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4(a)(ii) Sampling Methods………….Contd.
• STRATIFIED RANDOM SAMPLING :
In this method the population is first divided in to mutually exclusive
groups or strata and then a simple random sample is chosen within
each strata/group.
For example human population can be divided in to strata/group based
on age, occupation, income, gender. After that samples can be drawn
from each stratum by simple random sampling (SRS).
The stratification is done on the basis of characteristic of interest. The
elements within a stratum should be homogeneous while those in
different strata should be as heterogeneous as possible, from the point
of view of characteristic of interest.
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Reasons for Stratified Random Sampling:
1. When marketers want information about the component parts
of the universe.
Example: MDH Pickle sales in “large”, “medium” and “small” stores.
In such a case, separate sampling from within each of these strata
would be called for. The results might then be used to plan different
promotional activities for each store-size stratum.
2. Stratified random sampling is also used to increase the
precision of sampling estimates.
Example: To estimate monthly MDH Pickles sales per store in a
universe of 100,000 grocery stores. A typical frequency distribution of
store sales would be as depicted in Figure 11-1. Very few stores would
have very high sales. A larger number would have moderate sales, and
an even larger number would have small sales. Page.
We can subdivide this store universe into three strata, A, B, C, as indicated in Figure 11-2. A relatively small sample taken within each stratum would provide a good estimate of the mean of the stratum because of the similarly of the items included in that stratum. The estimated means of these strata could then be weighted together so as to provide an estimate of the mean of the entire universe.
MDH Pickles sold
Stratified random sampling will provide greater precision ( a smaller standard error of the mean) than a simple random sample of the same total size.
2. ESTIMATION OF THE UNIVERSE MEAN: A stratified
random sample is a group of simple random samples, the sample mean of each stratum is an unbiased estimate of the actual mean of the stratum. Therefore, the individual stratum sample means can be combined (weighted ) into as unbiased estimate of the overall universe mean. Thus, the estimate of the overall universe mean is simply a weighted average of the strata sample means.
Store Size Sample Mean Number of store % of store Stratum Unit sales/ store n Large 200 20,000 20% Medium 80 30,000 30% Small 40 50,000 50% Total 1,00,000 100% To estimate the universe mean of monthly sales, each stratum sample mean is multiplied by its relative weight (i.e., percent of all stores), and the results are added together. In this illustration, the estimated universe mean is (200)(20%) + (80)(30%) + (40)(50%) = 84 units per store.
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4. THREE ISSUES IN THE SELECTION OF STRATIFIED RANDOM
SAMPLES:
4.1 How should the Universe Be Stratified?
Homogenous among sampling units within strata, and Heterogeneous among strata. As a result, a relatively small sample within each stratum will provide a precise measurement of that stratum’s mean. The weighting together of the different stratum sample means, will, generally, provide a better estimate of the universe mean than would be provided by a simple random sample of the same total number of units.
4.2 How many Strata Should Be Constructed?
Higher the numbers of strata more homogenous will be stratum
However, practical considerations limit the number of strata such as Cost.. Secondly it requires separate listing for all the strata and in many cases these lists are not available.
4.3 How many Observations Should be Taken in Each Stratum?
Proportional Allocation: The most obvious way is to use proportional allocation. Here, one samples each stratum in proportion to its relative weight in the universe as a whole.
Disproportional Allocation: As a general principal, when the variability among observations within a stratum is high, one samples that stratum at a higher rate than for strata with less internal variation
4.4 Concluding Remarks on Stratified Random Sampling:
a) Information can be obtained about different parts of the universe,
b) It often provides universe estimates of greater precision than
simple random sampling.
The price paid for these advantages is greater complexity of both
design and analysis. A separate list of the items within each stratum
is required. To be of maximum value, strata should be constructed
such that the variable being studied varies only a little bit within
strata – but a great deal among strata.
It is most useful when sampling highly skewed universe where items
vary greatly in size.
5.1 Relatively Efficiency of Cluster Sampling and Simple Random Sampling: Cluster sampling will be more statistically efficient if each cluster represent most of the possible observations obtained from the universe. If each cluster represents only a few different universe observations , then cluster sampling will be less statistically efficient than SRS. Higher economic efficiency – that is, the relative cost per observation – cluster sampling is the superior to SRS. Gain in economic efficiency usually offset the decline in statistical efficiency.
5.2 Concluding Remarks on Cluster Sampling:
- Cluster sampling may be either more or less statistically efficient than simple random sampling. This depends on the degree of intracluster heterogeneity obtained.
- In practice, clusters are often constructed in such a way that the observations within a
cluster are relatively homogeneous. When this is the case, cluster sampling will be less
efficient statistically than simple random sampling.
- The lower relative cost of obtaining observations in cluster sampling often offsets the loss in statistical efficiency. The net efficiency is often greater for cluster sampling.
Two types of cluster sampling – systematic sampling and area sampling – are discussed below.
6. SYSTEMATIC SAMPLING: This is a simpler method and is easier to practice than simple random sampling. In this method at first all the units are listed (thus each is allocated a number). After this we decide the sample size either by statistical formula or by judgment.
Let the sample size be 'n' and the population be 'N'. Then the fraction N/n is calculated. Say it is 600/30 = 20. Then as a first step, a number is chosen from 0 to 9 at random (say 4). Then the units 4, 24, 44, 64, 84, 104 are. chosen as samples.
Example: Assume one wishes to study dentist’s attitudes towards dental insurance and decided to sample 20 dentists from a list of 100 dentists. One way of doing this is as follows:
- Draw a random number between 1 and 5. Assume the number chosen is 2.
- Include in the sample the dentists numbers 2,7,12,17,22,--------,97. That is, starting with number 2, take every fifth number. The above is an illustration of systematic sampling. That this is a particular kind of cluster sampling is readily seen if all possible samples produced by this procedure are considered. This particular example has only five possible samples.
6.2 Advantages of Systematic Sampling: The principal advantage of this technique is its simplicity. When sampling from a list, it is easier to choose a random start and select every Kth item thereafter than to make a simple random selection. The technique is faster and less subject to error than simple random selection. Hence, systematic sampling is often used in place of simple random sampling.
6.3 Disadvantages of Systematic Sampling: If the order is considered random, the standard error can be evaluated as the simple random sampling. Alphabetical lists are usually assumed to be in random order. If the order of the items on the list is not random, then estimating the standard error of the mean requires more complex methods.
6.4 Concluding Comments on Systematic Sampling: Appealing, easy to execute, and valid under most circumstances, used mush more often than simple random sampling. It is often combined with stratification, being used in place of simple random sampling to choose sample items within strata.
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7. AREA SAMPLING:
***** Area sampling is a special form of cluster sampling in which the sample items are clustered on a geographic area basis. The practical motivation underlying area sampling is that for many problems there is no current and accurate list of universe elements.
***** The original universe of interest- for which there is no list- is transformed into a universe for which there is a list. Such a list consists of city blocks, or PIN code areas, or countries, or other geographically defined area that can be identified on maps.
***** A rule of association, uniquely linking each item in the universe of interest to a single physical area, is established. By drawing a probability sample of area and using the rule of association, one obtains a probability sample from the universe of interest.
7.1 Application of Area Sampling: It enjoys wide usage in situations where very high quality data are wanted but for which no list of universe items exists. For instances, many governmental agencies use area sampling. However, the practical execution of a large scale area sample is highly complex. Typically, an area sampling is conducted in multiple stages, with successively smaller area clusters being sub- sampled at each stage.
8.1 Convenience Sampling: In this the choice of the sampling units is done primarily by the interviewer. The interviewer chooses anyone who is conveniently available during the time of interview. The elements might or might not be representative of the target population.
An extreme example is soliciting opinions from people conveniently in camera range (also SMS on TV). The major problem with this (and other nonprobability methods) is that one is unable to draw objective inference about a rigorously defined universe.
Convenience sampling is sometimes useful in exploratory work, to help understand the range of variability of response in a subject area, just taking to a few consumers may help identify issues.
8.2 Judgment Sampling: Specialists in the subject matter of the survey choose what they believe to be the best sample for that particular study. For example, a group of sales managers might select a sample of grocery stores in a city that they regarded as “representative”. This approach has been found empirically to produce unsatisfactory results. And, of course, there is no objective way of evaluation the precision of sample results. Despite these limitations, this method may be useful when the total sample size is extremely small.
8.3 Quota Sampling: As in stratified random sampling, the researchers begins by constructing strata, Bases for stratification in consumer surveys are commonly demographic, e.g., age, sex, income, and so on. Often compound stratification is used- for example, age groups within sex.
Next, sample sizes (called quotas) are established for each stratum. As with stratified random sampling, the sampling within strata may be proportional or disproportional. Field-workers are then instructed to conduct interviews with the designed quotas, with the identification of individual respondents being left to the field-workers.
*Concluding Comments of the Use of Quota Sampling: Owning to this relative economy and speed of execution, quota sampling will continue to enjoy wide usage. Because it uses the principal of stratification, this method is likely to be superior to ordinary convenience sampling or judgment sampling.
However, a quota sample should not be mistaken to be stratified random sample, because the two differ importantly. The difference lies in how the samples are selected within strata. With stratified random sampling, the process is objective, based on random identification of respondents. In quota sampling, the process is subjective, being done by field-workers using what amounts to convenience sampling. As a result, quota sample respondents may differ- in ways very important to the study’s purpose-when compared with respondents selected at random. Because respondents are not selected objectively, confidence interval statement cannot be made in quota sampling with the same legitimacy as when probability sampling has been used.
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9.3 Controlled Panel Samples: This technique, pioneered by national Family Opinion, Inc. (NFO), of Toledo, Ohio, is an elaborate and highly controlled form of quota sampling. NFO and similar organizations have developed huge files of names, addresses, telephone numbers, and a wide array of demographic characteristics for households willing to be interviewed by mail of telephone. Using computers, they have constructed “panels” (often of 1,000 households each) that approximately replicate the U.S. household universe in demographic characteristics, such as age, income, and the like, known to be related to consumer attitudes and behavior. In a given project one or more panels are interviewed via mail or telephone to obtain the requisite information.
A major advantage of this approach is that large national samples can be provided relatively cheaply and easily.
The disadvantages of controlled panel samples are those attendant on any quota sample plus the obvious bias that such samples are comprised of people who are willing to be included in panels and to participate in surveys from time to time. Such bias may be particularly acute when the panel is a continuing one that demands extensive cooperation over an extended interval.
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10. CHOICE OF SAMPLE DESIGN IN PRACTICE:
10.1 Quality of Sample Design Required: The “Quality” of sample design required varies from one problem situation to another. It is convenient to think of a continuum of “quality of sample design required”, as schematized below:
Quality of Sample Design Required
Extremely Low Extremely High
(Convenience sampling, from an accessible universe)
(Probability sampling, from most relevant universe)
Page. 411 In some situations, a low-quality sample design, as represented by convenience sampling from as accessible universe, may be adequate. An example would be an exploratory study to help define issues when virtually nothing is known of the subject. At the other extreme, exceptionally high-quality data will sometimes be necessary. If the analyst requires universe estimates with calculable precision from a universe that corresponds closely to the universe of interest, then probability sampling is essential.
