# Other probabilistic sampling methods, Comparative characteristics...

## Other probabilistic sampling methods

Along with the four basic methods of constructing the sample, there are others, designed specifically to address any specific problems (most of them are modifications of the main methods). Consider only two of these modifications, which have a definite relationship to marketing research: sequential sampling and double sampling, two-phase sampling.

If the sample is consistently constructed, its size is not determined in advance. Only the rule is determined on the basis of which a decision is made about the necessary sample size. Data are collected in stages. At the end of each selection phase, the data is analyzed and a decision is made about the need to continue the selection.

This method of constructing a sample is convenient, for example, when an alternative arises. At each stage, respondents are asked which of the two possible products they would prefer. When their preferences become clear with a sufficiently high degree of certainty, the process of collecting new data ceases.

With double (two-stage) sampling , a large sample is constructed in the first stage and a short survey is conducted. Based on this information, a small sample is constructed from the elements covered by the first survey, and additional, in-depth information is collected.

This method is useful when it is not possible to obtain a basis for constructing the required sample, but it is known that it forms part of the basis for a larger sample. Then, at the first stage, it turns out, for example, which of the respondents drinks apple juice and in which approximately the volume, and at the second stage a sample stratified according to the volume of juice consumption is built, and information, for example, about the subtleties of choice is collected. If stratification is not carried out, the stages can be carried out simultaneously.

## Comparative characteristics and a brief outline of the use of basic sampling methods

Concluding the review of sampling methods, we present the results of their brief comparative analysis (Table 9.3).

Table 9.3. Comparative characteristics of different sampling methods

 Methods Advantages Disadvantages Incredible Sampling of consonants ( convenience sampling ) Requires least time and money, most convenient to use Offset selection, the sample is not representative. Not recommended for descriptive and causal research Sampling at discretion ( judgmental sampling ) It takes a little time and money, it's easy to use It does not allow to generalize the results obtained Quota method ( quota sampling ) Allows you to control certain characteristics Offset selection, there is no certainty of representativeness Snowball method ( snowball sampling ) Allows you to evaluate the characteristics of rare individuals Time-consuming Probabilistic Simple random sampling ( simple random sampling, or SRS ) Easily explain, you can generalize the results It is difficult to design the sampling frame, high cost, insignificant accuracy, for small samples, unrepresentation is possible Systematic random sampling ( systematic sampling ) May increase representativeness, easier to apply than SRS , does not require constructing a sampling frame In rare cases, it may reduce representativeness Stratification method ( stratified sampling ) High accuracy, the sample includes all important categories of objects of the target population It is difficult to find the appropriate stratification parameters, it is difficult to stratify in many variables at once, high costs Clustering method ( cluster sampling ) Low cost, simplicity Low accuracy, it is difficult to evaluate and interpret results

Simple random sampling ( simple random sampling, or SRS )

1. A suitable sampling frame is selected.

2. Elements are numbered from 1 to N (sample size).

3. It is generated on the computer or is in the table n (sample size) of various random numbers in the interval from 1 to N.

4. The selection includes the selection units with the corresponding numbers.

Systematic random sampling ( systematic sampling )

1. A suitable sampling frame is selected.

2. Elements are numbered from 1 to N (sample size).

3. The sampling step is determined:

4. A random number r is chosen in the interval from 1 to i.

5. The sample includes elements with the numbers r, r + i, r + 2i, r + 3i, ..., (n - 1) i. If they are fractions, they are rounded to the nearest whole number.

Stratification method (stratified sampling)

1. A suitable sampling frame is selected.

2. One or more stratification variables is selected and the number of strata is chosen.

3. The investigated population is divided into H stratum so that each element enters one and only one stratum depending on the values ​​of stratification parameters.

4. The elements entering each stratum are numbered from 1 to Nh, where Nh is the number of elements of the studied population in the stratum.

5. Based on proportional or disproportionate selection, the sample size extracted from each stratum nh is determined, where

6. In each stratum, a simple random sample of size nh is extracted.

Clustering method (cluster sampling)

We describe the procedure of two-stage proportional selection, since it is most often used.

1. The investigated population is divided into C clusters, of which c will be included in the sample.

2. Elements of the studied population are numbered from 1 to N so that first the elements of the first cluster are renumbered, then the second one, etc.

3. The selection step i, is calculated. If it is a fraction, it

is rounded to the nearest whole number.

4. As in the construction of a systematic random sample in the interval from 1 to r, a random number r is chosen.

5. Elements with the numbers r, r + i, r + 2i, r + 3i, ..., r + (c - 1) i are identified. If they are fractions, they are rounded to the nearest whole number.

6. Clusters are selected that contain the identified elements.

7. In each cluster, selection units are selected by simple or systematic selection. The number of selection units from each cluster is approximately the same and is equal to .

8. If the number of elements in any cluster exceeds the selection step, this cluster will be selected regardless of which random number fell on the fourth step of the algorithm. Such a cluster is included in the sample and is excluded from further consideration. The new size of the investigated population N *, the new number of clusters, which should be selected randomly from * (equal to c-1) and a new selection step r * is calculated. This procedure is repeated until the number of elements in all clusters is less than the selection step. If b clusters are selected with certainty, then the remaining c-b clusters are selected in accordance with the procedure described in clauses 1-7. For one unit of selection, which should fall into the sample, an average of units of selection in the study population. Therefore, from b clusters, with definite representation in the sample, the number of selection units, determined by the formula

(9.4)

Accordingly, the remaining randomly selected clusters are n * = n - ns units of selection.

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