sampling

Examples of sampling in the following topics:

• Samples

  • This process of collecting information from a sample is referred to as sampling.
  • The best way to avoid a biased or unrepresentative sample is to select a random sample, also known as a probability 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.

• What Is a Sampling Distribution?

  • The sampling distribution of a statistic is the distribution of the statistic for all possible samples from the same population of a given size.
  • Similarly, if you took a second sample of 10 women from the same population, you would not expect the mean of this second sample to equal the mean of the first sample.
  • Sampling distributions allow analytical considerations to be based on the sampling distribution of a statistic rather than on the joint probability distribution of all the individual sample values.
  • The sampling distribution depends on: the underlying distribution of the population, the statistic being considered, the sampling procedure employed, and the sample size used.
  • An alternative to the sample mean is the sample median.

• Sampling

  • Sampling involves providing a sample of a consumer product to consumers so that they may try said product before committing to a purchase.
  • During the product promotion process, sampling involves providing a sample of a consumer product to consumers so that they may try said product before committing to a purchase.
  • According to the Product Sampling Study by Arbitron, sampling successfully reaches 70 million consumers every quarter, and one-third of customers who try a sample will buy the sampled product in the same shopping trip, and 58 percent of those surveyed reported that they would buy the product again.
  • Marketers who are considering sampling their next product introduction should define the objectives of the sampling program.
  • There are a number of popular sampling techniques:

• t-Test for Two Samples: Independent and Overlapping

  • Two-sample t-tests for a difference in mean involve independent samples, paired samples, and overlapping samples.
  • The two sample t-test is used to compare the means of two independent samples.
  • For the null hypothesis, the observed t-statistic is equal to the difference between the two sample means divided by the standard error of the difference between the sample means.
  • Two-sample t-tests for a difference in mean involve independent samples, paired samples and overlapping samples.
  • An overlapping samples t-test is used when there are paired samples with data missing in one or the other samples (e.g., due to selection of "I don't know" options in questionnaires, or because respondents are randomly assigned to a subset question).

• Defining the Sample and Collecting Data

  • The stages of the sampling process are defining the population of interest, specifying the sampling frame, determining the sampling method and sample size, and sampling and data collecting.
  • There are various types of samples.
  • Examples of types of samples include simple random samples, stratified samples, cluster samples, and convenience samples.
  • Sampling errors and biases, such as selection bias and random sampling error, are induced by the sample design.
  • Non-sampling errors are other errors which can impact the results, caused by problems in data collection, processing, or sample design.

• Sampling Techniques

  • 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 population is first segmented into mutually exclusive subgroups, just as in stratified sampling.
  • In quota sampling the selection of the sample is non-random.
  • Accidental sampling (or grab, convenience, or opportunity sampling) is a type of non-probability sampling which involves the sample being drawn from that part of the population which is close to hand.

• Sample Atom

• Properties of Sampling Distributions

  • The most common measure of how much sample means differ from each other is the standard deviation of the sampling distribution of the mean.
  • For the case where the statistic is the sample mean, and samples are uncorrelated, the standard error is:
  • Where $s$ is the sample standard deviation and $n$ is the size (number of items) in the sample.
  • This spread is determined by the sampling design and the size of the sample.
  • Larger samples give smaller spread.

• Lab 2: Sampling Experiment

  • In this lab, you will be asked to pick several random samples.
  • Pick a stratified sample, by city, of 20 restaurants.
  • Pick a stratified sample, by entree cost, of 21 restaurants.
  • Pick a cluster sample of restaurants from two cities.
  • 1.14.7 Restaurants Stratified by City and Entree CostRestaurants Used in Sample

• Introduction to one-sample means with the t distribution

  • The motivation in Chapter 4 for requiring a large sample was two-fold.
  • First, a large sample ensures that the sampling distribution of $\bar{x}$ is nearly normal.
  • The second motivation for a large sample was that we get a better estimate of the standard error when using a large sample.
  • We will see that the t distribution is a helpful substitute for the normal distribution when we model a sample mean $\bar{x}$ that comes from a small sample.
  • While we emphasize the use of the t distribution for small samples, this distribution may also be used for means from large samples.