Probibility Of Error
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removed. (December 2009) (Learn how and when to remove this template message) In statistics, the term "error" arises in two ways. Firstly, it arises in the context of decision making, where the
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probability of error may be considered as being the probability of making a wrong probability of error formula decision and which would have a different value for each type of error. Secondly, it arises in the context of probability of error and bit error rate statistical modelling (for example regression) where the model's predicted value may be in error regarding the observed outcome and where the term probability of error may refer to the probabilities of various amounts of
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error occurring. Hypothesis testing[edit] In hypothesis testing in statistics, two types of error are distinguished. Type I errors which consist of rejecting a null hypothesis that is true; this amounts to a false positive result. Type II errors which consist of failing to reject a null hypothesis that is false; this amounts to a false negative result. The probability of error is similarly distinguished. For a Type
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I error, it is shown as α (alpha) and is known as the size of the test and is 1 minus the specificity of the test. It should also be noted that α (alpha) is sometimes referred to as the confidence of the test, or the level of significance (LOS) of the test. For a Type II error, it is shown as β (beta) and is 1 minus the power or 1 minus the sensitivity of the test. Statistical and econometric modelling[edit] The fitting of many models in statistics and econometrics usually seeks to minimise the difference between observed and predicted or theoretical values. This difference is known as an error, though when observed it would be better described as a residual. The error is taken to be a random variable and as such has a probability distribution. Thus distribution can be used to calculate the probabilities of errors with values within any given range. This statistics-related article is a stub. You can help Wikipedia by expanding it. v t e Retrieved from "https://en.wikipedia.org/w/index.php?title=Probability_of_error&oldid=721278136" Categories: ErrorStatistical modelsStatistics stubsHidden categories: Articles lacking sources from December 2009All articles lacking sourcesAll stub articles Navigation menu Personal tools Not logged inTalkContributionsCreate accountLog in Namespaces Article
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Online Psychology -- Psychotherapy Facts -- Psychotropic Medication Guide Disorders Tests Fun & Games advertisement AllPsychPsych Central's beta is the probability of Virtual Psychology Classroom AllPsych > Research Methods > Chapter 9.5 Probability of Error Chapter 9.5 Probability of Error By Dr. Christopher L. Heffner Dr. Christopher L. Heffner https://en.wikipedia.org/wiki/Probability_of_error August 21, 2014 Chapter 9.5 Probability of Error2014-11-22T03:10:51+00:00 Probability of Error Since every score has some level of error researchers must decide how much error they are willing to accept prior to performing their research. This acceptable error is then compared with the probability of error and if it is less, the study is http://allpsych.com/researchmethods/errorprobability/ said to be significant. For example, if we stated that we would accept 5% error at the onset of the study and our results indicated that the probability of error was 3%, we would reject the null hypothesis and state that the difference between the two groups was significant. If, however, the probability of error were shown to be 6%, we would accept the null hypothesis and state that the difference between the two groups was not significant. The probability of error is often abbreviated with a lower case ‘p,’ and the acceptable error is abbreviated with a lower case alpha (a). When we accept the null, then p > a, and when we reject the null, then p < = a. You will often see these symbols at the end of significance statements in research reports. While alpha can change, depending on the level set at the onset of the experiment, it should not change once the experiment begins. Common
the null hypothesis should not be accepted when the effect is not significant In the Physicians' Reactions case study, the probability value associated with the significance test is 0.0057. Therefore, the null hypothesis was rejected, and it was concluded that physicians intend to http://onlinestatbook.com/2/logic_of_hypothesis_testing/errors.html spend less time with obese patients. Despite the low probability value, it is possible that https://www.youtube.com/watch?v=PQ48szd9cw0 the null hypothesis of no true difference between obese and average-weight patients is true and that the large difference between sample means occurred by chance. If this is the case, then the conclusion that physicians intend to spend less time with obese patients is in error. This type of error is called a Type I error. More generally, a Type of error I error occurs when a significance test results in the rejection of a true null hypothesis. By one common convention, if the probability value is below 0.05, then the null hypothesis is rejected. Another convention, although slightly less common, is to reject the null hypothesis if the probability value is below 0.01. The threshold for rejecting the null hypothesis is called the α (alpha) level or simply α. It is also called the significance level. As probability of error discussed in the section on significance testing, it is better to interpret the probability value as an indication of the weight of evidence against the null hypothesis than as part of a decision rule for making a reject or do-not-reject decision. Therefore, keep in mind that rejecting the null hypothesis is not an all-or-nothing decision. The Type I error rate is affected by the α level: the lower the α level, the lower the Type I error rate. It might seem that α is the probability of a Type I error. However, this is not correct. Instead, α is the probability of a Type I error given that the null hypothesis is true. If the null hypothesis is false, then it is impossible to make a Type I error. The second type of error that can be made in significance testing is failing to reject a false null hypothesis. This kind of error is called a Type II error. Unlike a Type I error, a Type II error is not really an error. When a statistical test is not significant, it means that the data do not provide strong evidence that the null hypothesis is false. Lack of significance does not support the conclusion that the null hypothesis is true. Therefore, a researcher should not make the mistake of incorrectly concluding that the
22 Probability of Error Calculation nptelhrd SubscribeSubscribedUnsubscribe626,856626K Loading... Loading... Working... Add to Want to watch this again later? Sign in to add this video to a playlist. Sign in Share More Report Need to report the video? Sign in to report inappropriate content. Sign in Transcript Statistics 28,445 views 36 Like this video? Sign in to make your opinion count. Sign in 37 0 Don't like this video? Sign in to make your opinion count. Sign in 1 Loading... Loading... Transcript The interactive transcript could not be loaded. Loading... Loading... Rating is available when the video has been rented. This feature is not available right now. Please try again later. Uploaded on Aug 28, 2008Lecture Series on Digital Communication by Prof.Bikash. Kumar. Dey , Department of Electrical Engineering,IIT Bombay. For more details on NPTEL visit http://nptel.iitm.ac.in Category Education License Standard YouTube License Show more Show less Loading... Autoplay When autoplay is enabled, a suggested video will automatically play next. Up next QAM, QPSK Explanation - Duration: 28:21. Robert Webber 166,251 views 28:21 Lecture - 23 Calculation of Probability of Error - Duration: 53:39. nptelhrd 17,069 views 53:39 Lecture 06: Bit Error Rate (BER) Performance - Duration: 23:17. NOC15 July-Sep EC05 8,587 views 23:17 Detector with Minimum Error Probability - Duration: 5:51. Anish Turlapaty 803 views 5:51 Some Digital Modulation Techniques & their Probability of Error Calculations - Duration: 40:06. Sourav Guha Roy 634 views 40:06 Super Easy Tutorial on the Probability of a Type 2 Error! - Statistics Help - Duration: 15:29. Quant Concepts 24,682 views 15:29 36. Error Performance of BFSK and M-ARY PSK - Duration: 56:21. kashyap B 4,635 views 56:21 Lecture - 15 Error Detection and Correction - Duration: 58:27. nptelhrd 116,220 views 58:27 Calculating Power and the Probability of a Type II Error (A One-Tailed Example) - Duration: 11:32. jbstatistics 121,287 views 11:32 30 Error Rates for Binary Signalling: Coherent Receivers - Duration: 53:32. IIT Video Lectures 757 vie