Overall Error Rate
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the experimentwise error rate is: where αew decision wise error rate is experimentwise error rate αpc is the per-comparison error rate, and c is the number of comparisons. For example, if 5 independent comparisons per comparison error rate were each to be done at the .05 level, then the probability that at least one of them would result in a Type I error is: 1 - (1 - .05)5 = 0.226. If the comparisons are not independent then the experimentwise error rate is less than . Finally, regardless of whether the comparisons are independent, αew ≤ (c)(αpc) For this example, .226 < (5)(.05) = 0.25.
may be challenged and removed. (June 2016) (Learn how and when to remove this template message) In statistics, family-wise error rate (FWER) is the probability of making one or more false discoveries, or type
Pairwise Error Rate
I errors, among all the hypotheses when performing multiple hypotheses tests. Contents 1 family wise error rate post hoc History 2 Background 2.1 Classification of multiple hypothesis tests 3 Definition 4 Controlling procedures 4.1 The Bonferroni procedure 4.2 The
How Does The Bonferroni Correction Control For Inflated Type I Error?
Šidák procedure 4.3 Tukey's procedure 4.4 Holm's step-down procedure (1979) 4.5 Hochberg's step-up procedure 4.6 Dunnett's correction 4.7 Scheffé's method 4.8 Resampling procedures 5 Alternative approaches 6 References History[edit] Tukey coined the terms http://davidmlane.com/hyperstat/A43646.html experimentwise error rate and "error rate per-experiment" to indicate error rates that the researcher could use as a control level in a multiple hypothesis experiment.[citation needed] Background[edit] Within the statistical framework, there are several definitions for the term "family": Hochberg & Tamhane defined "family" in 1987 as "any collection of inferences for which it is meaningful to take into account some combined measure of error".[1][pageneeded] https://en.wikipedia.org/wiki/Family-wise_error_rate According to Cox in 1982, a set of inferences should be regarded a family:[citation needed] To take into account the selection effect due to data dredging To ensure simultaneous correctness of a set of inferences as to guarantee a correct overall decision To summarize, a family could best be defined by the potential selective inference that is being faced: A family is the smallest set of items of inference in an analysis, interchangeable about their meaning for the goal of research, from which selection of results for action, presentation or highlighting could be made (Yoav Benjamini).[citation needed] Classification of multiple hypothesis tests[edit] Main article: Classification of multiple hypothesis tests The following table defines various errors committed when testing multiple null hypotheses. Suppose we have a number m of multiple null hypotheses, denoted by: H1,H2,...,Hm. Using a statistical test, we reject the null hypothesis if the test is declared significant. We do not reject the null hypothesis if the test is non-significant. Summing the test results over Hi will give us the following table and related random variables: Null hypothesis is true (H0) Alternative hypothesis is true (HA) Total Test is declared significant V {\displaystyle V
updates Recent press releases Upcoming events European Commission Daily News Related links European Union Newsroom Other press releases databases Latest press releases from all EU institutions European Commission News Contact Search Login Subscribe Sign up Info Additional tools RSS Other available languages: FR DE DA ES http://europa.eu/rapid/press-release_IP-12-1174_en.htm NL IT SV PT FI EL CS ET HU LT LV MT PL SK SL BG RO Expand Collapse Back to the search results DOC PDF European Commission Press release Brussels, 6 November 2012 Overall error rate for EU spending below 4% for third year in a row: Court of Auditors' annual report The overwhelming majority of payments made from the EU budget last year were free from quantifiable error. In its annual report, the Court of Auditors confirmed error rate that, in 2011, the overall quantified error rate for EU spending remained stable, at below 4%. With regard to the EU's account keeping, it has been given a clean bill of health by the Court of Auditors for the fifth year in a row. "Over the past few years, the Commission has delivered on its promise to ensure high quality management and control of EU funds. Our work is by no means finished, but now it is time for wise error rate our partners to step up their game too," said Algirdas Šemeta, Commissioner for Taxation, Customs, Audit and Anti-fraud. "Member States can do this through two simple steps. First, they can endorse the simpler rules proposed by the Commission for the new programming period. Simpler rules are easier to respect and easier to control, and could help to drastically reduce the number of mistakes in EU spending. Secondly, I repeat my call for Member States to take their responsibilities more seriously when it comes to their role in protecting EU taxpayers' money. A little more effort by Member States to control projects properly and retrieve misused funds could go a long way, particularly in this time of economic difficulty." Today's Court of Auditors' report confirms that the improvement in the management of EU funds over the past decade is being consistently maintained. This is particularly significant given that the current programming period is coming to a close. This meant that the volume of payments, and the reporting requirements that apply to them, increased substantially in 2011 compared to the last few years. And yet the error rate remained stable. Errors do not mean that EU money is lost, wasted or affected by fraud. In fact, fraud affects only 0.2% of the total EU budget, and there are strong instruments in place to detect it so that the money can be recovered when it occurs. When the Cou