper
Graphic cover design
SELF ASSESSMENT
1. Define.
Sample
Population
2. Describe the sampling approach of randomization.
3. Define stratification as related to sampling.
4. Explain clusters regarding a sample.
5. Describe proportional in relation to sampling.
6. Define and explain systematic sampling.
7. Explain the use of purposive sampling.
8. Explain how to determine the sample size needed to give the most
representative sample.
9. Describe the type of sampling method that would be used for your
research and explain why this would be the best choice.