Management Notes

# Management Notes

Reference Notes for Management

# Sampling Methods – Probability and Non-Probability Sampling | Business Statistics

## Sampling Methods

There are several sampling methods that may be used with any of the types of frames described above, individually or in combination. They are influenced by many factors, including:

• Nature and quality of the frame
• Availability of auxiliary information about units on the frame
• Accuracy requirements, and the need to measure accuracy
• Whether detailed analysis of the sample is expected
• Cost/operational concerns

### Types of Sampling Methods

#### Simple Random Sampling

Simple random sampling (SRS) of a given size gives equal probability to such subsets. There is no subdividing or partitioning of the frame: each element has the same chance of being selected. Additionally, any given pair of elements has the same chance of selection as any other pair (and similarly for triples, and so forth).

In this way, the results are easily analyzed and biased results are avoided. The variance between individual results within a sample is a good indicator of variation across the entire population, so estimating the accuracy of results is relatively simple. In spite of this, SRS is susceptible to sampling error since the randomness of the selection can result in a sample that doesn’t reflect the population.

As an example, a random sample of ten people from a given country will generally produce five men and five women, but any given trial may over represent one sex and underrepresent the other.

Stratified and systematic sampling, discussed below, use information about the population to choose a more representative sample. In addition to being tedious and time-consuming, SRS can also be cumbersome when sampling from an unusually large target population.

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##### A) If we consider the simple random sampling process as an experiment, the sample mean is

Options

a) always zero

b) always smaller than the population mean

c) a random variable

d) exactly equal to the population mean

c) a random variable

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#### Systematic sampling

For some situations, the most practical way to sample is to choose every nth item from a list. This type of sampling is called systematic sampling. It is important to remember that random numbers are used to select the unit from which to start this type of sampling.

As an example, if 4% of items are to be sampled, the first item would be chosen randomly from the first 25 and every item after that would be automatically included in the sample.

Systematic sampling, therefore, only selects the first unit randomly, while the remaining units are chosen at fixed intervals.

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#### Stratified Sampling

To obtain a representative sample from a population that is not homogeneous, a stratified sampling technique is generally applied.

The stratified sampling method breaks the population into sub-populations greater in homogeneity than the total population (the different sub-populations are called strata) and then we take items from each stratum to constitute a sample.

The strata are more homogeneous than the total population, so we can estimate each stratum more precisely, and by estimating more accurately each of the components, we can estimate the total population better.

Stratified sampling provides more reliable and detailed information.

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#### Cluster Sampling

To take a sample from a large area, it is convenient to divide the area into small, non-overlapping bits and then to randomly choose bits from each of those pieces of the larger area (usually called clusters), followed by taking samples from all (or parts of) these smaller pieces.

In cluster sampling, the total population is divided into a number of relatively small subdivisions, which themselves are clusters of even smaller units, and then some of these clusters are selected at random for inclusion in the sample as a whole.

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#### Multi-stage Sampling

Multi-stage sampling is an extension of the principle of cluster sampling.

To examine the efficiency of nationalized banks in India, let us select a sample of a few banks. In the first stage, a large primary sampling unit, such as a state in a country, is selected. Following that, we may select certain districts and interview all banks in those districts.

In this case, a two-stage sampling design is used with clusters of districts as the sampling units. Instead of taking a census of all banks within the selected districts, we interview all banks within the selected towns. This is a three-stage sampling process.

In that case, a four-stage sampling plan is used instead of taking a census of all banks within the selected towns. Random selection at all stages is referred to as ‘multistage random sampling design’.

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#### Sequential Sampling

The sampling design for this sample is somewhat complex. Under this method, the size of the sample is not fixed in advance, but is determined based on mathematical decision rules as the survey progresses. When applied to a statistical quality control plan, this is typically the case for acceptance sampling.

Taking a decision on a lot based on only one sample is called single sampling; taking a decision on the basis of two samples is called double sampling; and if there are more than two samples but the number of samples is certain and decided in advance, it is called multiple sampling.

Sequential sampling is often used when the number of samples is more than two but it is neither predetermined nor planned in advance.

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