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Explore the people, places, events, achievements, struggles and stories that shaped our journey.
Movements, leaders, victories and the continuing fight for equality.
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Meet the people whose lives, choices and achievements shaped the journey.
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In August 1908, a white mob attacked Springfield, Illinois’s Black community, destroying homes and businesses and lynching two Black men. National outrage over the violence helped spur the movement that created the NAACP the following year.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
In statistics, a sampling frame is the source material or device from which a sample is drawn.[1] It is a list of all those within a population who can be sampled, and may include individuals, households or institutions.[1]
Importance of the sampling frame is stressed by Jessen[2] and Salant and Dillman.[3]
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
A slightly more general concept of sampling frame includes area sampling frames, whose elements have a geographic nature. Area sampling frames can be useful for example in agricultural statistics when a suitable and updated agricultural census is not available. In environmental surveys, area sampling frames may be the only option.
In the most straightforward cases, 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.[1] However, in many other cases 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 used for more advanced sample techniques, such as stratified sampling, may contain additional information (such as demographic information).[1] 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:[1]
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 an 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.[1][5] On a more practical levels, sampling frames have the form of computer files.[1]
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.
The sampling frame must be representative of the population and this is a question outside the scope of statistical theory demanding the judgment 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 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.[5] In some cases, this may lead to sampling bias.[1] Such bias should be minimized, and identified, although avoiding it completely in a real world is nearly impossible.[1] One should also not assume that sources which claim to be unbiased and representative are such.[1]
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:[6]
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
Leslie Kish posited four basic problems of sampling frames:[7]
Problems like those listed can be identified by the use of pre-survey tests and pilot studies.
Source: Wikipedia. Article content is retrieved live through the MediaWiki API.
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 and Salant and Dillman. 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. A slightly more general concept of sampling frame includes area sampling frames, whose elements have a geographic nature. Area sampling frames can be useful for example in agricultural statistics when a suitable and updated agricultural census is not available. In environmental surveys, area sampling frames may be the only option.
An area sampling frame is an alternative to the most traditional type of sampling frames. A sampling frame is often defined as a list of elements of the population we want to explore through a sample survey. A slightly more general concept considers that a sampling frame is a tool that allows the identification and access to the elements of the population, even if an explicit list does not exist. Traditional sampling frames are sometimes referred to as list frames. In many cases, suitable lists are not available. This can happen for several reasons, for example: Existing lists, such as population censuses, are too old and do not correspond anymore to the current reality. We are targeting a population whose list is not feasible, for example a wild animal species. The population is a continuous feature in a given geographic area and the definition of its elements is not straightforward. This often happens for sample surveys designed to produce environmental statistics. Area sampling frames are generally defined by two elements: The boundaries of a target region in a given cartographic projection. The type of geographic units to be sampled. We can mention three main types of units: Points. In principle, points are dimensionless, but, for practical reasons, we can attribute them a certain size, such as 1 m × 1 m. The suitable size is linked to the accuracy of the tool used for the location of the point. Possible tools are GPS devices, orthophotos or satellite images. Point sampling can be based on a two-stage scheme, sampling clusters in the first stage and sampling points in the second stage. Another option is a two-phase scheme of unclustered points: a large first-phase sample is selected. A stratification is conducted only for the first-phase sample and a stratified sample is chosen in the second phase. Transects. A transect is a piece of straight line of a given length. Transect sampling is useful to estimate the total length of linear landscape elements Areal units defined by polygons. In the jargon of agricultural surveys, areal units are generally called "segments", even if a segment in geometry rather corresponds to the concept of transect used in area sampling frames. Segments can be delineated by photo-interpretation or generated automatically, usually on the basis of a regular grid. The optimal size of segments depends on the spatial auto-correlation of the monitored processes and the cost function that links the price of data collection with the size of the sample unit
In survey methodology, one-dimensional systematic sampling is a statistical method involving the selection of elements from an ordered sampling frame. The most common form of systematic sampling is equal probability sampling (also known as epsem), an equiprobability method. This applies in particular when the sampled units are individuals, households or corporations. When a geographic area is sampled for a spatial analysis, bi-dimensional systematic sampling on an area sampling frame can be applied. In one-dimensional systematic sampling, progression through the list is treated circularly, with a return to the top once the list ends. The sampling starts by selecting an element from the list at random and then every kth element in the frame is selected, where k, is the sampling interval (sometimes known as the skip): this is calculated as: k = N n {\displaystyle k={\frac {N}{n}}} where n is the sample size, and N is the population size. Using this procedure each element in the population has a known and equal probability of selection. This makes systematic sampling functionally similar to simple random sampling (SRS). However, it is not the same as SRS because not every possible sample of a certain size has an equal chance of being chosen (e.g. samples with at least two elements adjacent to each other will never be chosen by systematic sampling). It is, however, much more efficient (if the variance within a systematic sample is more than the variance of the population). Systematic sampling is to be applied only if the given population is logically homogeneous, because systematic sample units are uniformly distributed over the population. The researcher must ensure that the chosen sampling interval does not hide a pattern. Any pattern would threaten randomness. Example: Suppose a supermarket wants to study buying habits of their customers, then using systematic sampling they can choose every 10th or 15th customer entering the supermarket and conduct the study on this sample. This is random sampling with a system. From the sampling frame, a starting point is chosen at random, and choices thereafter are at regular intervals. For example, suppose you want to sample 8 houses from a street of 120 houses. 120/8=15, so every 15th house is chosen after a random starting point between 1 and 15. If the random starting point is 11, then the houses selected are 11, 26, 41, 56, 71, 86, 101, and 116. As an aside, if every 15th house was a "corner house" then this corner pattern could destroy the randomness of the sample. If, more frequently, the population is not evenly divisible (suppose you want to sample 8 houses out of 125, where 125/8=15.625), should you take every 15th house or every 16th house? If you take every 16th house, 8*16=128, there is a risk that the last house chosen does not exist. On the other hand, if you take every 15th house, 8*15=120, so the last five houses will never be selected. The random starting point should instead be selected as a non-integer between 0 and 15.625 (inclusive on one endpoint only) to ensure that every house has an equal chance of being selected; the interval should now be non-integral (15.625); and each non-integer selected should be rounded up to the next integer. If the random starting point is 3.6, then the houses selected are 4, 20, 35, 50, 66, 82, 98, and 113, where there are 3 cyclic intervals of 15 and 4 intervals of 16. To illustrate the danger of systematic skip concealing a pattern, suppose we were to sample a planned neighborhood where each street has ten houses on each block. This places houses No. 1, 10, 11, 20, 21, 30... on block corners; corner blocks may be less valuable, since more of their area is taken up by street front etc. that is unavailable for building purposes. If we then sample every 10th household, our sample will either be made up only of corner houses (if we start at 1 or 10) or have no corner houses (any other start); either way, it will not be representative. Systematic sampling may also be used with non-equal selection probabilities. In this case, rather than simply counting through elements of the population and selecting every kth unit, we allocate each element a space along a number line according to its selection probability. We then generate a random start from a uniform distribution between 0 and 1, and move along the number line in steps of 1. Example: We have a population of 5 units (A to E). We want to give unit A a 20% probability of selection, unit B a 40% probability, and so on up to unit E (100%). Assuming we maintain alphabetical order, we allocate each unit to the following interval: A: 0 to 0.2 B: 0.2 to 0.6 (= 0.2 + 0.4) C: 0.6 to 1.2 (= 0.6 + 0.6) D: 1.2 to 2.0 (= 1.2 + 0.8) E: 2.0 to 3.0 (= 2.0 + 1.0) If our random start was 0.156, we would first select the unit whose interval contains this number (i.e. A). Next, we would select the interval containing 1.156 (element C), then 2.156 (element E). If instead our random start was 0.350, we would select from points 0.350 (B), 1.350 (D), and 2.350 (E).
In sociology and statistics research, snowball sampling (or chain sampling, chain-referral sampling, referral sampling, qongqothwane sampling) is a nonprobability sampling technique where existing study subjects recruit future subjects from among their acquaintances. Thus the sample group is said to grow like a rolling snowball. As the sample builds up, enough data are gathered to be useful for research. This sampling technique is often used in hidden populations, such as drug users or sex workers, which are difficult for researchers to access. As sample members are not selected from a sampling frame, snowball samples are subject to numerous biases. For example, people who have many friends are more likely to be recruited into the sample. When virtual social networks are used, then this technique is called virtual snowball sampling. It was widely believed that it was impossible to make unbiased estimates from snowball samples, but a variation of snowball sampling called respondent-driven sampling has been shown to allow researchers to make asymptotically unbiased estimates from snowball samples under certain conditions. Snowball sampling and respondent-driven sampling also allows researchers to make estimates about the social network connecting the hidden population.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Mae Jemison, aboard Space Shuttle Endeavour in 1992.
