Stratified Sampling
Stratified-Sample is a method of sampling from a population where the population is divided into smaller groups, known as strata, before the sample is taken. Each stratum is formed based on shared attributes or characteristics, ensuring that each group is homogeneous in some way. This technique is used to increase the precision of the sample by reducing sampling error and ensuring that subgroups within the population are adequately represented.
History and Development
The concept of Stratified-Sample can be traced back to the early 20th century when statisticians began to realize the limitations of simple random sampling in accurately representing diverse populations. One of the pioneering works in this area was by William Gosset (who published under the pseudonym "Student") with his work on Student's t-test and later by Ronald Fisher, who formalized many sampling techniques. The method was further developed and popularized in the context of survey sampling by statisticians like William Edwards Deming and Morris Hansen during the mid-20th century.
How It Works
- Stratum Formation: The population is divided into strata based on characteristics relevant to the research question. These could be demographic details like age, gender, income level, or other categorical variables.
- Sample Size Allocation: Decide how many observations or samples to take from each stratum. This can be proportional to the size of the stratum (proportional allocation) or can be disproportionate based on the study's objectives (optimum allocation).
- Sampling Within Strata: Within each stratum, a simple random sample or another sampling method like Systematic Sampling is applied to select the units to be included in the sample.
Advantages
- Improved Precision: By ensuring that all important subgroups are represented in the sample, the accuracy of estimates about population parameters can be improved.
- Comparability: Allows for comparisons between different strata, which can be crucial in many analytical contexts.
- Control of Sampling Error: Reduces sampling error compared to simple random sampling, especially when strata differ significantly in terms of the variable of interest.
Disadvantages
- Complexity: Requires detailed knowledge about the population structure, which might not always be available.
- Cost: Can be more expensive and time-consuming than simple random sampling due to the need for stratification.
- Over-stratification: If too many strata are created, it might lead to inefficiency due to small sample sizes within each stratum.
Applications
Stratified-Sample is widely used in:
- Public health studies to ensure representation of different health risk groups.
- Election polling to account for different demographic groups.
- Quality control in manufacturing to assess product quality across different production lines.
- Environmental studies to examine the distribution of species or pollutants in different ecosystems.
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