Limited Time Offer: Save 10% on all 2022 Premium Study Packages with promo code: BLOG10

Simple Random vs. Stratified Random Sampling

Simple Random vs. Stratified Random Sampling

Simple random and stratified random sampling are both sampling techniques used by analysts during statistical analyses.

Simple Random Sampling

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. The method attempts to come up with a sample that represents the population in an unbiased manner.

However, it is not appropriate when there are glaring differences within the population such that statisticians can divide the members into different, distinctive categories. That’s where stratified random sampling comes in.

Stratified Random Sampling

In stratified random sampling, analysts subdivide the population into separate groups known as strata (singular – stratum). Each stratum is composed of elements that have a common characteristic (attribute) that distinguishes them from all the others. The method is most appropriate for large populations that are heterogeneous in nature.

A simple random sample is then taken from within each stratum and combined to form the overall, final sample that takes heterogeneity into account. The number of members chosen from any one stratum depends on its size relative to the population as a whole.

Example: Stratified Random Sampling

An advertising firm wants to determine the extent to which they should emphasize television ads in a district. They decide to carry out a survey aimed at estimating the mean number of hours spent by households watching TV per week. The district has three distinct towns – A, B, which are urbanized, and C, located in a rural area. Town A is adjacent a major factory where most residents work, with most having school-aged kids. Town B mainly harbors retirees while most people in town C practice agriculture.

There are 160 households in town A, 60 in town B, and 80 in C. 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.

Determine the number of homes that have been sampled in each region.

Solution

We have 3 strata: A, B, and C. We use the following formula to determine the number of households to be included in the sample from each region:

$$ \text{Number of households in sample} = \left( \cfrac {\text{number of households in region}}{ \text {total number of households} }\right) * \text {the required sample size} $$

Therefore, the number of households to be sampled in A = \(\frac {160}{300} * 50 = 27\) (approximately)

Similarly, the number of households to be sampled in B = \(\frac {60}{300} * 50 = 10\)

Finally, the firm would need \( \left(\frac {80}{300} * 50 \right) = 13\) households in region C.

Advantages of Stratified Sampling over Simple Random Sampling

  1. Stratification is associated with a smaller error of estimation compared to simple random sampling, especially when each stratum is homogeneous.
  2. Stratification enables analysts to estimate the population parameter, say, the mean for all the subgroups of the entire population.
Shop CFA® Exam Prep

Offered by AnalystPrep

Featured Shop FRM® Exam Prep Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Shop Actuarial Exams Prep Shop GMAT® Exam Prep


    Sergio Torrico
    Sergio Torrico
    2021-07-23
    Excelente para el FRM 2 Escribo esta revisión en español para los hispanohablantes, soy de Bolivia, y utilicé AnalystPrep para dudas y consultas sobre mi preparación para el FRM nivel 2 (lo tomé una sola vez y aprobé muy bien), siempre tuve un soporte claro, directo y rápido, el material sale rápido cuando hay cambios en el temario de GARP, y los ejercicios y exámenes son muy útiles para practicar.
    diana
    diana
    2021-07-17
    So helpful. I have been using the videos to prepare for the CFA Level II exam. The videos signpost the reading contents, explain the concepts and provide additional context for specific concepts. The fun light-hearted analogies are also a welcome break to some very dry content. I usually watch the videos before going into more in-depth reading and they are a good way to avoid being overwhelmed by the sheer volume of content when you look at the readings.
    Kriti Dhawan
    Kriti Dhawan
    2021-07-16
    A great curriculum provider. James sir explains the concept so well that rather than memorising it, you tend to intuitively understand and absorb them. Thank you ! Grateful I saw this at the right time for my CFA prep.
    nikhil kumar
    nikhil kumar
    2021-06-28
    Very well explained and gives a great insight about topics in a very short time. Glad to have found Professor Forjan's lectures.
    Marwan
    Marwan
    2021-06-22
    Great support throughout the course by the team, did not feel neglected
    Benjamin anonymous
    Benjamin anonymous
    2021-05-10
    I loved using AnalystPrep for FRM. QBank is huge, videos are great. Would recommend to a friend
    Daniel Glyn
    Daniel Glyn
    2021-03-24
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    2021-03-18
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.