sample

(noun)

a subset of a population selected for measurement, observation, or questioning to provide statistical information about the population

Related Terms

Examples of sample 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.

  • 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).

  • 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.

  • 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.
    • Stratified sampling is a divide-and-conquer sampling strategy.
    • Cluster sampling is much like a two-stage simple random sample.
    • Strati ed sampling requires observations be sampled from every stratum.

  • Determining Sample Size

    • Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample.
    • The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample.
    • In complicated studies there may be several different sample sizes involved.
    • For example, in a survey sampling involving stratified sampling there would be different sample sizes for each population.
    • Sample sizes are judged based on the quality of the resulting estimates.

  • Inferential Statistics

    • In this sense, we can say that simple random sampling chooses a sample by pure chance.
    • What is the sample?
    • Was the sample picked by simple random sampling?
    • Sometimes it is not feasible to build a sample using simple random sampling.
    • 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.

  • Variation in Samples

    • Doreen and Jung each take samples of 500 students.
    • Doreen uses systematic sampling and Jung uses cluster sampling.
    • Doreen's sample will be different from Jung's sample.
    • Even if Doreen and Jung used the same sampling method, in all likelihood their samples would be different.
    • Be aware that many large samples are biased.