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Stratified Sampling
In statistics, stratified sampling is a method of sampling from a population which can be partitioned into subpopulations. In statistical surveys, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation (stratum) independently. Stratification is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should define a partition of the population. That is, it should be ''collectively exhaustive'' and ''mutually exclusive'': every element in the population must be assigned to one and only one stratum. Then sampling is done in each stratum, for example: by simple random sampling. The objective is to improve the precision of the sample by reducing sampling error. It can produce a weighted mean that has less variability than the arithmetic mean of a simple random sample of the population. In computational statistics, stratified sampling is a method of variance reduction when Monte C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ', "description of a State (polity), 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 statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sampling Fraction
In sampling theory, the sampling fraction is the ratio of sample size to population size or, in the context of stratified sampling, the ratio of the sample size to the size of the stratum. The formula for the sampling fraction is :f=\frac, where ''n'' is the sample size and ''N'' is the population size. A sampling fraction value close to 1 will occur if the sample size is relatively close to the population size. When sampling from a finite population without replacement, this may cause dependence between individual samples. To correct for this dependence when calculating the sample variance In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion ..., a finite population correction (or finite population multiplier) of (N-n)/(N-1) may be used. If the sampling fraction is small, less than ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simpson's Paradox
Simpson's paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined. This result is often encountered in social-science and medical-science statistics, and is particularly problematic when frequency data are unduly given causal interpretations. Judea Pearl. ''Causality: Models, Reasoning, and Inference'', Cambridge University Press (2000, 2nd edition 2009). . The paradox can be resolved when confounding variables and causal relations are appropriately addressed in the statistical modeling (e.g., through cluster analysis). Simpson's paradox has been used to illustrate the kind of misleading results that the misuse of statistics can generate. Edward H. Simpson first described this phenomenon in a technical paper in 1951; the statisticians Karl Pearson (in 1899) and Udny Yule (in 1903) had mentioned similar effects earlier. The name ''Simpson's paradox'' was introduced by Col ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimax
Minimax (sometimes Minmax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, combinatorial game theory, statistics, and philosophy for ''minimizing'' the possible loss function, loss for a Worst-case scenario, worst case (''max''imum loss) scenario. When dealing with gains, it is referred to as "maximin" – to maximize the minimum gain. Originally formulated for several-player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves, it has also been extended to more complex games and to general decision-making in the presence of uncertainty. Game theory In general games The maximin value is the highest value that the player can be sure to get without knowing the actions of the other players; equivalently, it is the lowest value the other players can force the player to receive when they know the player's action. Its formal definition is: :\underline = \max_ \min_ W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sample Size
Sample size determination or estimation is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power. In complex studies, different sample sizes may be allocated, such as in stratified surveys or experimental designs with multiple treatment groups. In a census, data is sought for an entire population, hence the intended sample size is equal to the population. In experimental design, where a study may be divided into different treatment groups, there may be different sample sizes for each group. Sample sizes may be chosen in several ways: *using experience – small samples, though sometimes unavoidable, can result in wid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
F-test
An F-test is a statistical test that compares variances. It is used to determine if the variances of two samples, or if the ratios of variances among multiple samples, are significantly different. The test calculates a Test statistic, statistic, represented by the random variable F, and checks if it follows an F-distribution. This check is valid if the null hypothesis is true and standard assumptions about the errors (ε) in the data hold. F-tests are frequently used to compare different statistical models and find the one that best describes the population (statistics), population the data came from. When models are created using the least squares method, the resulting F-tests are often called "exact" F-tests. The F-statistic was developed by Ronald Fisher in the 1920s as the variance ratio and was later named in his honor by George W. Snedecor. Common examples Common examples of the use of ''F''-tests include the study of the following cases * The hypothesis that the Arithme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ontario
Ontario is the southernmost Provinces and territories of Canada, province of Canada. Located in Central Canada, Ontario is the Population of Canada by province and territory, country's most populous province. As of the 2021 Canadian census, it is home to 38.5% of the country's population, and is the second-largest province by total area (after Quebec). Ontario is Canada's fourth-largest jurisdiction in total area of all the Canadian provinces and territories. It is home to the nation's capital, Ottawa, and its list of the largest municipalities in Canada by population, most populous city, Toronto, which is Ontario's provincial capital. Ontario is bordered by the province of Manitoba to the west, Hudson Bay and James Bay to the north, and Quebec to the east and northeast. To the south, it is bordered by the U.S. states of (from west to east) Minnesota, Michigan, Ohio, Pennsylvania, and New York (state), New York. Almost all of Ontario's border with the United States follows riv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Power
In frequentist statistics, power is the probability of detecting a given effect (if that effect actually exists) using a given test in a given context. In typical use, it is a function of the specific test that is used (including the choice of test statistic and significance level), the sample size (more data tends to provide more power), and the effect size (effects or correlations that are large relative to the variability of the data tend to provide more power). More formally, in the case of a simple hypothesis test with two hypotheses, the power of the test is the probability that the test correctly rejects the null hypothesis (H_0) when the alternative hypothesis (H_1) is true. It is commonly denoted by 1-\beta, where \beta is the probability of making a type II error (a false negative) conditional on there being a true effect or association. Background Statistical testing uses data from samples to assess, or make inferences about, a statistical population. Fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Parameter
In statistics, as opposed to its general use in mathematics, a parameter is any quantity of a statistical population that summarizes or describes an aspect of the population, such as a mean or a standard deviation. If a population exactly follows a known and defined distribution, for example the normal distribution, then a small set of parameters can be measured which provide a comprehensive description of the population and can be considered to define a probability distribution for the purposes of extracting samples from this population. A "parameter" is to a population as a "statistic" is to a sample; that is to say, a parameter describes the true value calculated from the full population (such as the population mean), whereas a statistic is an estimated measurement of the parameter based on a sample (such as the sample mean, which is the mean of gathered data per sampling, called sample). Thus a "statistical parameter" can be more specifically referred to as a population ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Random Sample
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. 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 with the same number 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, either electronically or from a t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sample Size Determination
Sample size determination or estimation is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power. In complex studies, different sample sizes may be allocated, such as in stratified surveys or experimental designs with multiple treatment groups. In a census, data is sought for an entire population, hence the intended sample size is equal to the population. In experimental design, where a study may be divided into different treatment groups, there may be different sample sizes for each group. Sample sizes may be chosen in several ways: *using experience – small samples, though sometimes unavoidable, can result in wid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Systematic Sampling
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 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 ''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 selectio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
