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Sampling With Replacement
In statistics, a simple random sample (or SRS) is a subset of individuals (a sample) chosen from a larger set (a population) in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way. In SRS, each subset of ''k'' individuals has the same probability of being chosen for the sample as any other subset of ''k'' individuals. A simple random sample is an unbiased sampling technique. Simple random sampling is a basic type of sampling and can be a component of other more complex sampling methods. Introduction The principle of simple random sampling is that every set of items has the same probability of being chosen. For example, suppose ''N'' college students want to get a ticket for a basketball game, but there are only ''X'' < ''N'' tickets for them, so they decide to have a fair way to see who gets to go. Then, everybody is given a number in the range from 0 to ''N''-1, and random numbers are generated, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Systematic Sampling
In survey methodology, systematic sampling is a statistical method involving the selection of elements from an ordered sampling frame. The most common form of systematic sampling is an equiprobability method. In this approach, 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 ''k''th element in the frame is selected, where ''k'', is the sampling interval (sometimes known as the ''skip''): this is calculated as: :k = \frac Nn 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 (also known as epsem). This makes systematic sampling functionally similar to simple random sampling In statistics, a simple random sample (or SRS) is a subset of individuals (a sample) chosen from a larger set (a population) in which a subset of individuals are cho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernoulli Sampling
In the theory of finite population sampling, Bernoulli sampling is a sampling process where each element of the population is subjected to an independent Bernoulli trial which determines whether the element becomes part of the sample. An essential property of Bernoulli sampling is that all elements of the population have equal probability of being included in the sample. Bernoulli sampling is therefore a special case of Poisson sampling. In Poisson sampling each element of the population may have a different probability of being included in the sample. In Bernoulli sampling, the probability is equal for all the elements. Because each element of the population is considered separately for the sample, the sample size is not fixed but rather follows a binomial distribution. Example The most basic Bernoulli method generates ''n'' random variates to extract a sample from a population of ''n'' items. Suppose you want to extract a given percentage ''pct'' of the population. The algo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sampling Design
Sampling may refer to: *Sampling (signal processing), converting a continuous signal into a discrete signal * Sampling (graphics), converting continuous colors into discrete color components *Sampling (music), the reuse of a sound recording in another recording **Sampler (musical instrument), an electronic musical instrument used to record and play back samples *Sampling (statistics), selection of observations to acquire some knowledge of a statistical population *Sampling (case studies), selection of cases for single or multiple case studies * Sampling (audit), application of audit procedures to less than 100% of population to be audited *Sampling (medicine), gathering of matter from the body to aid in the process of a medical diagnosis and/or evaluation of an indication for treatment, further medical tests or other procedures. *Sampling (occupational hygiene), detection of hazardous materials in the workplace *Sampling (for testing or analysis), taking a representative portion of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantitative Marketing Research
Quantitative marketing research is the application of quantitative research techniques to the field of marketing research. It has roots in both the positivist view of the world, and the modern marketing viewpoint that marketing is an interactive process in which both the buyer and seller reach a satisfying agreement on the "four Ps" of marketing: Product, Price, Place (location) and Promotion. As a social research method, it typically involves the construction of questionnaires and scales. People who respond (respondents) are asked to complete the survey. Marketers use the information to obtain and understand the needs of individuals in the marketplace, and to create strategies and marketing plans. Data collection The most popular quantitative marketing research method is a survey. Surveys typically contain a combination of structured questions and open questions. Survey participants respond to the same set of questions, which allows the researcher to easily compare responses ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Opinion Poll
An opinion poll, often simply referred to as a survey or a poll (although strictly a poll is an actual election) is a human research survey of public opinion from a particular sample. Opinion polls are usually designed to represent the opinions of a population by conducting a series of questions and then extrapolating generalities in ratio or within confidence intervals. A person who conducts polls is referred to as a pollster. History The first known example of an opinion poll was a tallies of voter preferences reported on Telegram Messenger to the 1824 presidential election, showing Andrew Jackson leading John Quincy Adams by 335 votes to 169 in the contest for the United States Presidency. Since Jackson won the popular vote in that state and the whole country, such straw votes gradually became more popular, but they remained local, usually citywide phenomena. In 1916, '' The Literary Digest'' embarked on a national survey (partly as a circulation-raising exercise) and cor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonprobability Sampling
Sampling is the use of a subset of the population to represent the whole population or to inform about (social) processes that are meaningful beyond the particular cases, individuals or sites studied. Probability sampling, or random sampling, is a sampling technique in which the probability of getting any particular sample may be calculated. In cases where external validity is not of critical importance to the study's goals or purpose, researchers might prefer to use nonprobability sampling. Nonprobability sampling does not meet this criterion. Nonprobability sampling techniques ''are not intended to'' be used to infer from the sample to the general population in statistical terms. Instead, for example, grounded theory can be produced through iterative nonprobability sampling until theoretical saturation is reached (Strauss and Corbin, 1990). Thus, one cannot say the same on the basis of a nonprobability sample than on the basis of a probability sample. The grounds for drawing g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multistage Sampling
In statistics, multistage sampling is the taking of samples in stages using smaller and smaller sampling units at each stage. Multistage sampling can be a complex form of cluster sampling because it is a type of sampling which involves dividing the population into groups (or clusters). Then, one or more clusters are chosen at random and everyone within the chosen cluster is sampled. Using all the sample elements in all the selected clusters may be prohibitively expensive or unnecessary. Under these circumstances, multistage cluster sampling becomes useful. Instead of using all the elements contained in the selected clusters, the researcher randomly selects elements from each cluster. Constructing the clusters is the first stage. Deciding what elements within the cluster to use is the second stage. The technique is used frequently when a complete list of all members of the population does not exist and is inappropriate. In some cases, several levels of cluster selection may be ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reservoir Sampling
Reservoir sampling is a family of randomized algorithms for choosing a simple random sample, without replacement, of items from a population of unknown size in a single pass over the items. The size of the population is not known to the algorithm and is typically too large for all items to fit into main memory. The population is revealed to the algorithm over time, and the algorithm cannot look back at previous items. At any point, the current state of the algorithm must permit extraction of a simple random sample without replacement of size over the part of the population seen so far. Motivation Suppose we see a sequence of items, one at a time. We want to keep ten items in memory, and we want them to be selected at random from the sequence. If we know the total number of items and can access the items arbitrarily, then the solution is easy: select 10 distinct indices between 1 and with equal probability, and keep the -th elements. The problem is that we do not always k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypergeometric Distribution
In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of k successes (random draws for which the object drawn has a specified feature) in n draws, ''without'' replacement, from a finite population of size N that contains exactly K objects with that feature, wherein each draw is either a success or a failure. In contrast, the binomial distribution describes the probability of k successes in n draws ''with'' replacement. Definitions Probability mass function The following conditions characterize the hypergeometric distribution: * The result of each draw (the elements of the population being sampled) can be classified into one of two mutually exclusive categories (e.g. Pass/Fail or Employed/Unemployed). * The probability of a success changes on each draw, as each draw decreases the population ('' sampling without replacement'' from a finite population). A random variable X follows the hyper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Distribution
In probability theory and statistics, the binomial distribution with parameters ''n'' and ''p'' is the discrete probability distribution of the number of successes in a sequence of ''n'' independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: ''success'' (with probability ''p'') or ''failure'' (with probability q=1-p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., ''n'' = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance. The binomial distribution is frequently used to model the number of successes in a sample of size ''n'' drawn with replacement from a population of size ''N''. If the sampling is carried out without replacement, the draws are not independent and so the resulting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multistage Sampling
In statistics, multistage sampling is the taking of samples in stages using smaller and smaller sampling units at each stage. Multistage sampling can be a complex form of cluster sampling because it is a type of sampling which involves dividing the population into groups (or clusters). Then, one or more clusters are chosen at random and everyone within the chosen cluster is sampled. Using all the sample elements in all the selected clusters may be prohibitively expensive or unnecessary. Under these circumstances, multistage cluster sampling becomes useful. Instead of using all the elements contained in the selected clusters, the researcher randomly selects elements from each cluster. Constructing the clusters is the first stage. Deciding what elements within the cluster to use is the second stage. The technique is used frequently when a complete list of all members of the population does not exist and is inappropriate. In some cases, several levels of cluster selection may be ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
