Стратификациялық сынама алу әдісі

Sampling from a population which can be partitioned into subpopulations

In statistics, stratified sampling is a method of sampling from a population which can be partitioned into subpopulations. In statistical surveys, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation (stratum) independently. Stratification is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should define a partition of the population. That is, it should be collectively exhaustive and mutually exclusive: every element in the population must be assigned to one and only one stratum. Then simple random sampling is applied within each stratum. The objective is to improve the precision of the sample by reducing sampling error. It can produce a weighted mean that has less variability than the arithmetic mean of a simple random sample of the population. In computational statistics, stratified sampling is a method of variance reduction when Monte Carlo methods are used to estimate population statistics from a known population.

Assume that we need to estimate the average number of votes for each candidate in an election. Assume that a country has 3 towns: Town A has 1 million factory workers, Town B has 2 million office workers and Town C has 3 million retirees. We can choose to get a random sample of size 60 over the entire population but there is some chance that the resulting random sample is poorly balanced across these towns and hence is biased, causing a significant error in estimation (when the outcome of interest has a different distribution, in terms of the parameter of interest, between the towns). Instead, if we choose to take a random sample of 10, 20 and 30 from Town A, B and C respectively, then we can produce a smaller error in estimation for the same total sample size. This method is generally used when a population is not a homogeneous group.

Proportionate allocation uses a sampling fraction in each of the strata that are proportional to that of the total population. For instance, if the population consists of n total individuals, m of which are male and f female (and where m + f = n), then the relative size of the two samples (x1 = m/n males, x2 = f/n females) should reflect this proportion. Optimum allocation (or disproportionate allocation) – The sampling fraction of each stratum is proportionate to both the proportion (as above) and the standard deviation of the distribution of the variable. Larger samples are taken in the strata with the greatest variability to generate the least possible overall sampling variance. A real world example of using stratified sampling would be for a political survey. If the respondents needed to reflect the diversity of the population, the researcher would specifically seek to include participants of various minority groups such as race or religion, based on their proportionality to the total population as mentioned above. A stratified survey could thus claim to be more representative of the population than a survey of simple random sampling or systematic sampling. Both mean and variance can be corrected for disproportionate sampling costs using stratified sample sizes.