probability sample

(noun)

a sample in which every unit in the population has a chance (greater than zero) of being selected in the sample, and this probability can be accurately determined

Related Terms

  • nonresponse
  • undercoverage

Examples of probability sample in the following topics:

  • How Well Do Probability Methods Work?

    • Failure to use probability sampling may result in bias or systematic errors in the way the sample represents the population.
    • However, even probability sampling methods that use chance to select a sample are prone to some problems.
    • Recall some of the methods used in probability sampling: simple random samples, stratified samples, cluster samples, and systematic samples.
    • In these methods, each member of the population has a chance of being chosen for the sample, and that chance is a known probability.
    • Random sampling eliminates some of the bias that presents itself in sampling, but when a sample is chosen by human beings, there are always going to be some unavoidable problems.
  • Using Chance in Survey Work

    • A probability sampling is one in which every unit in the population has a chance (greater than zero) of being selected in the sample, and this probability can be accurately determined.
    • In the above example, not everybody has the same probability of selection; what makes it a probability sample is the fact that each person's probability is known.
    • Probability sampling includes: Simple Random Sampling, Systematic Sampling, Stratified Sampling, Probability Proportional to Size Sampling, and Cluster or Multistage Sampling.
    • These various ways of probability sampling have two things in common: every element has a known nonzero probability of being sampled, and random selection is involved at some point.
    • Non-probability sampling methods include accidental sampling, quota sampling, and purposive sampling.
  • 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.
  • 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.
    • 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.
    • At this stage, a simple random sample would be chosen from each stratum and combined to form the full sample.
    • Each sample would be 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
  • Hypergeometric Distribution

    • The hypergeometric distribution is used to calculate probabilities when sampling without replacement.
    • For example, suppose you first randomly sample one card from a deck of 52.
    • Given this sampling procedure, what is the probability that exactly two of the sampled cards will be aces (4 of the 52 cards in the deck are aces).
    • You can calculate this probability using the following formula based on the hypergeometric distribution:
    • In this example, k = 4 because there are four aces in the deck, x = 2 because the problem asks about the probability of getting two aces, N = 52 because there are 52 cards in a deck, and n = 3 because 3 cards were sampled.
  • 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.
    • The two-sample t-test is probably the most widely used (and misused) statistical test.
    • If, for any reason, one is forced to use haphazard rather than probability sampling, then every effort must be made to minimize selection bias.
    • Two-sample t-tests for a difference in mean involve independent samples, paired samples and overlapping samples.
  • Misconceptions

    • State why the probability value is not the probability the null hypothesis is false
    • Misconception: The probability value is the probability that the null hypothesis is false.
    • Proper interpretation: The probability value is the probability of a result as extreme or more extreme given that the null hypothesis is true.
    • Proper interpretation: A low probability value indicates that the sample outcome (or one more extreme) would be very unlikely if the null hypothesis were true.
    • A low probability value can occur with small effect sizes, particularly if the sample size is large.
  • Marginal and joint probabilities

    • These totals represent marginal probabilities for the sample, which are the probabilities based on a single variable without conditioning on any other variables.
    • For instance, a probability based solely on the student variable is a marginal probability:
    • If a probability is based on a single variable, it is a marginal probability.
    • We use table proportions to summarize joint probabilities for the drug use sample.
    • We can compute marginal probabilities using joint probabilities in simple cases.
  • Continuous Sampling Distributions

    • Now we will consider sampling distributions when the population distribution is continuous.
    • Therefore, it is more convenient to use our second conceptualization of sampling distributions, which conceives of sampling distributions in terms of relative frequency distributions-- specifically, the relative frequency distribution that would occur if samples of two balls were repeatedly taken and the mean of each sample computed.
    • Moreover, in continuous distributions, the probability of obtaining any single value is zero.
    • Therefore, these values are called probability densities rather than probabilities.
    • Boxplot and probability density function of a normal distribution $N(0, 2)$.
  • 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.
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