Simple Random Sampling

Examples of Simple Random Sampling in the following topics:

• Three sampling methods (special topic)

  • Here we consider three random sampling techniques: simple, strati ed, and cluster sampling.
  • Simple random sampling is probably the most intuitive form of random sampling.
  • Cluster sampling is much like a two-stage simple random sample.
  • Then we sample a fixed number of clusters and collect a simple random sample within each cluster.
  • Examples of simple random, stratified, and cluster sampling.

• Random Samples

  • A simple random sample is a subset of individuals chosen from a larger set (a population).
  • A simple random sample is an unbiased surveying technique.
  • Simple random sampling is a basic type of sampling, since it can be a component of other more complex sampling methods.
  • Although simple random sampling can be conducted with replacement instead, this is less common and would normally be described more fully as simple random sampling with replacement.
  • Conceptually, simple random sampling is the simplest of the probability sampling techniques.

• Assumption

  • Your data should be a simple random sample that comes from a population that is approximately normally distributed.
  • You use the sample standard deviation to approximate the population standard deviation.
  • When you perform a hypothesis test of a single population mean µ using a normal distribution (often called a z-test), you take a simple random sample from the population.
  • The population you are testing is normally distributed or your sample size is sufficiently large.
  • When you perform a hypothesis test of a single population proportion p, you take a simple random sample from the population.

• Random Sampling

  • A simple random sample (SRS) is one of the most typical ways.
  • Also commonly referred to as a probability sample, a simple random sample of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance of being in the selected sample.
  • Simple random samples are not perfect and should not always be used.
  • At this stage, a simple random sample would be chosen from each stratum and combined to form the full sample.
  • Categorize a random sample as a simple random sample, a stratified random sample, a cluster sample, or a systematic sample

• Lab 2: Sampling Experiment

  • The student will demonstrate the simple random, systematic, stratified, and cluster sampling techniques.
  • In this lab, you will be asked to pick several random samples.
  • In each case, describe your procedure briefly, including how you might have used the random number generator, and then list the restaurants in the sample you obtained
  • Pick a stratified sample, by city, of 20 restaurants.
  • Pick a cluster sample of restaurants from two cities.

• Inferential Statistics

  • The most straightforward is simple random sampling.
  • In this sense, we can say that simple random sampling chooses a sample by pure chance.
  • Was the sample picked by simple random sampling?
  • Just this defect alone means the sample was not formed through simple random sampling.
  • Sometimes it is not feasible to build a sample using simple random sampling.

• Summary

  • Each member of the population has an equal chance of being selected- Sampling Methods

• Sampling

  • The easiest method to describe is called a simple random sample.
  • Besides simple random sampling, there are other forms of sampling that involve a chance process for getting the sample.
  • Number each department and then choose four different numbers using simple random sampling.
  • However for practical reasons, in most populations, simple random sampling is done without replacement.
  • Determine the type of sampling used (simple random, stratified, systematic, cluster, or convenience).

• Sampling Techniques

  • In a simple random sample (SRS) of a given size, all such subsets of the frame are given an equal probability.
  • However, SRS can be vulnerable to sampling error because the randomness of the selection may result in a sample that doesn't reflect the makeup of the population.
  • As long as the starting point is randomized, systematic sampling is a type of probability sampling.
  • Cluster sampling generally increases the variability of sample estimates above that of simple random sampling, depending on how the clusters differ between themselves, as compared with the within-cluster variation.
  • In quota sampling the selection of the sample is non-random.

• Samples

  • The best way to avoid a biased or unrepresentative sample is to select a random sample, also known as a probability sample.
  • A random sample is defined as a sample wherein each individual member of the population has a known, non-zero chance of being selected as part of the sample.
  • Several types of random samples are simple random samples, systematic samples, stratified random samples, and cluster random samples.
  • A sample that is not random is called a non-random sample, or a non-probability sampling.
  • Some examples of nonrandom samples are convenience samples, judgment samples, and quota samples.