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Šidák Correction
In statistics, the Šidák correction, or Dunn–Šidák correction, is a method used to counteract the problem of multiple comparisons. It is a simple method to control the family-wise error rate. When all null hypotheses are true, the method provides familywise error control that is exact for tests that are stochastically independent, conservative for tests that are positively dependent, and liberal for tests that are negatively dependent. It is credited to a 1967 paper by the statistician A statistician is a person who works with Theory, theoretical or applied statistics. The profession exists in both the private sector, private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, a ... and probabilist Zbyněk Šidák. The Šidák method can be used to adjust alpha levels, p-values, or confidence intervals. Usage * Given ''m'' different null hypotheses and a familywise alpha level of \alpha, each null hypothesis is rejec ... [...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] |
Multiple Comparisons
Multiple comparisons, multiplicity or multiple testing problem occurs in statistics when one considers a set of statistical inferences simultaneously or estimates a subset of parameters selected based on the observed values. The larger the number of inferences made, the more likely erroneous inferences become. Several statistical techniques have been developed to address this problem, for example, by requiring a stricter significance threshold for individual comparisons, so as to compensate for the number of inferences being made. Methods for family-wise error rate give the probability of false positives resulting from the multiple comparisons problem. History The problem of multiple comparisons received increased attention in the 1950s with the work of statisticians such as Tukey and Scheffé. Over the ensuing decades, many procedures were developed to address the problem. In 1996, the first international conference on multiple comparison procedures took place in Tel Aviv. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Family-wise Error Rate
In statistics, family-wise error rate (FWER) is the probability of making one or more false discoveries, or type I errors when performing multiple hypotheses tests. Familywise and experimentwise error rates John Tukey developed in 1953 the concept of a familywise error rate as the probability of making a Type I error among a specified group, or "family," of tests. Based on Tukey (1953), Ryan (1959) proposed the related concept of an ''experimentwise error rate'', which is the probability of making a Type I error in a given experiment. Hence, an experimentwise error rate is a familywise error rate where the family includes all the tests that are conducted within an experiment. As Ryan (1959, Footnote 3) explained, an experiment may contain two or more families of multiple comparisons, each of which relates to a particular statistical inference and each of which has its own separate familywise error rate. Hence, familywise error rates are usually based on theoretically informative ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypothesis
A hypothesis (: hypotheses) is a proposed explanation for a phenomenon. A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess or thought. If a hypothesis is repeatedly independently demonstrated by experiment to be true, it becomes a scientific theory. In colloquial usage, the words "hypothesis" and "theory" are often used interchangeably, but this is incorrect in the context of science. A working hypothesis is a provisionally-accepted hypothesis used for the purpose of pursuing further progress in research. Working hypotheses are frequently discarded, and often proposed with knowledge (and warning) that they are incomplete and thus false, with the intent of moving research in at least somewhat the right direction, especially when scientists are stuck on an issue and brainstorming ideas. A different meaning of the term ''hypothesis'' is used in formal l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistician
A statistician is a person who works with Theory, theoretical or applied statistics. The profession exists in both the private sector, private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, and statisticians may work as employees or as statistical consultants. Overview According to the United States Bureau of Labor Statistics, as of 2014, 26,970 jobs were classified as ''statistician'' in the United States. Of these people, approximately 30 percent worked for governments (federal, state, or local). As of October 2021, the median pay for statisticians in the United States was $92,270. Additionally, there is a substantial number of people who use statistics and data analysis in their work but have job titles other than ''statistician'', such as Actuary, actuaries, Applied mathematics, applied mathematicians, economists, data scientists, data analysts (predictive analytics), financial analysts, psychometricians, sociologists, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zbyněk Šidák
Zbyněk Šidák (24 October 1933 – 12 November 1999) was a Czech mathematician. He is known for developing the Šidák correction. Early life and education Šidák was born and raised in Golčův Jeníkov. He completed his undergraduate studies in statistics at Charles University in Prague in 1956, received a Ph.D. in 1961, and a DrSc. in 1973. Career Beginning in 1956, and continuing until his death, Šidák was a researcher in the mathematical department of the Czechoslovak Academy of Sciences and spent several years as head of the Department of Probability Theory and Mathematical Statistics. During his life, Šidák held posts as a visiting faculty member at the Stockholm University, University of North Carolina, Moscow State University, Michigan State University, and others. He also served as chief editor of the scholarly journal ''Applications of Mathematics''. The Šidák correction, a method used to counteract the problem of multiple comparisons Multiple comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bonferroni Correction
In statistics, the Bonferroni correction is a method to counteract the multiple comparisons problem. Background The method is named for its use of the Bonferroni inequalities. Application of the method to confidence intervals was described by Olive Jean Dunn. Statistical hypothesis testing is based on rejecting the null hypothesis when the likelihood of the observed data would be low if the null hypothesis were true. If multiple hypotheses are tested, the probability of observing a rare event increases, and therefore, the likelihood of incorrectly rejecting a null hypothesis (i.e., making a Type I error) increases. The Bonferroni correction compensates for that increase by testing each individual hypothesis at a significance level of \alpha/m, where \alpha is the desired overall alpha level and m is the number of hypotheses. For example, if a trial is testing m = 20 hypotheses with a desired overall \alpha = 0.05, then the Bonferroni correction would test each individual hypot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence (probability Theory)
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two event (probability theory), events are independent, statistically independent, or stochastically independent if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds. Similarly, two random variables are independent if the realization of one does not affect the probability distribution of the other. When dealing with collections of more than two events, two notions of independence need to be distinguished. The events are called Pairwise independence, pairwise independent if any two events in the collection are independent of each other, while mutual independence (or collective independence) of events means, informally speaking, that each event is independent of any combination of other events in the collection. A similar notion exists for collections of random variables. M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiple Comparisons
Multiple comparisons, multiplicity or multiple testing problem occurs in statistics when one considers a set of statistical inferences simultaneously or estimates a subset of parameters selected based on the observed values. The larger the number of inferences made, the more likely erroneous inferences become. Several statistical techniques have been developed to address this problem, for example, by requiring a stricter significance threshold for individual comparisons, so as to compensate for the number of inferences being made. Methods for family-wise error rate give the probability of false positives resulting from the multiple comparisons problem. History The problem of multiple comparisons received increased attention in the 1950s with the work of statisticians such as Tukey and Scheffé. Over the ensuing decades, many procedures were developed to address the problem. In 1996, the first international conference on multiple comparison procedures took place in Tel Aviv. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Family-wise Error Rate
In statistics, family-wise error rate (FWER) is the probability of making one or more false discoveries, or type I errors when performing multiple hypotheses tests. Familywise and experimentwise error rates John Tukey developed in 1953 the concept of a familywise error rate as the probability of making a Type I error among a specified group, or "family," of tests. Based on Tukey (1953), Ryan (1959) proposed the related concept of an ''experimentwise error rate'', which is the probability of making a Type I error in a given experiment. Hence, an experimentwise error rate is a familywise error rate where the family includes all the tests that are conducted within an experiment. As Ryan (1959, Footnote 3) explained, an experiment may contain two or more families of multiple comparisons, each of which relates to a particular statistical inference and each of which has its own separate familywise error rate. Hence, familywise error rates are usually based on theoretically informative ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed Testing Procedure
In statistics, the closed testing procedure is a general method for performing more than one hypothesis test simultaneously. The closed testing principle Suppose there are ''k'' hypotheses ''H''1,..., ''H''''k'' to be tested and the overall type I error rate is α. The closed testing principle allows the rejection of any one of these elementary hypotheses, say ''H''''i'', if all possible intersection hypotheses involving ''H''''i'' can be rejected by using valid local level α tests; the adjusted p-value is the largest among those hypotheses. It controls the family-wise error rate for all the ''k'' hypotheses at level α in the strong sense. Example Suppose there are three hypotheses ''H''1,''H''2, and ''H''3 to be tested and the overall type I error rate is 0.05. Then ''H''1 can be rejected at level α if ''H''1 ∩ ''H''2 ∩ ''H''3, ''H''1 ∩ ''H''2, ''H''1 ∩ ''H''3 and ''H''1 can all be rejected using valid tests with level α. Special cases The Holm–Bonferroni meth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
