random sampling

Examples of random sampling in the following topics:

• Random Sampling

  • A random sample, also called a probability sample, is taken when each individual has an equal probability of being chosen for the sample.
  • A simple random sample (SRS) is one of the most typical ways.
  • 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

• 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.

• 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.

• Inferential Statistics

  • The most straightforward is simple random sampling.
  • Was the sample picked by simple random sampling?
  • Sometimes it is not feasible to build a sample using simple random sampling.
  • This random division of the sample into two groups is called random assignment.
  • Since simple random sampling often does not ensure a representative sample, a sampling method called stratified random sampling is sometimes used to make the sample more representative of the population.

• 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.

• Summary

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

• 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.

• Chance Error and Bias

  • In sampling, there are two main types of error: systematic errors (or biases) and random errors (or chance errors).
  • Random sampling is used to ensure that a sample is truly representative of the entire population.
  • Random error always exists.
  • The size of the random error, however, can generally be controlled by taking a large enough random sample from the population.
  • It results in a biased sample, a non-random sample of a population in which all individuals, or instances, were not equally likely to have been selected.

• 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.
  • In this way, researchers can draw inferences about specific subgroups that may be lost in a more generalized random sample.
  • In quota sampling the selection of the sample is non-random.

• Sampling Distributions and the Central Limit Theorem

  • The central limit theorem for sample means states that as larger samples are drawn, the sample means form their own normal distribution.
  • In its common form, the random variables must be identically distributed.
  • Suppose we are interested in the sample average of these random variables.
  • The sample means are generated using a random number generator, which draws numbers between 1 and 100 from a uniform probability distribution.
  • Illustrate that as the sample size gets larger, the sampling distribution approaches normality