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Per-comparison Error Rate
In statistics, per-comparison error rate (PCER) is the probability of a Type I error in the absence of any multiple hypothesis testing correction. This is a liberal error rate relative to the false discovery rate and 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 Tukey (1953) developed the concept of a ..., in that it is always less than or equal to those rates. References Statistical hypothesis testing Rates {{statistics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "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.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 sample (statistics), samples. Representative sampling as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type I Error
In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the failure to reject a null hypothesis that is actually false (also known as a "false negative" finding or conclusion; example: "a guilty person is not convicted"). Much of statistical theory revolves around the minimization of one or both of these errors, though the complete elimination of either is a statistical impossibility if the outcome is not determined by a known, observable causal process. By selecting a low threshold (cut-off) value and modifying the alpha (α) level, the quality of the hypothesis test can be increased. The knowledge of type I errors and type II errors is widely used in medical science, biometrics and computer science. Intuitively, type I errors can be thought of as errors of ''commission'', i.e. the researcher unluck ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiple Comparisons
In statistics, the multiple comparisons, multiplicity or multiple testing problem occurs when one considers a set of statistical inferences simultaneously or infers a subset of parameters selected based on the observed values. The more inferences are made, the more likely erroneous inferences become. Several statistical techniques have been developed to address that problem, typically by requiring a stricter significance threshold for individual comparisons, so as to compensate for the number of inferences being made. 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 Israel. Definition Multiple comparisons arise when a statistical analysis involves multiple simultaneous statistical tests, each of which has a potent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The Royal Statistical Society, Series B
The ''Journal of the Royal Statistical Society'' is a peer-reviewed scientific journal of statistics. It comprises three series and is published by Wiley for the Royal Statistical Society. History The Statistical Society of London was founded in 1834, but would not begin producing a journal for four years. From 1834 to 1837, members of the society would read the results of their studies to the other members, and some details were recorded in the proceedings. The first study reported to the society in 1834 was a simple survey of the occupations of people in Manchester, England. Conducted by going door-to-door and inquiring, the study revealed that the most common profession was mill-hands, followed closely by weavers. When founded, the membership of the Statistical Society of London overlapped almost completely with the statistical section of the British Association for the Advancement of Science. In 1837 a volume of ''Transactions of the Statistical Society of London'' were wri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
False Discovery Rate
In statistics, the false discovery rate (FDR) is a method of conceptualizing the rate of type I errors in null hypothesis testing when conducting multiple comparisons. FDR-controlling procedures are designed to control the FDR, which is the expected proportion of "discoveries" (rejected null hypotheses) that are false (incorrect rejections of the null). Equivalently, the FDR is the expected ratio of the number of false positive classifications (false discoveries) to the total number of positive classifications (rejections of the null). The total number of rejections of the null include both the number of false positives (FP) and true positives (TP). Simply put, FDR = FP / (FP + TP). FDR-controlling procedures provide less stringent control of Type I errors compared to family-wise error rate (FWER) controlling procedures (such as the Bonferroni correction), which control the probability of ''at least one'' Type I error. Thus, FDR-controlling procedures have greater power, at the co ... [...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 Tukey (1953) developed 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 for all of 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 collections of multiple c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Hypothesis Testing
A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. History Early use While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see . Modern origins and early controversy Modern significance testing is largely the product of Karl Pearson ( ''p''-value, Pearson's chi-squared test), William Sealy Gosset ( Student's t-distribution), and Ronald Fisher ("null hypothesis", analysis of variance, "significance test"), while hypothesis testing was developed by Jerzy Neyman and Egon Pearson (son of Karl). Ronald Fisher began his life in statistics as a Bayesian (Zabell 1992), but Fisher soon grew disenchanted with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
