In some cases, investigators are interested in "research questions specific" to subgroups of the population. For example, researchers might be interested in examining whether cognitive ability as review a predictor of job performance is equally applicable across racial groups. Srs cannot accommodate the needs of researchers in this situation because it does not provide subsamples of the population. "Stratified sampling" addresses this weakness of srs. Systematic sampling edit main article: Systematic sampling a visual representation of selecting a random sample using the systematic sampling technique systematic sampling (also known as interval sampling) relies on arranging the study population according to some ordering scheme and then selecting elements at regular intervals. Systematic sampling involves a random start and then proceeds with the selection of every k th element from then onwards. In this case, k (population size/sample size).
Furthermore, any given pair of elements has the same chance of selection as any other such pair (and similarly for triples, and so on). This minimizes bias and simplifies analysis of results. In particular, the variance between individual results within the sample is a good indicator of variance in the overall population, which makes it relatively easy to estimate the accuracy of results. Srs can be vulnerable to sampling error because the randomness of the selection may result in a sample that doesn't reflect the makeup of the population. For instance, a simple random sample of ten people from a given country will on hippie average produce five men and five women, but any given trial is likely to overrepresent one sex and underrepresent the other. Systematic and stratified techniques attempt to overcome this problem by "using information about the population" to choose a more "representative" sample. Srs may also be cumbersome and tedious when sampling from an unusually large target population.
In any household with more than one occupant, this is a nonprobability sample, because some people are more likely to answer the door (e.g. An unemployed person who spends most of their time at home is more likely to answer than an employed housemate who might be at work when the interviewer calls) and it's not practical to calculate these probabilities. Nonprobability sampling methods include convenience sampling," sampling and purposive sampling. In addition, nonresponse effects may turn any probability design into a nonprobability design if the characteristics of nonresponse are not well understood, since nonresponse effectively modifies each element's probability of being sampled. Sampling methods edit within any of the types of frames identified above, a variety of sampling methods can be employed, individually or in combination. Factors commonly influencing the choice between these designs include: Nature and quality of the frame availability of auxiliary information about units on the frame Accuracy requirements, and the need to measure accuracy Whether detailed analysis of the sample is expected Cost/operational concerns Simple random sampling. Each element of the frame thus has an equal probability of selection: the frame is not subdivided partitioned.
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When every element in the population does paper have the same probability of selection, this is known as an 'equal probability of selection' (EPS) design. Such designs are also referred to as 'self-weighting' because all sampled units are given the same weight. 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 involves magi random selection at some point. Nonprobability sampling edit main article: Nonprobability sampling Nonprobability sampling is any sampling method where some elements of the population have no chance of selection (these are sometimes referred to as 'out of coverage undercovered or where the probability of selection can't be accurately determined.
It involves the selection of elements based on assumptions regarding the population of interest, which forms the criteria for selection. Hence, because the selection of elements is nonrandom, nonprobability sampling does not allow the estimation of sampling errors. These conditions give rise to exclusion bias, placing limits on how much information a sample can provide about the population. Information about the relationship between sample and population is limited, making it difficult to extrapolate from the sample to the population. Example: we visit every household in a given street, and interview the first person to answer the door.
For example, in an opinion poll, possible sampling frames include an electoral register and a telephone directory. A probability sample is 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. The combination of these traits makes it possible to produce unbiased estimates of population totals, by weighting sampled units according to their probability of selection. Example: we want to estimate the total income of adults living in a given street. We visit each household in that street, identify all adults living there, and randomly select one adult from each household.
(For example, we can allocate each person a random number, generated from a uniform distribution between 0 and 1, and select the person with the highest number in each household). We then interview the selected person and find their income. People living on their own are certain to be selected, so we simply add their income to our estimate of the total. But a person living in a household of two adults has only a one-in-two chance of selection. To reflect this, when we come to such a household, we would count the selected person's income twice towards the total. (The person who is selected from that household can be loosely viewed as also representing the person who isn't selected.) 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.
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Time spent in making the sampled population and population of concern precise is often well spent, because it raises many issues, ambiguities and questions that would essay otherwise have been overlooked at this stage. Sampling frame edit main article: Sampling frame In the most straightforward case, such as the sampling of a batch of material from production (acceptance sampling by lots it would be most desirable to identify and measure every single item in the population and to include. However, in the more general case this is not usually possible or practical. There is no way to identify all rats in the set of all rats. Where voting is not compulsory, there is no way to identify which people will actually vote at a forthcoming election (in advance of the election). These imprecise populations are not amenable to sampling in any of the ways below and to which we could apply statistical theory. As a remedy, we seek a sampling frame which has the property writing that we can identify every single element and include any in our sample. 3 4 5 6 The most straightforward type of frame is a list of elements of the population (preferably the entire population) with appropriate contact information.
This situation often arises when we online seek knowledge about the cause system of which the observed population is an outcome. In such cases, sampling theory may treat the observed population as a sample from a larger 'superpopulation'. For example, a researcher might study the success rate of a new 'quit smoking' program on a test group of 100 patients, in order to predict the effects of the program if it were made available nationwide. Here the superpopulation is "everybody in the country, given access to this treatment" a group which does not yet exist, since the program isn't yet available to all. Note also that the population from which the sample is drawn may not be the same as the population about which we actually want information. Often there is large but not complete overlap between these two groups due to frame issues etc. Sometimes they may be entirely separate for instance, we might study rats in order to get a better understanding of human health, or we might study records from people born in 2008 in order to make predictions about people born in 2009.
examine checkout line length at various times, or a study on endangered penguins might aim to understand their usage of various hunting grounds over time. For the time dimension, the focus may be on periods or discrete occasions. In other cases, our 'population' may be even less tangible. For example, joseph Jagger studied the behaviour of roulette wheels at a casino in, monte carlo, and used this to identify a biased wheel. In this case, the 'population' jagger wanted to investigate was the overall behaviour of the wheel (i.e. The probability distribution of its results over infinitely many trials while his 'sample' was formed from observed results from that wheel. Similar considerations arise when taking repeated measurements of some physical characteristic such as the electrical conductivity of copper.
In business and medical research, sampling is widely used for gathering information about a population. 2, essay acceptance sampling is used to determine if a production lot of material meets the governing specifications. Contents, population definition edit, successful statistical practice is based on focused problem definition. In sampling, this includes defining the population from which our sample is drawn. A population can be defined as including all people or items with the characteristic one wishes to understand. Because there is very rarely enough time or money to gather information from everyone or everything in a population, the goal becomes finding a representative sample (or subset) of that population. Sometimes what defines a population is obvious. For example, a manufacturer needs to decide whether a batch of material from production is of high enough quality to be released to the customer, or should be sentenced for scrap or rework due to poor quality.
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For computer simulation, see pseudo-random number sampling. A visual representation of the sampling process. In essay statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample ) of individuals from within a statistical population to estimate characteristics of the whole population. Two advantages of sampling are that the cost is lower and data collection is faster than measuring the entire population. Each observation measures one or more properties (such as weight, location, colour) of observable bodies distinguished as independent objects or individuals. In survey sampling, weights can be applied to the data to adjust for the sample design, particularly stratified sampling. 1, results from probability theory and statistical theory are employed to guide the practice.