Stratified Sampling

Divide the population into strata according to a feature of a population. Then take a simple random sample from each strata. Each of the samples are taken independently.

Ideally, variation between strata is large but variation within strata are small. Heterogenous between but homogenous within. This would help in the accuracy of the

H is the letter used to denote the strata. Capital N with subscripts from 1 to H denote the number of population units in the strata. Small n with subscripts 1 to H denotes the samples taken from the strata.

sum of samples taken from strata = overall sample size

sum of strata = overall population

Why stratified sampling?
 * More representativeness
 * More precision
 * Study specific subpopulations
 * To assist in implementing operational aspects of survey research

Estimation strategy
 * Think Logically. Think slow. Not too complicated.
 * When using proportions, treat proportions as means
 * Total estimate for each stratum can be calculated using proportions(ph) as Nhph
 * Can add the estimate for each stratum to get total estimate
 * Total variation is just addition of the variables for each strata
 * sampling from each strata is independent so they can be added
 * Nh/N is weight.

Allocation of population to strata
 * Equal Allocation
 * when all stratas have the same number drawn from the population
 * Proportional Allocation
 * nh/Nh = Nh/N
 * Allocation to produce estimates for subpopulations
 * Optimal Allocation
 * http://stattrek.com/statistics/dictionary.aspx?definition=Neyman_allocation
 * When we want to maximise survey precision