What is one of the primary benefits of stratifying a population?
|
Suggest a new Definition Show
Proposed definitions will be considered for inclusion in the Economictimes.com Marketing
Definition: Stratified sampling is a type of sampling method in which the total population is divided into smaller groups or strata to complete the sampling process. The strata is formed based on some common characteristics in the population data. After dividing the population into strata, the researcher randomly selects the sample proportionally. Description: Stratified sampling is a common sampling technique used by researchers when trying to draw conclusions from different sub-groups or strata. The strata or sub-groups should be different and the data should not overlap. While using stratified sampling, the researcher should use simple probability sampling. The population is divided into various subgroups such as age, gender, nationality, job profile, educational level etc. Stratified sampling is used when the researcher wants to understand the existing relationship between two groups. The researcher can represent even the smallest sub-group in the population. There are two types of stratified sampling – one is proportionate stratified random sampling and another is disproportionate stratified random sampling. In the proportionate random sampling, each stratum would have the same sampling fraction. For example, you have three sub-groups with a population size of 150, 200, 250 subjects in each subgroup respectively. Now, to make it proportionate, the researcher uses one specific fraction or a percentage to be applied on its subgroups of population. The sample for first group would be 150*0.5= 75, 200*0.5=100 and 250*0.5= 125. Here the constant factor is the proportion ration for each population subset. The only difference is the sampling fraction in the disproportionate stratified sampling technique. The researcher could use different fractions for various subgroups depending on the type of research or conclusion he wants to derive from the population. The only disadvantage to that is the fact that if the researcher lays too much emphasis on one subgroup, the result could be skewed.
Stratified Random Sampling In statistics, stratified sampling is a method of sampling from a population which can be partitioned into subpopulations.  Stratified sampling example 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.[1] Example[edit]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. Stratified sampling strategies[edit]
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. Advantages[edit]The reasons to use stratified sampling rather than simple random sampling include[2]
If the population density varies greatly within a region, stratified sampling will ensure that estimates can be made with equal accuracy in different parts of the region, and that comparisons of sub-regions can be made with equal statistical power. For example, in Ontario a survey taken throughout the province might use a larger sampling fraction in the less populated north, since the disparity in population between north and south is so great that a sampling fraction based on the provincial sample as a whole might result in the collection of only a handful of data from the north. Disadvantages[edit]Stratified sampling is not useful when the population cannot be exhaustively partitioned into disjoint subgroups. It would be a misapplication of the technique to make subgroups' sample sizes proportional to the amount of data available from the subgroups, rather than scaling sample sizes to subgroup sizes (or to their variances, if known to vary significantly—e.g. using an F Test). Data representing each subgroup are taken to be of equal importance if suspected variation among them warrants stratified sampling. If subgroup variances differ significantly and the data needs to be stratified by variance, it is not possible to simultaneously make each subgroup sample size proportional to subgroup size within the total population. For an efficient way to partition sampling resources among groups that vary in their means, variance and costs, see "optimum allocation". The problem of stratified sampling in the case of unknown class priors (ratio of subpopulations in the entire population) can have a deleterious effect on the performance of any analysis on the dataset, e.g. classification.[3] In that regard, minimax sampling ratio can be used to make the dataset robust with respect to uncertainty in the underlying data generating process.[3] Combining sub-strata to ensure adequate numbers can lead to Simpson's paradox, where trends that exist in different groups of data disappear or even reverse when the groups are combined. Mean and standard error[edit]The mean and variance of stratified random sampling are given by:[2] where, number of strata the sum of all stratum sizes size of stratum sample mean of stratum number of observations in stratum sample standard deviation of stratumNote that the term ( − ) / (), which equals (1 − / ), is a finite population correction and must be expressed in "sample units". Foregoing the finite population correction gives: where the = / is the population weight of stratum . Sample size allocation[edit]For the proportional allocation strategy, the size of the sample in each stratum is taken in proportion to the size of the stratum. Suppose that in a company there are the following staff:[4]
and we are asked to take a sample of 40 staff, stratified according to the above categories. The first step is to calculate the percentage of each group of the total.
This tells us that of our sample of 40,
Another easy way without having to calculate the percentage is to multiply each group size by the sample size and divide by the total population size (size of entire staff):
See also[edit]
References[edit]
Further reading[edit]
What is the primary objective of monetary unit sampling?Monetary-unit sampling (MUS) is a method of statistical sampling used to assess the amount of monetary misstatement that may exist in an account balance. The method, also known as dollar-unit sampling or probability-proportional-to-size sampling, has been used for many years and is widely accepted among auditors.
What is one disadvantage of stratified sampling quizlet?What are the disadvantages of stratified sampling? Within the strata there are the same problems as in simple random sampling, and the strata may overlap if they are not clearly defined.
What is a mus sample?Monetary unit sampling (MUS) is a statistical sampling method that is used to determine if the account balances or monetary amounts in a population contain any misstatements.
Why is defining the population so important in a sampling application?Why is defining the population so important in a sampling application? To reduce sampling risk to the appropriate level. To permit the auditor to select the appropriate type of substantive procedure. To allow the auditor to appropriately measure sample items.
|
