Stratified sampling| Definition, Allocation rules with advantages and disadvantages

Stratified Sampling

Stratified random sampling is a sampling plan in which we divide the population into several non overlapping strata and select a random sample from each stratum in such a way that units within the strata are homogeneous but between strata they are heterogeneous.
Stratum is a group of elements where all the units of elements "within the strata are homogeneous but  between strata they are heterogeneous". Homogeneous means alike or contains same characteristics and heterogeneous means different from each other or contains different characteristics. [Note: ‘Stratum’  is singular form and ‘strata’  is plural form]. 
Stratified sampling is a probability sampling.

Stratified sampling 

Allocation rules of stratified sampling

  •        Equal allocation
  •        Proportional allocation
  •        Neyman allocation
  •        Optimum allocation

Equal Allocation

In equal allocation we have to divide the sample size(n) by the number of strata.


Proportional allocation

In proportional allocation we have divide the sample size(n) by the total smple size(N) and multiply with stratum size(Ni).
proportional allocation

Neyman or optimal allocation

Neyman allocation is a special case of optimal allocation.
optimal allocation

Advantages of stratified sampling

  • Stratification tends to decrease the variances of the sample estimates. This results is smaller bound on the error of estimation. This is particularly true if measurement within strata are homogenous.
  • By stratification, the cost per observation in the survey may be reduced by stratification of the population elements into convenient groupings.
  •  When separate estimates for population parameters for each sub population within an overall population is required , stratification is rewarding.
  • Stratification makes it possible to use different sampling designs in different strata.
  • Stratification is particularly more effective when there are extremely values in the population, which can be segregated into separate strata. Thereby reducing the variability within strata.
  • Stratified sampling is most effective in handling heterogeneous population.
  • In stratified sampling, confidence intervals may be constructed individually for the parameter of interest in each stratum.

Disadvantages of stratified sampling

·  The major disadvantages of stratified sampling is that it may take more time to select the sample than would be the case for simple random sampling. More time is involved because complete frames are necessary within each of the strata and each stratum must be sampled.

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