Examples of probability sample in the following topics:
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- 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.
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- 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.
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- 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.
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- 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
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- 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.
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- 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.
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- 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.
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- 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.
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- 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 $N(0, 2)$.
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- 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.