The Upper Confidence Limit: Multilevel Statistical Models Many kinds of data, including observational data collected in the human and biological sciences, have a hierarchical or clustered structure.
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.
In this case, the batch sample survey questionnaire for business plan the population. Although the population of interest often consists of physical objects, sometimes we need to sample over time, space, or some combination of these dimensions.
For instance, an investigation of supermarket staffing could 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 Carloand used this to identify a biased wheel.
In this case, the 'population' Jagger wanted to investigate was the overall behaviour of the wheel i. Similar considerations arise when taking repeated measurements of some physical characteristic such as the electrical conductivity of copper. This situation often arises when we 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 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 in order to make predictions about people born in 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 otherwise have been overlooked at this stage.
Sampling frame In the most straightforward case, such as the sampling of a batch of material from production acceptance sampling by lotsit would be most desirable to identify and measure every single item in the population and to include any one of them in our sample.
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 that we can identify every single element and include any in our sample.
For example, in an opinion pollpossible 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. 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 is known.In 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.
Statisticians attempt for the samples to represent the population in question. Two advantages of sampling are lower cost and faster data collection than measuring the.
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