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. Advantages The reasons to use stratified sampling rather than simple random sampling include If measurements within strata have a lower standard deviation (as compared to the overall standard deviation in the population), stratification gives a smaller error in estimation. For many applications, measurements become more manageable and/or cheaper when the population is grouped into strata. When it is desirable to have estimates of the population parameters for groups within the population - stratified sampling verifies we have enough samples from the strata of interest. 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 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