# Stratified Sampling

Stratified sampling is an effective probability sampling method that differs from random and systematic sampling in that the chance of inclusion of the elements is not equal. It is particularly useful when the target population is composed of distinct clusters or segments. For such populations, stratification allows for achieving the same level of precision with a significantly smaller sample size.

The process of stratification involves dividing the universe or population into groups known as strata or cells. The objective is to select a sample from each group and analyse them separately. In the context of market measurement, where stratification is the norm, the retail channels such as provision stores, supermarkets, minimarkets, and convenience stores form different strata. Each stratum is internally homogeneous, meaning that elements within the same stratum share similar characteristics, while they are externally heterogeneous, differing from elements in other strata. For instance, supermarkets are similar to one another but different from convenience stores in terms of store type, retail chain, geographical location, and shop size.

By utilizing stratified sampling, researchers can observe a substantial reduction in variance within each stratum, leading to more precise estimates. To illustrate this, let us consider the following example:

Population of numbers: {1, 2, 1, 3, 3, 12, 12, 13, 13, 10}

Mean = 7,

Variance = 28.9.

Stratum I: {1, 2, 1, 3, 3}

Mean = 2,

Variance = 1.0.

Stratum II: (12, 12, 13, 13, 10}

Mean = 12,

Variance = 1.5.

In this example, the population of ten numbers exhibits two distinct clusters. The total population has a variance of 28.9. However, by breaking down the population into two strata, the variance within each stratum is significantly reduced. This demonstrates the benefit of stratification in reducing variance and increasing precision within specific segments of the population.

Consider a target population consisting of strata, such as provision stores and supermarkets. The variance within each stratum (provision stores and supermarkets) is much lower compared to the variance within the combined population of all outlets. Since sample size requirements are proportional to variance, stratification enables a substantial reduction in the sample size.

In summary, stratified sampling is a valuable probability sampling technique, especially when dealing with populations that exhibit distinct clusters or segments. By dividing the population into strata and analysing each separately, researchers can reduce the required sample size.

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