probability sample

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.

• Sampling Techniques

  • In a simple random sample (SRS) of a given size, all such subsets of the frame are given an equal probability.
  • Each element has an equal probability of selection.
  • As long as the starting point is randomized, systematic sampling is a type of probability sampling.
  • As described above, systematic sampling is an EPS method, because all elements have the same probability of selection.
  • 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.

• 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

• 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.
  • 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.
  • Nonprobability sampling is any sampling method where some elements of the population have no chance of selection or where the probability of selection can't be accurately determined.
  • 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.

• 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.

• 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.