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Sampling frame

In statistics, a sampling frame is the source material or device from which a sample is drawn. It is a list of all those within a population who can be sampled, and may include individuals, households or institutions.

Importance of the sampling frame is stressed by Jessen:

In many practical situations the frame is a matter of choice to the survey planner, and sometimes a critical one. [...] Some very worthwhile investigations are not undertaken at all because of the lack of an apparent frame; others, because of faulty frames, have ended in a disaster or in cloud of doubt.|Raymond James Jessen

Sampling frame types and qualities

In the most straightforward case, such as when dealing with a batch of material from a production run, or using a census, it is possible to identify and measure every single item in the population and to include any one of them in our sample; this is known as direct element sampling. However, in many other case this is not possible; either because it is cost-prohibitive (reaching every citizen of a country) or impossible (reaching all humans alive).

Having established the frame, there are a number of ways for organizing it to improve efficiency and effectiveness. It's at this stage that the researcher should decide whether the sample is in fact to be the whole population and would therefore be a census.

This list should also facilitate access to the selected sampling units. A frame may also provide additional 'auxiliary information' about its elements; when this information is related to variables or groups of interest, it may be used to improve survey design. While not necessary for simple sampling, a sampling frame more advanced sample techniques, such as stratified sampling may contain additional information (such as demographic information). For instance, an electoral register might include name and sex; this information can be used to ensure that a sample taken from that frame covers all demographic categories of interest. (Sometimes the auxiliary information is less explicit; for instance, a telephone number may provide some information about location.)

An ideal sampling frame will have the following qualities:

  • all units have a logical, numerical identifier
  • all units can be found - their contact information, map location or other relevant information is present
  • the frame is organized in a logical, systematic fashion
  • the frame has additional information about the units that allow the use of more advanced sampling frames
  • every element of the population of interest is present in the frame
  • every element of the population is present only once in the frame
  • no elements from outside the population of interest are present in the frame

The most straightforward type of frame is a list of elements of the population (preferably the entire population) with appropriate contact information. For example, in an opinion poll, possible sampling frames include a electoral register or a telephone directory. Other sampling frames can include employment records, school class lists, patient files in a hospital, organizations listed in a thematic database, and so on. On a more practical levels, sampling frames have the form of computer files.

Not all frames explicitly list population elements; some list only 'clusters'. For example, a street map can be used as a frame for a door-to-door survey; although it doesn't show individual houses, we can select streets from the map and then select houses on those streets. This offers some advantages: such a frame would include people who have recently moved and are not yet on the list frames discussed above, and it may be easier to use because it doesn't require storing data for every unit in the population, only for a smaller number of clusters.

Sampling frames problems

The sampling frame must be representative of the population and this is a question outside the scope of statistical theory demanding the judgement of experts in the particular subject matter being studied. All the above frames omit some people who will vote at the next election and contain some people who will not; some frames will contain multiple records for the same person. People not in the frame have no prospect of being sampled.

Because a cluster-based frame contains less information about the population, it may place constraints on the sample design, possibly requiring the use of less efficient sampling methods and/or making it harder to interpret the resulting data.

Statistical theory tells us about the uncertainties in extrapolating from a sample to the frame. It should be expected that sample frames, will always contain some mistakes. In some cases, this may lead to sampling bias and in extreme cases to an unrepresentative sample. Such bias should be minimized, and identified, although avoiding it completely in a real world is nearly impossible. One should also not assume that sources which claim to be unbiased and representative are such.

In defining the frame, practical, economic, ethical, and technical issues need to be addressed. The need to obtain timely results may prevent extending the frame far into the future. The difficulties can be extreme when the population and frame are disjoint. This is a particular problem in forecasting where inferences about the future are made from historical data. In fact, in 1703, when Jacob Bernoulli proposed to Gottfried Leibniz the possibility of using historical mortality data to predict the probability of early death of a living man, Gottfried Leibniz recognized the problem in replying:

Nature has established patterns originating in the return of events but only for the most part. New illnesses flood the human race, so that no matter how many experiments you have done on corpses, you have not thereby imposed a limit on the nature of events so that in the future they could not vary.|Gottfried Leibniz

Kish posited four basic problems of sampling frames:

  1. Missing elements: Some members of the population are not included in the frame.
  2. Foreign elements: The non-members of the population are included in the frame.
  3. Duplicate entries: A member of the population is surveyed more than once.
  4. Groups or clusters: The

Quota sampling

Quota sampling is a method for selecting survey participants. In quota sampling, a population is first segmented into mutually exclusive sub-groups, just as in stratified sampling. Then judgment is used to select the subjects or units from each segment based on a specified proportion. For example, an interviewer may be told to sample 200 females and 300 males between the age of 45 and 60. This means that individuals can put a demand on who they want to sample (targeting)

This second step makes the technique non-probability sampling. In quota sampling, the selection of the sample is non-random unlike random sampling and can often be found unreliable. For example interviewers might be tempted to interview those people in the street who look most helpful, or may choose to use accidental sampling to question those closest to them, for time-keeping sake. The problem is that these samples may be biased because not everyone gets a chance of selection. This non-random element is its greatest weakness and quota versus probability has been a matter of controversy for many years.

Quota sampling is useful when time is limited, a sampling frame is not available, the research budget is very tight or when detailed accuracy is not important. You can also choose how many of each category is selected.

A quota sample is a convenience sample, with an effort made to ensure a certain distribution of demographic variables. Subjects are recruited as they arrive, and the researcher assigns them to demographic groups based on variables like age and gender. When the quota for a given demographic group is filled, the researcher stops recruiting subjects from that particular group.

This is the non probability version of stratified sampling. Subsets are chosen and then either convenience or judgment sampling is used to choose people from each subset.

Stratified sampling is probably the most commonly used probability method. Subsets of the population are created so that each subset has a common characteristic, such as gender. Random sampling chooses a number of subjects from each subset.

Sample space

In probability theory, the sample space or universal sample space, often denoted S, Ω, or U (for "universe"), of an experiment or random trial is the set of all possible outcomes. For example, if the experiment is tossing a coin, the sample space is the set {head, tail}. For tossing a single six-sided die, the sample space is {1, 2, 3, 4, 5, 6}. For some kinds of experiments, there may be two or more plausible sample spaces available. For example, when drawing a card from a standard deck of 52 playing cards, one possibility for the sample space could be the rank (Ace through King), while another could be the suit (clubs, diamonds, hearts, or spades). A complete description of outcomes, however, would specify both the denomination and the suit, and a sample space describing each individual card can be constructed as the Cartesian product of the two sample spaces noted above.

In an elementary approach to probability, any subset of the sample space is usually called an event. However, this gives rise to problems when the sample space is infinite, so that a more precise definition of event is necessary. Under this definition only measurable subsets of the sample space, constituting a σ-algebra over the sample space itself, are considered events. However, this has essentially only theoretical significance, since in general the σ-algebra can always be defined to include all subsets of interest in applications.

From Encyclopedia

systematic sample Dictionary definition of systematic sample ...

Sample of Systematic - BK

simple random sampling Dictionary definition of simple random ...

simple random sample

From Yahoo Answers

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From Youtube

5.3 Sample source and sampling frames :The sampling frame should include summary information of key features of all units in the population of interest. Sampling frames must be up to date, complete, affordable and easy to use and sources must be checked for duplicates. Poor frames are old, incomplete and inappropriate. Common sources include: the Electoral Register; the postcode address file (PAF); telephone directories; subscriber/membership records; customer records. www.oxfordtextbooks.co.uk

Taylor Spatial Frame [HD] :Short video showing a sample Taylor Spatial Frame. These devices are used in Orthopaedics to treat complex fractures and bone deformities. (the device in the video is a sample device used only for educational purposes - not for surgical use)