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Dina basa sejen, anggapan yen null hypothesis sederhana ditolak lamun tes [[statistic]] ''T'' leuwih gede tinimbang nilai kritis ''c''. Kira-kira dina sabagean kasus T nu di-observasi sarua jeung t<sub>observed</sub>. Mangka nilai-p tina T dina eta kasus probabiliti yen T bakal sarua atawa leuwih ti t<sub>observed</sub>. |
Dina basa sejen, anggapan yen null hypothesis sederhana ditolak lamun tes [[statistic]] ''T'' leuwih gede tinimbang nilai kritis ''c''. Kira-kira dina sabagean kasus T nu di-observasi sarua jeung t<sub>observed</sub>. Mangka nilai-p tina T dina eta kasus probabiliti yen T bakal sarua atawa leuwih ti t<sub>observed</sub>. |
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The p-value does not depend on unobservable parameters, but only on the data, i.e., it is observable; it is a "statistic." In classical frequentist inference, one rejects the null hypothesis if the p-value is smaller than a number called the ''level'' of the test. In effect, the p-value itself is then being used as the test statistic. If the level is 0.05, then the probability that the p-value is less than 0.05, given that the null hypothesis is true, is 0.05, provided the test statistic has a continuous distribution. In that case, the p-value is [[ |
The p-value does not depend on unobservable parameters, but only on the data, i.e., it is observable; it is a "statistic." In classical frequentist inference, one rejects the null hypothesis if the p-value is smaller than a number called the ''level'' of the test. In effect, the p-value itself is then being used as the test statistic. If the level is 0.05, then the probability that the p-value is less than 0.05, given that the null hypothesis is true, is 0.05, provided the test statistic has a continuous distribution. In that case, the p-value is [[sebaran seragam|uniformly distributed]] if the null hypothesis is true. |
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==Frequent misunderstandings== |
==Frequent misunderstandings== |
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Révisi nurutkeun 24 Désémber 2004 03.20
Dina statistik, nilai-p tina variabel random T nyaeta probability Pr(T ≤ tobserved) numana T bakal dianggap leuwih gede atawa sarua jeung nilai observasi tobserved, dina kayaan null hypothesis dianggap bener.
Dina basa sejen, anggapan yen null hypothesis sederhana ditolak lamun tes statistic T leuwih gede tinimbang nilai kritis c. Kira-kira dina sabagean kasus T nu di-observasi sarua jeung tobserved. Mangka nilai-p tina T dina eta kasus probabiliti yen T bakal sarua atawa leuwih ti tobserved.
The p-value does not depend on unobservable parameters, but only on the data, i.e., it is observable; it is a "statistic." In classical frequentist inference, one rejects the null hypothesis if the p-value is smaller than a number called the level of the test. In effect, the p-value itself is then being used as the test statistic. If the level is 0.05, then the probability that the p-value is less than 0.05, given that the null hypothesis is true, is 0.05, provided the test statistic has a continuous distribution. In that case, the p-value is uniformly distributed if the null hypothesis is true.
Frequent misunderstandings
There are several common misunderstandings about p-values. All of the following statements are FALSE:
a) The p-value is the probability that the null hypothesis is true, justifying the "rule" of considering as significant p-values closer to 0 (zero).
Comment: In fact, frequentist statistics does not, and cannot, attach probabilities to hypotheses. Comparison of Bayesian and classical approaches shows that p can be very close to zero while the posterior probability of the null is very close to unity. This is the Jeffreys-Lindley Paradox.
b)The p-value is the probability of falsely rejecting the null hypothesis. This error is called the prosecutor's fallacy.
Comment: Suppose one selects the 5% significance level. The Type I error rate is the average value over all possible outcomes of the p-value in the range 0 to 0.05. If after carrying out the calculation the p-value is computed to be, say, 0.049999 then the Type I error rate is in fact around 29%. On the other hand, if the p-value is very close to zero then the Type I error rate is much lower than 5%.
c) The p-value is the probability that a replicating experiment would not yield the same conclusion.
Rujukan
"Calibration of P-values for Testing Precise Null Hypotheses". Sellke, T., Bayarri, M.J. and Berger, J. (2001) The American Statistician (55), 62--71.