S138 Chapter 3

• Stratification - the act of sorting data, people, and objects into distinct groups or layers
• In each stratum, we conduct SRS
• Advantage of Stratification

  It will yield samples with better representation of variability
• Choice of Stratification Variable

  1. With known values
  2. Highly correlated with the population of interest
• When is stratified sampling better than SRSWOR?

  1. Smaller variance
  2. Finer groupings
• Is there a limit on the number of strata?

  Yes
• Properties of Stratified Random Sampling

  1. The stratified variable must satisfy its two properties
  2. The units must be homogenous within a stratum and heterogenous between strata
  3. The samples from the strata are independent
• Stratum Size

  $N_h$
• Population Size

  $N$
• Value of the unit $j$ in stratum$h$

  $y_{hj}$
• Stratum Total

  $t_h$
• Population Total

  $t$
• Population mean in stratum $h$

  $\bar{y}_{hU}$
• Population mean

  $\bar{y}_U$
• Sampling Weights Under Stratified Sampling

  $w_{hj}=$$N_h/n_h$
• Equal Allocation

  $n_h=$$n/H$
• Proportional Allocation

  $n_h=$$(N_h/N)n$

  • Suitable when variance is somehow the same in all strata
• Optimal Allocation

  • Fixed cost
  • Suitable when variance is not constant for all
• Neyman Allocation

  A special case of optimal allocation when the costs are approximately constant in all strata