Examples of purposive sampling in the following topics:
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- 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.
- Samples of only a few hundred observations, or even smaller, are sufficient for many purposes.
- Be aware that many large samples are biased.
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- In order to conduct a survey, a sample from the population must be chosen.
- Probability sampling includes: Simple Random Sampling, Systematic Sampling, Stratified Sampling, Probability Proportional to Size Sampling, and Cluster or Multistage Sampling.
- Hence, because the selection of elements is nonrandom, non-probability sampling does not allow the estimation of sampling errors.
- Information about the relationship between sample and population is limited, making it difficult to extrapolate from the sample to the population.
- Non-probability sampling methods include accidental sampling, quota sampling, and purposive sampling.
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- The purpose of a One-Way ANOVA test is to determine the existence of a statistically significant difference among several group means.
- Each population from which a sample is taken is assumed to be normal.
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- In the previous section, we created a sampling distribution out of a population consisting of three pool balls.
- Now we will consider sampling distributions when the population distribution is continuous.
- Note that although this distribution is not really continuous, it is close enough to be considered continuous for practical purposes.
- As before, we are interested in the distribution of the means we would get if we sampled two balls and computed the mean of these two.
- 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.
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- Statistics teaches people to use a limited sample to make intelligent and accurate conclusions about a greater population.
- What they may not mention is that the cat owners questioned were those they found in a supermarket buying Cato, which doesn't represent an unbiased sample of cat owners.
- With the appropriate tools and solid grounding in the field, one can use a limited sample (e.g., reading the first five chapters of Pride & Prejudice) to make intelligent and accurate statements about the population (e.g., predicting the ending of Pride & Prejudice).
- Statistics teaches people to use a limited sample to make intelligent and accurate conclusions about a greater population.
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- Similarly, if you took a second sample of 10 people from the same population, you would not expect the mean of this second sample to equal the mean of the first sample.
- Specifically, it is the sampling distribution of the mean for a sample size of 2 (N = 2).
- Then this process is repeated for a second sample, a third sample, and eventually thousands of samples.
- It is also important to keep in mind that there is a sampling distribution for various sample sizes.
- (Although this distribution is not really continuous, it is close enough to be considered continuous for practical purposes. ) As before, we are interested in the distribution of means we would get if we sampled two balls and computed the mean of these two balls.
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- In calculating the arithmetic mean of a sample, for example, the algorithm works by summing all the data values observed in the sample and then dividing this sum by the number of data items.
- This single measure, the mean of the sample, is called a statistic; its value is frequently used as an estimate of the mean value of all items comprising the population from which the sample is drawn.
- Once a sample that is representative of the population is determined, data is collected for the sample members in an observational or experimental setting.
- This data can then be subjected to statistical analysis, serving two related purposes: description and inference.
- Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole.
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- If we take $k$ samples from a normal distribution with fixed unknown mean and variance, and if we compute the sample mean and sample variance for these $k$ samples, then the $t$-distribution (for $k$) can be defined as the distribution of the location of the true mean, relative to the sample mean and divided by the sample standard deviation, after multiplying by the normalizing term $\sqrt { n }$, where $n$ is the sample size.
- The $t$-distribution with $n − 1$ degrees of freedom is the sampling distribution of the $t$-value when the samples consist of independent identically distributed observations from a normally distributed population.
- Thus, for inference purposes, $t$ is a useful "pivotal quantity" in the case when the mean and variance ($\mu$, $\sigma^2$) are unknown population parameters, in the sense that the $t$-value has then a probability distribution that depends on neither $\mu$ nor $\sigma^2$.
- Gosset worked at the Guinness Brewery in Dublin, Ireland, and was interested in the problems of small samples, for example of the chemical properties of barley where sample sizes might be as small as three participants.
- Gosset's paper refers to the distribution as the "frequency distribution of standard deviations of samples drawn from a normal population."
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- Once a sample that is representative of the population is determined, data is collected for the sample members in an observational or experimental setting.
- This data can then be subjected to statistical analysis, serving two related purposes: description and inference.
- Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole.
- A major problem lies in determining the extent that the sample chosen is actually representative.
- Probability is used in "mathematical statistics" (alternatively, "statistical theory") to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures.
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- Under its principle, a buyer cannot recover damages from a seller for defects on the property that render the property unfit for ordinary purposes.
- Along with the confidence level, the sample design for a survey (in particular its sample size) determines the magnitude of the margin of error.
- If the exact confidence intervals are used, then the margin of error takes into account both sampling error and non-sampling error.
- For a simple random sample from a large population, the maximum margin of error is a simple re-expression of the sample size $n$.
- The larger the sample is, the smaller the margin of error is.