This is known as proportionate stratification (as opposed to disproportionate stratification, where the sample size of each of the stratum is not proportionate to the population size of the same stratum). If this was the case, we would want to ensure that the sample we selected had a proportional number of male and female students. These strata are expressed as H.įor example, imagine we were interested in comparing the differences in career goals between male and female students at the University of Bath. Therefore, the stratified random sample involves dividing the population into two or more strata (groups). However, sometimes we are interested in particular strata ( groups) within the population. In order to select a sample ( n) of students from this population of 10,000 students, we could choose to use a simple random sample or a systematic random sample. These 10,000 students are our population ( N). Let's say that the university has roughly 10,000 students. Stratification enables analysts to estimate the population parameter, say, the mean for all the subgroups of the entire population.Imagine that a researcher wants to understand more about the career goals of students at the University of Bath.Stratification is associated with a smaller error of estimation compared to simple random sampling, especially when each stratum is homogeneous.Advantages of Stratified Sampling over Simple Random Sampling $$ \text * 50 \right) = 13\) households in region C. We use the following formula to determine the number of households to be included in the sample from each region: Given the differences in the composition of each region, the firm decides to draw a sample of 50 households, taking the total number of families in each into account.ĭetermine the number of homes that have been sampled in each region. There are 160 households in town A, 60 in town B, and 80 in C. Town B mainly harbors retirees while most people in town C practice agriculture. Town A is adjacent a major factory where most residents work, with most having school-aged kids. The district has three distinct towns – A, B, which are urbanized, and C, located in a rural area. They decide to carry out a survey aimed at estimating the mean number of hours spent by households watching TV per week. Example: Stratified Random SamplingĪn advertising firm wants to determine the extent to which they should emphasize television ads in a district. The number of members chosen from any one stratum depends on its size relative to the population as a whole. The method is most appropriate for large populations that are heterogeneous in nature.Ī simple random sample is then taken from within each stratum and combined to form the overall, final sample that takes heterogeneity into account. Each stratum is composed of elements that have a common characteristic (attribute) that distinguishes them from all the others. In stratified random sampling, analysts subdivide the population into separate groups known as strata (singular – stratum). That’s where stratified random sampling comes in. However, it is not appropriate when there are glaring differences within the population such that statisticians can divide the members into different, distinctive categories. The method attempts to come up with a sample that represents the population in an unbiased manner. Simple random sampling involves the selection of a sample from an entire population such that each member or element of the population has an equal probability of being picked. Simple random and stratified random sampling are both sampling techniques used by analysts during statistical analyses.
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