1469:. The US rate of false positive mammograms is up to 15%, the highest in world. One consequence of the high false positive rate in the US is that, in any 10-year period, half of the American women screened receive a false positive mammogram. False positive mammograms are costly, with over $ 100 million spent annually in the U.S. on follow-up testing and treatment. They also cause women unneeded anxiety. As a result of the high false positive rate in the US, as many as 90â95% of women who get a positive mammogram do not have the condition. The lowest rate in the world is in the Netherlands, 1%. The lowest rates are generally in Northern Europe where mammography films are read twice and a high threshold for additional testing is set (the high threshold decreases the power of the test).
242:. This is conceptually similar to the judgement in a court trial. The null hypothesis corresponds to the position of the defendant: just as he is presumed to be innocent until proven guilty, so is the null hypothesis presumed to be true until the data provide convincing evidence against it. The alternative hypothesis corresponds to the position against the defendant. Specifically, the null hypothesis also involves the absence of a difference or the absence of an association. Thus, the null hypothesis can never be that there is a difference or an association.
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must be exact, that is free from vagueness and ambiguity, because it must supply the basis of the 'problem of distribution', of which the test of significance is the solution." As a consequence of this, in experimental science the null hypothesis is generally a statement that a particular treatment has no effect; in observational science, it is that there is
658:
experimenter could adjust the threshold (black vertical line in the figure) and people would be diagnosed as having diseases if any number is detected above this certain threshold. According to the image, changing the threshold would result in changes in false positives and false negatives, corresponding to movement on the curve.
145:(i.e., the researcher unluckily concludes that something is the fact). For instance, consider a study where researchers compare a drug with a placebo. If the patients who are given the drug improve more than the patients given the placebo by chance, it may appear that the drug is effective, but in fact the opposite is true.
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which means, if the true speed of a vehicle is 125, the driver has the probability of 0.36% to avoid the fine when the statistic is performed at level α=0.05, since the recorded average speed is lower than 121.9. If the true speed is closer to 121.9 than 125, then the probability of avoiding the
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Here, the critical region. That is to say, if the recorded speed of a vehicle is greater than critical value 121.9, the driver will be fined. However, there are still 5% of the drivers are falsely fined since the recorded average speed is greater than 121.9 but the true speed does not pass 120, which
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Varying different threshold (cut-off) values could also be used to make the test either more specific or more sensitive, which in turn elevates the test quality. For example, imagine a medical test, in which an experimenter might measure the concentration of a certain protein in the blood sample. The
367:
In terms of false positives and false negatives, a positive result corresponds to rejecting the null hypothesis, while a negative result corresponds to failing to reject the null hypothesis; "false" means the conclusion drawn is incorrect. Thus, a type I error is equivalent to a false positive, and a
1506:
False positives can also produce serious and counter-intuitive problems when the condition being searched for is rare, as in screening. If a test has a false positive rate of one in ten thousand, but only one in a million samples (or people) is a true positive, most of the positives detected by that
633:
The type I error rate is the probability of rejecting the null hypothesis given that it is true. The test is designed to keep the type I error rate below a prespecified bound called the significance level, usually denoted by the Greek letter α (alpha) and is also called the alpha level. Usually, the
1627:
The relative cost of false results determines the likelihood that test creators allow these events to occur. As the cost of a false negative in this scenario is extremely high (not detecting a bomb being brought onto a plane could result in hundreds of deaths) whilst the cost of a false positive is
623:
The results obtained from negative sample (left curve) overlap with the results obtained from positive samples (right curve). By moving the result cutoff value (vertical bar), the rate of false positives (FP) can be decreased, at the cost of raising the number of false negatives (FN), or vice versa
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On the basis that it is always assumed, by statistical convention, that the speculated hypothesis is wrong, and the so-called "null hypothesis" that the observed phenomena simply occur by chance (and that, as a consequence, the speculated agent has no effect) â the test will determine whether
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A perfect test would have zero false positives and zero false negatives. However, statistical methods are probabilistic, and it cannot be known for certain whether statistical conclusions are correct. Whenever there is uncertainty, there is the possibility of making an error. Considering this, all
122:
Much of statistical theory revolves around the minimization of one or both of these errors, though the complete elimination of either is an 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)
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has led to circumstances where many understand the term "the null hypothesis" as meaning "the nil hypothesis" â a statement that the results in question have arisen through chance. This is not necessarily the case â the key restriction, as per Fisher (1966), is that "the null hypothesis
1232:
In 1933, they observed that these "problems are rarely presented in such a form that we can discriminate with certainty between the true and false hypothesis". They also noted that, in deciding whether to fail to reject, or reject a particular hypothesis amongst a "set of alternative hypotheses",
653:
The same idea can be expressed in terms of the rate of correct results and therefore used to minimize error rates and improve the quality of hypothesis test. To reduce the probability of committing a type I error, making the alpha value more stringent is both simple and efficient. To decrease the
344:
The second kind of error is the mistaken failure to reject the null hypothesis as the result of a test procedure. This sort of error is called a type II error (false negative) and is also referred to as an error of the second kind. In terms of the courtroom example, a type II error corresponds to
335:
The first kind of error is the mistaken rejection of a null hypothesis as the result of a test procedure. This kind of error is called a type I error (false positive) and is sometimes called an error of the first kind. In terms of the courtroom example, a type I error corresponds to convicting an
1186:
The tradeoffs between type I error and type II error should also be considered. That is, in this case, if the traffic police do not want to falsely fine innocent drivers, the level α can be set to a smaller value, like 0.01. However, if that is the case, more drivers whose true speed is over 120
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False negatives produce serious and counter-intuitive problems, especially when the condition being searched for is common. If a test with a false negative rate of only 10% is used to test a population with a true occurrence rate of 70%, many of the negatives detected by the test will be false.
245:
If the result of the test corresponds with reality, then a correct decision has been made. However, if the result of the test does not correspond with reality, then an error has occurred. There are two situations in which the decision is wrong. The null hypothesis may be true, whereas we reject
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systems. The installed security alarms are intended to prevent weapons being brought onto aircraft; yet they are often set to such high sensitivity that they alarm many times a day for minor items, such as keys, belt buckles, loose change, mobile phones, and tacks in shoes.
698:
The speed limit of a freeway in the United States is 120 kilometers per hour (75 mph). A device is set to measure the speed of passing vehicles. Suppose that the device will conduct three measurements of the speed of a passing vehicle, recording as a random sample
654:
probability of committing a type II error, which is closely associated with analyses' power, either increasing the test's sample size or relaxing the alpha level could increase the analyses' power. A test statistic is robust if the type I error rate is controlled.
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While most anti-spam tactics can block or filter a high percentage of unwanted emails, doing so without creating significant false-positive results is a much more demanding task. A low number of false negatives is an indicator of the efficiency of spam filtering.
1227:
in testing hypotheses two considerations must be kept in view, we must be able to reduce the chance of rejecting a true hypothesis to as low a value as desired; the test must be so devised that it will reject the hypothesis tested when it is likely to be
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The type II error corresponds to the case that the true speed of a vehicle is over 120 kilometers per hour but the driver is not fined. For example, if the true speed of a vehicle Ό=125, the probability that the driver is not fined can be calculated as
1472:
The ideal population screening test would be cheap, easy to administer, and produce zero false negatives, if possible. Such tests usually produce more false positives, which can subsequently be sorted out by more sophisticated (and expensive) testing.
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relatively low (a reasonably simple further inspection) the most appropriate test is one with a low statistical specificity but high statistical sensitivity (one that allows a high rate of false positives in return for minimal false negatives).
1315:" concerning the observed phenomena of the world (or its inhabitants) can be supported. The results of such testing determine whether a particular set of results agrees reasonably (or does not agree) with the speculated hypothesis.
1038:
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hypothesis that is to be either nullified or not nullified by the test. When the null hypothesis is nullified, it is possible to conclude that data support the "alternative hypothesis" (which is the original speculated one).
1024:
1347:
If the probability of obtaining a result as extreme as the one obtained, supposing that the null hypothesis were true, is lower than a pre-specified cut-off probability (for example, 5%), then the result is said to be
1203:(1895â1980), both eminent statisticians, discussed the problems associated with "deciding whether or not a particular sample may be judged as likely to have been randomly drawn from a certain population": and, as
1619:
The ratio of false positives (identifying an innocent traveler as a terrorist) to true positives (detecting a would-be terrorist) is, therefore, very high; and because almost every alarm is a false positive, the
1567:
The probability of type I errors is called the "false reject rate" (FRR) or false non-match rate (FNMR), while the probability of type II errors is called the "false accept rate" (FAR) or false match rate (FMR).
1363:
is never proved or established, but is possibly disproved, in the course of experimentation. Every experiment may be said to exist only in order to give the facts a chance of disproving the null hypothesis.
1406:
Testing involves far more expensive, often invasive, procedures that are given only to those who manifest some clinical indication of disease, and are most often applied to confirm a suspected diagnosis.
823:
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Type II error (false match rate): The true fact is that the person is not someone in the searched list but the system concludes that the person is someone whom we are looking for according to the data.
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This sometimes leads to inappropriate or inadequate treatment of both the patient and their disease. A common example is relying on cardiac stress tests to detect coronary atherosclerosis, even though
1502:
Type II error (false negative): The true fact is that the disease is actually present but the test reports provide a falsely reassuring message to patients and physicians that the disease is absent.
1462:
have a significant rate of false positives; however, physicians use much more expensive and far more precise tests to determine whether a person is actually infected with either of these viruses.
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Although they display a high rate of false positives, the screening tests are considered valuable because they greatly increase the likelihood of detecting these disorders at a far earlier stage.
1780:
353:
The crossover error rate (CER) is the point at which type I errors and type II errors are equal. A system with a lower CER value provides more accuracy than a system with a higher CER value.
645:
These two types of error rates are traded off against each other: for any given sample set, the effort to reduce one type of error generally results in increasing the other type of error.
1575:
rate". On the other hand, if the system is used for validation (and acceptance is the norm) then the FAR is a measure of system security, while the FRR measures user inconvenience level.
155:. In the example above, if the patients who got the drug did not get better at a higher rate than the ones who got the placebo and this was a random fluke, that would be a type II error.
1327:
The consistent application by statisticians of Neyman and
Pearson's convention of representing "the hypothesis to be tested" (or "the hypothesis to be nullified") with the expression
2198:
Marascuilo, L.A. & Levin, J.R., "Appropriate Post Hoc
Comparisons for Interaction and nested Hypotheses in Analysis of Variance Designs: The Elimination of Type-IV Errors",
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Type II error (false negative): The true fact is that the newborns have phenylketonuria and hypothyroidism but we consider they do not have the disorders according to the data.
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Type I error (false positive): The true fact is that the newborns do not have phenylketonuria and hypothyroidism but we consider they have the disorders according to the data.
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this hypothesis is right or wrong. This is why the hypothesis under test is often called the null hypothesis (most likely, coined by Fisher (1935, p. 19)), because it is
666:
Since in a real experiment it is impossible to avoid all type I and type II errors, it is important to consider the amount of risk one is willing to take to falsely reject H
1665:
Type I error (false positive): Spam filtering or spam blocking techniques wrongly classify a legitimate email message as spam and, as a result, interfere with its delivery.
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Type I error (false positive): The true fact is that the patients do not have a specific disease but the physician judges the patient is ill according to the test reports.
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Type I error (false reject rate): The true fact is that the person is someone in the searched list but the system concludes that the person is not according to the data.
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682:α of the statistic. For example, if the p-value of a test statistic result is estimated at 0.0596, then there is a probability of 5.96% that we falsely reject H
2247:
139:
1173:{\displaystyle P=(T<121.9|\mu =125)=P\left({\frac {T-125}{\frac {2}{\sqrt {3}}}}<{\frac {121.9-125}{\frac {2}{\sqrt {3}}}}\right)=\phi (-2.68)=0.0036}
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61:
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significance level is set to 0.05 (5%), implying that it is acceptable to have a 5% probability of incorrectly rejecting the true null hypothesis.
30:
This article is about erroneous outcomes of statistical tests. For closely related concepts in binary classification and testing generally, see
3660:
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Screening involves relatively cheap tests that are given to large populations, none of whom manifest any clinical indication of disease (e.g.,
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remarked, "it is necessary to remember the adjective 'random' should apply to the method of drawing the sample and not to the sample itself".
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1972:
Neyman, J.; Pearson, E. S. (1928). "On the Use and
Interpretation of Certain Test Criteria for Purposes of Statistical Inference Part I".
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The notions of false positives and false negatives have a wide currency in the realm of computers and computer applications, including
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level, the quality of the hypothesis test can be increased. The knowledge of type I errors and type II errors is widely used in
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Neyman, J.; Pearson, E. S. (30 October 1933). "The testing of statistical hypotheses in relation to probabilities a priori".
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119:, is the failure to reject a null hypothesis that is actually false. For example: a guilty person may be not convicted.
31:
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Perhaps the most widely discussed false positives in medical screening come from the breast cancer screening procedure
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Type II error (false negative) The true fact is that the item is a weapon but the system keeps silent at this time.
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Type I error (false positive): The true fact is that the item is not a weapon but the system still sounds an alarm.
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at 5%. A significance level α of 0.05 is relatively common, but there is no general rule that fits all scenarios.
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test will be false. The probability that an observed positive result is a false positive may be calculated using
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1918:. Wiley series in probability and statistics (3rd ed.). Hoboken, New Jersey: John Wiley & Sons, Inc.
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If the system is designed to rarely match suspects then the probability of type II errors can be called the "
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In the same paper they call these two sources of error, errors of type I and errors of type II respectively.
863:) and the parameter Ό represents the true speed of passing vehicle. In this experiment, the null hypothesis H
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17:
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Mitroff, I.I. & Featheringham, T.R., "On
Systemic Problem Solving and the Error of the Third Kind",
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686:. Or, if we say, the statistic is performed at level α, like 0.05, then we allow to falsely reject H
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Type II error (false negative): Spam email is not detected as spam, but is classified as non-spam.
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2250: â presentation by Nigel Paneth, Graduate School of Public Health, University of Pittsburgh
714:
624:(TP = True Positives, TPR = True Positive Rate, FPR = False Positive Rate, TN = True Negatives).
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between the value of a particular measured variable, and that of an experimental prediction.
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Tabulated relations between truth/falseness of the null hypothesis and outcomes of the test:
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173:
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8:
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2007:
C. I. K. F. (July 1951). "Probability Theory for
Statistical Methods. By F. N. David. ".
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The rate of the type II error is denoted by the Greek letter ÎČ (beta) and related to the
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2147:
David, F.N., "A Power
Function for Tests of Randomness in a Sequence of Alternatives",
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711:. The traffic police will or will not fine the drivers depending on the average speed
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3589:
3577:
3203:
3120:
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2831:
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2532:
2406:
2103:
2091:
2024:
1989:
1954:
1944:
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1843:
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1637:
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629:
statistical hypothesis tests have a probability of making type I and type II errors.
1840:
A modern introduction to probability and statistics : understanding why and how
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2016:
1981:
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951:{\displaystyle P\left(Z\geqslant {\frac {c-120}{\frac {2}{\sqrt {3}}}}\right)=0.05}
327:
is rejected. Two types of error are distinguished: type I error and type II error.
132:
1557:
Null hypothesis: "The input does identify someone in the searched list of people".
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1985:
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Hypothesis: "The input does not identify someone in the searched list of people".
1411:
1302:
181:
124:
105:
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2020:
1019:{\displaystyle {\frac {c-120}{\frac {2}{\sqrt {3}}}}=1.645\Rightarrow c=121.9}
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1958:
960:
According to change-of-units rule for the normal distribution. Referring to
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are modeled as normal distribution N(Ό,2). Then, T should follow N(Ό,2/
108:
when it is actually true. For example, an innocent person may be convicted.
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4372:
4349:
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2890:
2788:
2723:
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the error of failing to reject a hypothesis that should have been rejected.
1215:
the error of rejecting a hypothesis that should have not been rejected, and
1200:
1196:
2161:
Gambrill, W., "False
Positives on Newborns' Disease Tests Worry Parents",
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In the practice of medicine, the differences between the applications of
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1447:
1410:
For example, most states in the US require newborns to be screened for
1312:
1223:
In 1930, they elaborated on these two sources of error, remarking that
1187:
kilometers per hour, like 125, would be more likely to avoid the fine.
180:. The test goes about choosing about two competing propositions called
128:
1811:
1275:
In all of the papers co-written by Neyman and
Pearson the expression H
3481:
3333:
2953:
2748:
2660:
2645:
2640:
2605:
2234:
Decision
Analysis: Introductory Lectures on Choices Under Uncertainty
2184:
Kimball, A.W., "Errors of the Third Kind in
Statistical Consulting",
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2997:
2615:
2492:
2487:
2482:
1527:
1426:
Hypothesis: "The newborns have phenylketonuria and hypothyroidism".
1400:
1781:
Statisticians' and engineers' cross-reference of statistical terms
4502:
4203:
1916:
An introduction to probability theory and mathematical statistics
1645:
1433:): "The newborns do not have phenylketonuria and hypothyroidism".
961:
675:
4424:
3405:
3379:
3359:
2610:
2401:
2068:
Mathematical Proceedings of the Cambridge Philosophical Society
1887:
Handbook of Parametric and Nonparametric Statistical Procedures
1481:
False negatives and false positives are significant issues in
2253:
619:
2191:
Lubin, A., "The Interpretation of Significant Interaction",
1269:
is true. (There are various notations for the alternative).
615:
False positive rate § Comparison with other error rates
2344:
818:{\displaystyle T={\frac {X_{1}+X_{2}+X_{3}}{3}}={\bar {X}}}
1455:
674:. The solution to this question would be to report the
577:
548:
515:
481:
440:
394:
306:
279:
252:
221:
190:
2151:, Vol.34, Nos.3/4, (December 1947), pp. 335â339.
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Hypothesis: "The patients have the specific disease".
1307:
It is standard practice for statisticians to conduct
1041:
972:
897:
845:
748:
717:
4166:
Autoregressive conditional heteroskedasticity (ARCH)
1680:
1311:
in order to determine whether or not a "speculative
885:
If we perform the statistic level at α=0.05, then a
356:
2177:Kaiser, H.F., "Directional Statistical Decisions",
2140:, "Type IV Errors and Analysis of Simple Effects",
1938:
1496:): "The patients do not have the specific disease".
52:
may be too technical for most readers to understand
3628:
2218:-Sample Slippage Test for an Extreme Population",
2209:, Vol.19, No.6, (November 1974), pp. 383â393.
1842:. Dekking, Michel, 1946-. London: Springer. 2005.
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732:
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1943:. Burgman, Mark A. Collingwood, Vic.: CSIRO Pub.
1593:False positives are routinely found every day in
648:
368:type II error is equivalent to a false negative.
4581:
2195:, Vol.21, No.4, (Winter 1961), pp. 807â817.
2188:, Vol.52, No.278, (June 1957), pp. 133â142.
1914:Rohatgi, V. K.; Saleh, A. K. Md Ehsanes (2015).
1279:always signifies "the hypothesis to be tested".
1210:They identified "two sources of error", namely:
273:. On the other hand, the alternative hypothesis
138:Intuitively, type I errors can be thought of as
3714:Multivariate adaptive regression splines (MARS)
2186:Journal of the American Statistical Association
2144:, Vol.3, No.2, (Summer 1978), pp. 121â144.
1550:, is susceptible to type I and type II errors.
827:In addition, we suppose that the measurements X
2229:, Vol.29, No.7, (July 1983), pp. 121â127.
1884:
1834:
1832:
1522:tests are known to only detect limitations of
1359:(1890â1962) stressed that the null hypothesis
2269:
2222:, Vol.19, No.1, (March 1948), pp. 58â65.
2202:, Vol.7., No.3, (May 1970), pp. 397â421.
2181:, Vol.67, No.3, (May 1960), pp. 160â167.
2065:
1971:
1913:
1655:For example, in the case of spam filtering:
1609:Null hypothesis: "The item is not a weapon".
27:Concepts from statistical hypothesis testing
2009:Journal of the Staple Inn Actuarial Society
2006:
1829:
1662:Null hypothesis: "The message is not spam".
1342:
2314:
2276:
2262:
1735:Information retrieval performance measures
693:
2927:
2193:Educational and Psychological Measurement
163:
80:Learn how and when to remove this message
64:, without removing the technical details.
1786:Testing hypotheses suggested by the data
618:
443:
397:
371:
348:
14:
4582:
4240:KaplanâMeier estimator (product limit)
2158:, Oliver & Boyd (Edinburgh), 1935.
2116:
1878:
1624:of these screening tests is very low.
1373:
4313:
3880:
3627:
2926:
2696:
2313:
2257:
2220:The Annals of Mathematical Statistics
2200:American Educational Research Journal
1578:
1352:and the null hypothesis is rejected.
740:. That is to say, the test statistic
383:
62:make it understandable to non-experts
4550:
4250:Accelerated failure time (AFT) model
1394:
36:
4562:
3845:Analysis of variance (ANOVA, anova)
2697:
2225:Moulton, R.T., "Network Security",
1606:Hypothesis: "The item is a weapon".
1241:..., it was easy to make an error,
363:False positives and false negatives
32:false positives and false negatives
24:
3940:CochranâMantelâHaenszel statistics
2566:Pearson product-moment correlation
2236:, AddisonâWesley, (Reading), 1968.
2121:(8th ed.). Edinburgh: Hafner.
1659:Hypothesis: "The message is spam".
1476:
1296:
1261:when some alternative hypothesis H
1245:these errors will be of two kinds:
456:{\textstyle {\boldsymbol {H_{0}}}}
410:{\textstyle {\boldsymbol {H_{0}}}}
25:
4611:
2241:
2142:Journal of Educational Statistics
2052:), and is not an "O" (indicating
1771:Receiver operating characteristic
357:False positive and false negative
4561:
4549:
4537:
4524:
4523:
4314:
2041:The subscript in the expression
1812:"Type I Error and Type II Error"
1683:
1538:Biometric matching, such as for
1285:
889:c should be calculated to solve
867:and the alternative hypothesis H
447:
401:
339:
148:By contrast, type II errors are
41:
4199:Least-squares spectral analysis
2129:
2110:
330:
4600:Statistical hypothesis testing
3180:Mean-unbiased minimum-variance
2283:
2059:
2035:
2000:
1965:
1941:Practical conservation biology
1932:
1907:
1804:
1161:
1152:
1074:
1061:
1048:
1004:
809:
724:
649:The quality of hypothesis test
94:statistical hypothesis testing
13:
1:
4493:Geographic information system
3709:Simultaneous equations models
1797:
1650:optical character recognition
1533:
604:
158:
3676:Coefficient of determination
3287:Uniformly most powerful test
1939:Lindenmayer, David. (2005).
1631:
1190:
7:
4245:Proportional hazards models
4189:Spectral density estimation
4171:Vector autoregression (VAR)
3605:Maximum posterior estimator
2837:Randomized controlled trial
1776:Sensitivity and specificity
1750:Probability of a hypothesis
1676:
1526:blood flow due to advanced
1378:
856:{\displaystyle {\sqrt {3}}}
611:Sensitivity and specificity
10:
4616:
4005:Multivariate distributions
2425:Average absolute deviation
1986:10.1093/biomet/20a.1-2.175
1595:airport security screening
1582:
1300:
1289:
1205:Florence Nightingale David
1183:fine will also be higher.
733:{\displaystyle {\bar {X}}}
661:
608:
360:
104:, is the rejection of the
29:
4519:
4473:
4410:
4363:
4326:
4322:
4309:
4281:
4263:
4230:
4221:
4179:
4126:
4087:
4036:
4027:
3993:Structural equation model
3948:
3905:
3901:
3876:
3835:
3801:
3755:
3722:
3684:
3651:
3647:
3623:
3563:
3472:
3391:
3355:
3346:
3329:Score/Lagrange multiplier
3314:
3267:
3212:
3138:
3129:
2939:
2935:
2922:
2881:
2855:
2807:
2762:
2744:Sample size determination
2709:
2705:
2692:
2596:
2551:
2525:
2507:
2463:
2415:
2335:
2326:
2322:
2309:
2291:
2156:The Design of Experiments
2119:The design of experiments
2088:10.1017/s030500410001152x
2021:10.1017/s0020269x00004564
1622:positive predictive value
1350:statistically significant
429:
386:
4488:Environmental statistics
4010:Elliptical distributions
3803:Generalized linear model
3732:Simple linear regression
3502:HodgesâLehmann estimator
2959:Probability distribution
2868:Stochastic approximation
2430:Coefficient of variation
1450:used to screen possible
1357:Sir Ronald Aylmer Fisher
1343:Statistical significance
1029:we say, a type I error.
4148:Cross-correlation (XCF)
3756:Non-standard predictors
3190:LehmannâScheffĂ© theorem
2863:Adaptive clinical trial
1885:Sheskin, David (2004).
1597:, which are ultimately
1540:fingerprint recognition
694:Vehicle speed measuring
345:acquitting a criminal.
176:is an integral part of
170:statistical test theory
4544:Mathematics portal
4365:Engineering statistics
4273:NelsonâAalen estimator
3850:Analysis of covariance
3737:Ordinary least squares
3661:Pearson product-moment
3065:Statistical functional
2976:Empirical distribution
2809:Controlled experiments
2538:Frequency distribution
2316:Descriptive statistics
2117:Fisher, R. A. (1966).
2048:is a zero (indicating
1870:: CS1 maint: others (
1752:for Bayesian inference
1730:Family-wise error rate
1720:False positive paradox
1371:
1273:
1230:
1174:
1020:
952:
857:
819:
734:
625:
591:
556:
523:
495:
494:{\textstyle 1-\alpha }
457:
411:
321:
294:
267:
236:
213:alternative hypothesis
205:
164:Statistical background
4590:Design of experiments
4460:Population statistics
4402:System identification
4136:Autocorrelation (ACF)
4064:Exponential smoothing
3978:Discriminant analysis
3973:Canonical correlation
3837:Partition of variance
3699:Regression validation
3543:(JonckheereâTerpstra)
3442:Likelihood-ratio test
3131:Frequentist inference
3043:Locationâscale family
2964:Sampling distribution
2929:Statistical inference
2896:Cross-sectional study
2883:Observational studies
2842:Randomized experiment
2671:Stem-and-leaf display
2473:Central limit theorem
1889:. CRC Press. p.
1715:Ethics in mathematics
1700:Binary classification
1361:
1355:British statistician
1243:
1225:
1175:
1021:
953:
878:: Ό=120 against H
858:
820:
735:
622:
592:
590:{\textstyle 1-\beta }
557:
524:
496:
458:
412:
384:Table of error types
361:Further information:
322:
300:may be true, whereas
295:
268:
237:
206:
4383:Probabilistic design
3968:Principal components
3811:Exponential families
3763:Nonlinear regression
3742:General linear model
3704:Mixed effects models
3694:Errors and residuals
3671:Confounding variable
3573:Bayesian probability
3551:Van der Waerden test
3541:Ordered alternative
3306:Multiple comparisons
3185:RaoâBlackwellization
3148:Estimating equations
3104:Statistical distance
2822:Factorial experiment
2355:Arithmetic-Geometric
2248:Bias and Confounding
2179:Psychological Review
1761:Prosecutor's fallacy
1756:Precision and recall
1740:NeymanâPearson lemma
1725:False discovery rate
1420:congenital disorders
1292:Coverage probability
1039:
970:
895:
843:
746:
715:
575:
555:{\textstyle \alpha }
546:
513:
479:
438:
392:
372:Table of error types
349:Crossover error rate
336:innocent defendant.
304:
277:
250:
219:
188:
4455:Official statistics
4378:Methods engineering
4059:Seasonal adjustment
3827:Poisson regressions
3747:Bayesian regression
3686:Regression analysis
3666:Partial correlation
3638:Regression analysis
3237:Prediction interval
3232:Likelihood interval
3222:Confidence interval
3214:Interval estimation
3175:Unbiased estimators
2993:Model specification
2873:Up-and-down designs
2561:Partial correlation
2517:Index of dispersion
2435:Interquartile range
2171:17 May 2018 at the
2080:1933PCPS...29..492N
1652:, and many others.
1585:Explosive detection
1374:Application domains
1257:we fail to reject H
641:, which equals 1âÎČ.
522:{\textstyle \beta }
380:
4475:Spatial statistics
4355:Medical statistics
4255:First hitting time
4209:Whittle likelihood
3860:Degrees of freedom
3855:Multivariate ANOVA
3788:Heteroscedasticity
3600:Bayesian estimator
3565:Bayesian inference
3414:KolmogorovâSmirnov
3299:Randomization test
3269:Testing hypotheses
3242:Tolerance interval
3153:Maximum likelihood
3048:Exponential family
2981:Density estimation
2941:Statistical theory
2901:Natural experiment
2847:Scientific control
2764:Survey methodology
2450:Standard deviation
2212:Mosteller, F., "A
2207:Behavioral Science
1766:Prozone phenomenon
1691:Mathematics portal
1579:Security screening
1544:facial recognition
1492:Null hypothesis (H
1429:Null hypothesis (H
1391:are considerable.
1368:Fisher, 1935, p.19
1170:
1016:
948:
853:
815:
730:
680:significance level
626:
587:
567:Correct inference
552:
519:
491:
453:
407:
379:
320:{\textstyle H_{0}}
317:
293:{\textstyle H_{1}}
290:
266:{\textstyle H_{0}}
263:
235:{\textstyle H_{1}}
232:
204:{\textstyle H_{0}}
201:
178:hypothesis testing
172:, the notion of a
4577:
4576:
4515:
4514:
4511:
4510:
4450:National accounts
4420:Actuarial science
4412:Social statistics
4305:
4304:
4301:
4300:
4297:
4296:
4232:Survival function
4217:
4216:
4079:Granger causality
3920:Contingency table
3895:Survival analysis
3872:
3871:
3868:
3867:
3724:Linear regression
3619:
3618:
3615:
3614:
3590:Credible interval
3559:
3558:
3342:
3341:
3158:Method of moments
3027:Parametric family
2988:Statistical model
2918:
2917:
2914:
2913:
2832:Random assignment
2754:Statistical power
2688:
2687:
2684:
2683:
2533:Contingency table
2503:
2502:
2370:Generalized/power
2165:, (5 June 2006).
2136:Betz, M.A. &
1925:978-1-118-79963-5
1849:978-1-85233-896-1
1638:computer security
1599:visual inspection
1395:Medical screening
1139:
1138:
1137:
1111:
1110:
1109:
996:
995:
994:
935:
934:
933:
851:
812:
798:
727:
602:
601:
471:Correct inference
388:Null hypothesis (
174:statistical error
90:
89:
82:
16:(Redirected from
4607:
4565:
4564:
4553:
4552:
4542:
4541:
4527:
4526:
4430:Crime statistics
4324:
4323:
4311:
4310:
4228:
4227:
4194:Fourier analysis
4181:Frequency domain
4161:
4108:
4074:Structural break
4034:
4033:
3983:Cluster analysis
3930:Log-linear model
3903:
3902:
3878:
3877:
3819:
3793:Homoscedasticity
3649:
3648:
3625:
3624:
3544:
3536:
3528:
3527:(KruskalâWallis)
3512:
3497:
3452:Cross validation
3437:
3419:AndersonâDarling
3366:
3353:
3352:
3324:Likelihood-ratio
3316:Parametric tests
3294:Permutation test
3277:1- & 2-tails
3168:Minimum distance
3140:Point estimation
3136:
3135:
3087:Optimal decision
3038:
2937:
2936:
2924:
2923:
2906:Quasi-experiment
2856:Adaptive designs
2707:
2706:
2694:
2693:
2571:Rank correlation
2333:
2332:
2324:
2323:
2311:
2310:
2278:
2271:
2264:
2255:
2254:
2123:
2122:
2114:
2108:
2107:
2063:
2057:
2039:
2033:
2032:
2004:
1998:
1997:
1980:(1â2): 175â240.
1969:
1963:
1962:
1936:
1930:
1929:
1911:
1905:
1904:
1882:
1876:
1875:
1869:
1861:
1836:
1827:
1826:
1824:
1822:
1808:
1705:Detection theory
1693:
1688:
1687:
1548:iris recognition
1369:
1254:when it is true,
1199:(1894â1981) and
1179:
1177:
1176:
1171:
1145:
1141:
1140:
1133:
1129:
1128:
1117:
1112:
1105:
1101:
1100:
1089:
1064:
1025:
1023:
1022:
1017:
997:
990:
986:
985:
974:
957:
955:
954:
949:
941:
937:
936:
929:
925:
924:
913:
862:
860:
859:
854:
852:
847:
824:
822:
821:
816:
814:
813:
805:
799:
794:
793:
792:
780:
779:
767:
766:
756:
739:
737:
736:
731:
729:
728:
720:
596:
594:
593:
588:
569:(true negative)
561:
559:
558:
553:
539:(false positive)
528:
526:
525:
520:
507:(false negative)
500:
498:
497:
492:
473:(true positive)
462:
460:
459:
454:
452:
451:
450:
416:
414:
413:
408:
406:
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404:
381:
378:
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241:
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210:
208:
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200:
199:
133:computer science
85:
78:
74:
71:
65:
45:
44:
37:
21:
4615:
4614:
4610:
4609:
4608:
4606:
4605:
4604:
4580:
4579:
4578:
4573:
4536:
4507:
4469:
4406:
4392:quality control
4359:
4341:Clinical trials
4318:
4293:
4277:
4265:Hazard function
4259:
4213:
4175:
4159:
4122:
4118:BreuschâGodfrey
4106:
4083:
4023:
3998:Factor analysis
3944:
3925:Graphical model
3897:
3864:
3831:
3817:
3797:
3751:
3718:
3680:
3643:
3642:
3611:
3555:
3542:
3534:
3526:
3510:
3495:
3474:Rank statistics
3468:
3447:Model selection
3435:
3393:Goodness of fit
3387:
3364:
3338:
3310:
3263:
3208:
3197:Median unbiased
3125:
3036:
2969:Order statistic
2931:
2910:
2877:
2851:
2803:
2758:
2701:
2699:Data collection
2680:
2592:
2547:
2521:
2499:
2459:
2411:
2328:Continuous data
2318:
2305:
2287:
2282:
2244:
2239:
2173:Wayback Machine
2132:
2127:
2126:
2115:
2111:
2064:
2060:
2046:
2040:
2036:
2005:
2001:
1970:
1966:
1951:
1937:
1933:
1926:
1912:
1908:
1901:
1883:
1879:
1863:
1862:
1850:
1838:
1837:
1830:
1820:
1818:
1810:
1809:
1805:
1800:
1795:
1745:Null hypothesis
1689:
1682:
1679:
1634:
1591:
1583:Main articles:
1581:
1536:
1524:coronary artery
1495:
1483:medical testing
1479:
1477:Medical testing
1432:
1412:phenylketonuria
1397:
1381:
1376:
1370:
1367:
1345:
1333:
1305:
1303:Null hypothesis
1299:
1297:Null hypothesis
1294:
1288:
1278:
1272:
1268:
1264:
1260:
1253:
1240:
1236:
1221:
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1118:
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834:
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771:
762:
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747:
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743:
719:
718:
716:
713:
712:
710:
706:
702:
696:
689:
685:
673:
669:
664:
651:
639:power of a test
617:
607:
576:
573:
572:
571:(probability =
568:
566:
547:
544:
543:
541:(probability =
540:
538:
514:
511:
510:
509:(probability =
508:
506:
480:
477:
476:
475:(probability =
472:
470:
466:
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441:
439:
436:
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400:
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195:
191:
189:
186:
185:
182:null hypothesis
166:
161:
125:medical science
106:null hypothesis
86:
75:
69:
66:
58:help improve it
55:
46:
42:
35:
28:
23:
22:
15:
12:
11:
5:
4613:
4603:
4602:
4597:
4592:
4575:
4574:
4572:
4571:
4559:
4547:
4533:
4520:
4517:
4516:
4513:
4512:
4509:
4508:
4506:
4505:
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4495:
4490:
4485:
4479:
4477:
4471:
4470:
4468:
4467:
4462:
4457:
4452:
4447:
4442:
4437:
4432:
4427:
4422:
4416:
4414:
4408:
4407:
4405:
4404:
4399:
4394:
4385:
4380:
4375:
4369:
4367:
4361:
4360:
4358:
4357:
4352:
4347:
4338:
4336:Bioinformatics
4332:
4330:
4320:
4319:
4307:
4306:
4303:
4302:
4299:
4298:
4295:
4294:
4292:
4291:
4285:
4283:
4279:
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4276:
4275:
4269:
4267:
4261:
4260:
4258:
4257:
4252:
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4236:
4234:
4225:
4219:
4218:
4215:
4214:
4212:
4211:
4206:
4201:
4196:
4191:
4185:
4183:
4177:
4176:
4174:
4173:
4168:
4163:
4155:
4150:
4145:
4144:
4143:
4141:partial (PACF)
4132:
4130:
4124:
4123:
4121:
4120:
4115:
4110:
4102:
4097:
4091:
4089:
4088:Specific tests
4085:
4084:
4082:
4081:
4076:
4071:
4066:
4061:
4056:
4051:
4046:
4040:
4038:
4031:
4025:
4024:
4022:
4021:
4020:
4019:
4018:
4017:
4002:
4001:
4000:
3990:
3988:Classification
3985:
3980:
3975:
3970:
3965:
3960:
3954:
3952:
3946:
3945:
3943:
3942:
3937:
3935:McNemar's test
3932:
3927:
3922:
3917:
3911:
3909:
3899:
3898:
3874:
3873:
3870:
3869:
3866:
3865:
3863:
3862:
3857:
3852:
3847:
3841:
3839:
3833:
3832:
3830:
3829:
3813:
3807:
3805:
3799:
3798:
3796:
3795:
3790:
3785:
3780:
3775:
3773:Semiparametric
3770:
3765:
3759:
3757:
3753:
3752:
3750:
3749:
3744:
3739:
3734:
3728:
3726:
3720:
3719:
3717:
3716:
3711:
3706:
3701:
3696:
3690:
3688:
3682:
3681:
3679:
3678:
3673:
3668:
3663:
3657:
3655:
3645:
3644:
3641:
3640:
3635:
3629:
3621:
3620:
3617:
3616:
3613:
3612:
3610:
3609:
3608:
3607:
3597:
3592:
3587:
3586:
3585:
3580:
3569:
3567:
3561:
3560:
3557:
3556:
3554:
3553:
3548:
3547:
3546:
3538:
3530:
3514:
3511:(MannâWhitney)
3506:
3505:
3504:
3491:
3490:
3489:
3478:
3476:
3470:
3469:
3467:
3466:
3465:
3464:
3459:
3454:
3444:
3439:
3436:(ShapiroâWilk)
3431:
3426:
3421:
3416:
3411:
3403:
3397:
3395:
3389:
3388:
3386:
3385:
3377:
3368:
3356:
3350:
3348:Specific tests
3344:
3343:
3340:
3339:
3337:
3336:
3331:
3326:
3320:
3318:
3312:
3311:
3309:
3308:
3303:
3302:
3301:
3291:
3290:
3289:
3279:
3273:
3271:
3265:
3264:
3262:
3261:
3260:
3259:
3254:
3244:
3239:
3234:
3229:
3224:
3218:
3216:
3210:
3209:
3207:
3206:
3201:
3200:
3199:
3194:
3193:
3192:
3187:
3172:
3171:
3170:
3165:
3160:
3155:
3144:
3142:
3133:
3127:
3126:
3124:
3123:
3118:
3113:
3112:
3111:
3101:
3096:
3095:
3094:
3084:
3083:
3082:
3077:
3072:
3062:
3057:
3052:
3051:
3050:
3045:
3040:
3024:
3023:
3022:
3017:
3012:
3002:
3001:
3000:
2995:
2985:
2984:
2983:
2973:
2972:
2971:
2961:
2956:
2951:
2945:
2943:
2933:
2932:
2920:
2919:
2916:
2915:
2912:
2911:
2909:
2908:
2903:
2898:
2893:
2887:
2885:
2879:
2878:
2876:
2875:
2870:
2865:
2859:
2857:
2853:
2852:
2850:
2849:
2844:
2839:
2834:
2829:
2824:
2819:
2813:
2811:
2805:
2804:
2802:
2801:
2799:Standard error
2796:
2791:
2786:
2785:
2784:
2779:
2768:
2766:
2760:
2759:
2757:
2756:
2751:
2746:
2741:
2736:
2731:
2729:Optimal design
2726:
2721:
2715:
2713:
2703:
2702:
2690:
2689:
2686:
2685:
2682:
2681:
2679:
2678:
2673:
2668:
2663:
2658:
2653:
2648:
2643:
2638:
2633:
2628:
2623:
2618:
2613:
2608:
2602:
2600:
2594:
2593:
2591:
2590:
2585:
2584:
2583:
2578:
2568:
2563:
2557:
2555:
2549:
2548:
2546:
2545:
2540:
2535:
2529:
2527:
2526:Summary tables
2523:
2522:
2520:
2519:
2513:
2511:
2505:
2504:
2501:
2500:
2498:
2497:
2496:
2495:
2490:
2485:
2475:
2469:
2467:
2461:
2460:
2458:
2457:
2452:
2447:
2442:
2437:
2432:
2427:
2421:
2419:
2413:
2412:
2410:
2409:
2404:
2399:
2398:
2397:
2392:
2387:
2382:
2377:
2372:
2367:
2362:
2360:Contraharmonic
2357:
2352:
2341:
2339:
2330:
2320:
2319:
2307:
2306:
2304:
2303:
2298:
2292:
2289:
2288:
2281:
2280:
2273:
2266:
2258:
2252:
2251:
2243:
2242:External links
2240:
2238:
2237:
2230:
2223:
2210:
2203:
2196:
2189:
2182:
2175:
2159:
2154:Fisher, R.A.,
2152:
2145:
2133:
2131:
2128:
2125:
2124:
2109:
2074:(4): 492â510.
2058:
2044:
2034:
2015:(3): 243â244.
1999:
1964:
1949:
1931:
1924:
1906:
1899:
1877:
1848:
1828:
1816:explorable.com
1802:
1801:
1799:
1796:
1794:
1793:
1791:Type III error
1788:
1783:
1778:
1773:
1768:
1763:
1758:
1753:
1747:
1742:
1737:
1732:
1727:
1722:
1717:
1712:
1707:
1702:
1696:
1695:
1694:
1678:
1675:
1670:
1669:
1666:
1663:
1660:
1642:spam filtering
1633:
1630:
1617:
1616:
1613:
1610:
1607:
1589:Metal detector
1580:
1577:
1565:
1564:
1561:
1558:
1555:
1535:
1532:
1520:cardiac stress
1509:Bayes' theorem
1504:
1503:
1500:
1497:
1493:
1490:
1478:
1475:
1441:
1440:
1437:
1434:
1430:
1427:
1418:, among other
1416:hypothyroidism
1396:
1393:
1380:
1377:
1375:
1372:
1365:
1344:
1341:
1331:
1301:Main article:
1298:
1295:
1287:
1284:
1276:
1271:
1270:
1266:
1262:
1258:
1255:
1251:
1247:
1238:
1234:
1220:
1219:
1216:
1212:
1192:
1189:
1169:
1166:
1163:
1160:
1157:
1154:
1151:
1148:
1144:
1136:
1132:
1127:
1124:
1121:
1115:
1108:
1104:
1099:
1096:
1093:
1086:
1082:
1079:
1076:
1073:
1070:
1067:
1063:
1059:
1056:
1053:
1050:
1047:
1044:
1015:
1012:
1009:
1006:
1003:
1000:
993:
989:
984:
981:
978:
947:
944:
940:
932:
928:
923:
920:
917:
911:
908:
904:
900:
887:critical value
879:
875:
868:
864:
850:
836:
832:
828:
811:
808:
802:
797:
791:
787:
783:
778:
774:
770:
765:
761:
754:
751:
726:
723:
708:
704:
700:
695:
692:
687:
683:
671:
667:
663:
660:
650:
647:
643:
642:
635:
606:
603:
600:
599:
586:
583:
580:
564:
551:
535:
531:
530:
518:
505:Type II error
503:
490:
487:
484:
468:
464:
449:
445:
427:
426:
423:
419:
418:
403:
399:
385:
373:
370:
358:
355:
350:
347:
341:
338:
332:
329:
314:
310:
287:
283:
260:
256:
229:
225:
198:
194:
165:
162:
160:
157:
117:false negative
102:false positive
88:
87:
49:
47:
40:
26:
9:
6:
4:
3:
2:
4612:
4601:
4598:
4596:
4593:
4591:
4588:
4587:
4585:
4570:
4569:
4560:
4558:
4557:
4548:
4546:
4545:
4540:
4534:
4532:
4531:
4522:
4521:
4518:
4504:
4501:
4499:
4498:Geostatistics
4496:
4494:
4491:
4489:
4486:
4484:
4481:
4480:
4478:
4476:
4472:
4466:
4465:Psychometrics
4463:
4461:
4458:
4456:
4453:
4451:
4448:
4446:
4443:
4441:
4438:
4436:
4433:
4431:
4428:
4426:
4423:
4421:
4418:
4417:
4415:
4413:
4409:
4403:
4400:
4398:
4395:
4393:
4389:
4386:
4384:
4381:
4379:
4376:
4374:
4371:
4370:
4368:
4366:
4362:
4356:
4353:
4351:
4348:
4346:
4342:
4339:
4337:
4334:
4333:
4331:
4329:
4328:Biostatistics
4325:
4321:
4317:
4312:
4308:
4290:
4289:Log-rank test
4287:
4286:
4284:
4280:
4274:
4271:
4270:
4268:
4266:
4262:
4256:
4253:
4251:
4248:
4246:
4243:
4241:
4238:
4237:
4235:
4233:
4229:
4226:
4224:
4220:
4210:
4207:
4205:
4202:
4200:
4197:
4195:
4192:
4190:
4187:
4186:
4184:
4182:
4178:
4172:
4169:
4167:
4164:
4162:
4160:(BoxâJenkins)
4156:
4154:
4151:
4149:
4146:
4142:
4139:
4138:
4137:
4134:
4133:
4131:
4129:
4125:
4119:
4116:
4114:
4113:DurbinâWatson
4111:
4109:
4103:
4101:
4098:
4096:
4095:DickeyâFuller
4093:
4092:
4090:
4086:
4080:
4077:
4075:
4072:
4070:
4069:Cointegration
4067:
4065:
4062:
4060:
4057:
4055:
4052:
4050:
4047:
4045:
4044:Decomposition
4042:
4041:
4039:
4035:
4032:
4030:
4026:
4016:
4013:
4012:
4011:
4008:
4007:
4006:
4003:
3999:
3996:
3995:
3994:
3991:
3989:
3986:
3984:
3981:
3979:
3976:
3974:
3971:
3969:
3966:
3964:
3961:
3959:
3956:
3955:
3953:
3951:
3947:
3941:
3938:
3936:
3933:
3931:
3928:
3926:
3923:
3921:
3918:
3916:
3915:Cohen's kappa
3913:
3912:
3910:
3908:
3904:
3900:
3896:
3892:
3888:
3884:
3879:
3875:
3861:
3858:
3856:
3853:
3851:
3848:
3846:
3843:
3842:
3840:
3838:
3834:
3828:
3824:
3820:
3814:
3812:
3809:
3808:
3806:
3804:
3800:
3794:
3791:
3789:
3786:
3784:
3781:
3779:
3776:
3774:
3771:
3769:
3768:Nonparametric
3766:
3764:
3761:
3760:
3758:
3754:
3748:
3745:
3743:
3740:
3738:
3735:
3733:
3730:
3729:
3727:
3725:
3721:
3715:
3712:
3710:
3707:
3705:
3702:
3700:
3697:
3695:
3692:
3691:
3689:
3687:
3683:
3677:
3674:
3672:
3669:
3667:
3664:
3662:
3659:
3658:
3656:
3654:
3650:
3646:
3639:
3636:
3634:
3631:
3630:
3626:
3622:
3606:
3603:
3602:
3601:
3598:
3596:
3593:
3591:
3588:
3584:
3581:
3579:
3576:
3575:
3574:
3571:
3570:
3568:
3566:
3562:
3552:
3549:
3545:
3539:
3537:
3531:
3529:
3523:
3522:
3521:
3518:
3517:Nonparametric
3515:
3513:
3507:
3503:
3500:
3499:
3498:
3492:
3488:
3487:Sample median
3485:
3484:
3483:
3480:
3479:
3477:
3475:
3471:
3463:
3460:
3458:
3455:
3453:
3450:
3449:
3448:
3445:
3443:
3440:
3438:
3432:
3430:
3427:
3425:
3422:
3420:
3417:
3415:
3412:
3410:
3408:
3404:
3402:
3399:
3398:
3396:
3394:
3390:
3384:
3382:
3378:
3376:
3374:
3369:
3367:
3362:
3358:
3357:
3354:
3351:
3349:
3345:
3335:
3332:
3330:
3327:
3325:
3322:
3321:
3319:
3317:
3313:
3307:
3304:
3300:
3297:
3296:
3295:
3292:
3288:
3285:
3284:
3283:
3280:
3278:
3275:
3274:
3272:
3270:
3266:
3258:
3255:
3253:
3250:
3249:
3248:
3245:
3243:
3240:
3238:
3235:
3233:
3230:
3228:
3225:
3223:
3220:
3219:
3217:
3215:
3211:
3205:
3202:
3198:
3195:
3191:
3188:
3186:
3183:
3182:
3181:
3178:
3177:
3176:
3173:
3169:
3166:
3164:
3161:
3159:
3156:
3154:
3151:
3150:
3149:
3146:
3145:
3143:
3141:
3137:
3134:
3132:
3128:
3122:
3119:
3117:
3114:
3110:
3107:
3106:
3105:
3102:
3100:
3097:
3093:
3092:loss function
3090:
3089:
3088:
3085:
3081:
3078:
3076:
3073:
3071:
3068:
3067:
3066:
3063:
3061:
3058:
3056:
3053:
3049:
3046:
3044:
3041:
3039:
3033:
3030:
3029:
3028:
3025:
3021:
3018:
3016:
3013:
3011:
3008:
3007:
3006:
3003:
2999:
2996:
2994:
2991:
2990:
2989:
2986:
2982:
2979:
2978:
2977:
2974:
2970:
2967:
2966:
2965:
2962:
2960:
2957:
2955:
2952:
2950:
2947:
2946:
2944:
2942:
2938:
2934:
2930:
2925:
2921:
2907:
2904:
2902:
2899:
2897:
2894:
2892:
2889:
2888:
2886:
2884:
2880:
2874:
2871:
2869:
2866:
2864:
2861:
2860:
2858:
2854:
2848:
2845:
2843:
2840:
2838:
2835:
2833:
2830:
2828:
2825:
2823:
2820:
2818:
2815:
2814:
2812:
2810:
2806:
2800:
2797:
2795:
2794:Questionnaire
2792:
2790:
2787:
2783:
2780:
2778:
2775:
2774:
2773:
2770:
2769:
2767:
2765:
2761:
2755:
2752:
2750:
2747:
2745:
2742:
2740:
2737:
2735:
2732:
2730:
2727:
2725:
2722:
2720:
2717:
2716:
2714:
2712:
2708:
2704:
2700:
2695:
2691:
2677:
2674:
2672:
2669:
2667:
2664:
2662:
2659:
2657:
2654:
2652:
2649:
2647:
2644:
2642:
2639:
2637:
2634:
2632:
2629:
2627:
2624:
2622:
2621:Control chart
2619:
2617:
2614:
2612:
2609:
2607:
2604:
2603:
2601:
2599:
2595:
2589:
2586:
2582:
2579:
2577:
2574:
2573:
2572:
2569:
2567:
2564:
2562:
2559:
2558:
2556:
2554:
2550:
2544:
2541:
2539:
2536:
2534:
2531:
2530:
2528:
2524:
2518:
2515:
2514:
2512:
2510:
2506:
2494:
2491:
2489:
2486:
2484:
2481:
2480:
2479:
2476:
2474:
2471:
2470:
2468:
2466:
2462:
2456:
2453:
2451:
2448:
2446:
2443:
2441:
2438:
2436:
2433:
2431:
2428:
2426:
2423:
2422:
2420:
2418:
2414:
2408:
2405:
2403:
2400:
2396:
2393:
2391:
2388:
2386:
2383:
2381:
2378:
2376:
2373:
2371:
2368:
2366:
2363:
2361:
2358:
2356:
2353:
2351:
2348:
2347:
2346:
2343:
2342:
2340:
2338:
2334:
2331:
2329:
2325:
2321:
2317:
2312:
2308:
2302:
2299:
2297:
2294:
2293:
2290:
2286:
2279:
2274:
2272:
2267:
2265:
2260:
2259:
2256:
2249:
2246:
2245:
2235:
2231:
2228:
2224:
2221:
2217:
2216:
2211:
2208:
2204:
2201:
2197:
2194:
2190:
2187:
2183:
2180:
2176:
2174:
2170:
2167:
2164:
2160:
2157:
2153:
2150:
2146:
2143:
2139:
2138:Gabriel, K.R.
2135:
2134:
2120:
2113:
2105:
2101:
2097:
2093:
2089:
2085:
2081:
2077:
2073:
2069:
2062:
2055:
2051:
2047:
2038:
2030:
2026:
2022:
2018:
2014:
2010:
2003:
1995:
1991:
1987:
1983:
1979:
1975:
1968:
1960:
1956:
1952:
1950:0-643-09310-9
1946:
1942:
1935:
1927:
1921:
1917:
1910:
1902:
1896:
1892:
1888:
1881:
1873:
1867:
1859:
1855:
1851:
1845:
1841:
1835:
1833:
1817:
1813:
1807:
1803:
1792:
1789:
1787:
1784:
1782:
1779:
1777:
1774:
1772:
1769:
1767:
1764:
1762:
1759:
1757:
1754:
1751:
1748:
1746:
1743:
1741:
1738:
1736:
1733:
1731:
1728:
1726:
1723:
1721:
1718:
1716:
1713:
1711:
1708:
1706:
1703:
1701:
1698:
1697:
1692:
1686:
1681:
1674:
1667:
1664:
1661:
1658:
1657:
1656:
1653:
1651:
1647:
1643:
1639:
1629:
1625:
1623:
1614:
1611:
1608:
1605:
1604:
1603:
1600:
1596:
1590:
1586:
1576:
1574:
1569:
1562:
1559:
1556:
1553:
1552:
1551:
1549:
1545:
1541:
1531:
1529:
1525:
1521:
1516:
1512:
1510:
1501:
1498:
1491:
1488:
1487:
1486:
1484:
1474:
1470:
1468:
1463:
1461:
1457:
1453:
1449:
1444:
1438:
1435:
1428:
1425:
1424:
1423:
1421:
1417:
1413:
1408:
1404:
1402:
1392:
1390:
1386:
1364:
1360:
1358:
1353:
1351:
1340:
1338:
1337:no difference
1330:
1325:
1322:
1316:
1314:
1310:
1304:
1293:
1286:Related terms
1283:
1280:
1256:
1249:
1248:
1246:
1242:
1229:
1224:
1217:
1214:
1213:
1211:
1208:
1206:
1202:
1198:
1188:
1184:
1180:
1167:
1164:
1158:
1155:
1149:
1146:
1142:
1134:
1130:
1125:
1122:
1119:
1113:
1106:
1102:
1097:
1094:
1091:
1084:
1080:
1077:
1071:
1068:
1065:
1057:
1054:
1051:
1045:
1042:
1034:
1030:
1026:
1013:
1010:
1007:
1001:
998:
991:
987:
982:
979:
976:
965:
964:, we can get
963:
958:
945:
942:
938:
930:
926:
921:
918:
915:
909:
906:
902:
898:
890:
888:
883:
872:
848:
825:
806:
800:
795:
789:
785:
781:
776:
772:
768:
763:
759:
752:
749:
741:
721:
691:
681:
677:
659:
655:
646:
640:
636:
632:
631:
630:
621:
616:
612:
598:
584:
581:
578:
565:
562:
549:
537:Type I error
536:
533:
532:
516:
504:
502:
488:
485:
482:
469:
465:
428:
424:
421:
420:
382:
377:
369:
364:
354:
346:
340:Type II error
337:
328:
312:
308:
285:
281:
258:
254:
243:
227:
223:
215:, denoted by
214:
196:
192:
184:, denoted by
183:
179:
175:
171:
156:
154:
153:
146:
144:
143:
136:
134:
130:
126:
120:
118:
114:
113:type II error
109:
107:
103:
99:
95:
84:
81:
73:
63:
59:
53:
50:This article
48:
39:
38:
33:
19:
4566:
4554:
4535:
4528:
4440:Econometrics
4390: /
4373:Chemometrics
4350:Epidemiology
4343: /
4316:Applications
4158:ARIMA model
4105:Q-statistic
4054:Stationarity
3950:Multivariate
3893: /
3889: /
3887:Multivariate
3885: /
3825: /
3821: /
3595:Bayes factor
3494:Signed rank
3406:
3380:
3372:
3360:
3055:Completeness
2891:Cohort study
2789:Opinion poll
2724:Missing data
2711:Study design
2666:Scatter plot
2588:Scatter plot
2581:Spearman's Ï
2543:Grouped data
2233:
2232:Raiffa, H.,
2226:
2219:
2214:
2213:
2206:
2199:
2192:
2185:
2178:
2162:
2155:
2148:
2141:
2130:Bibliography
2118:
2112:
2071:
2067:
2061:
2053:
2049:
2042:
2037:
2012:
2008:
2002:
1977:
1973:
1967:
1940:
1934:
1915:
1909:
1886:
1880:
1839:
1819:. Retrieved
1815:
1806:
1710:Egon Pearson
1671:
1654:
1635:
1626:
1618:
1592:
1570:
1566:
1537:
1517:
1513:
1505:
1480:
1471:
1464:
1452:blood donors
1445:
1442:
1409:
1405:
1398:
1382:
1362:
1354:
1346:
1336:
1328:
1326:
1320:
1317:
1306:
1281:
1274:
1244:
1231:
1226:
1222:
1209:
1201:Egon Pearson
1197:Jerzy Neyman
1194:
1185:
1181:
1035:
1031:
1027:
966:
959:
891:
884:
882:: Ό>120.
873:
826:
742:
697:
665:
656:
652:
644:
627:
570:
542:
474:
434:hypothesis (
375:
366:
352:
343:
334:
331:Type I error
244:
167:
151:
147:
141:
137:
121:
116:
112:
110:
101:
98:type I error
97:
91:
76:
67:
51:
18:Type 1 error
4568:WikiProject
4483:Cartography
4445:Jurimetrics
4397:Reliability
4128:Time domain
4107:(LjungâBox)
4029:Time-series
3907:Categorical
3891:Time-series
3883:Categorical
3818:(Bernoulli)
3653:Correlation
3633:Correlation
3429:JarqueâBera
3401:Chi-squared
3163:M-estimator
3116:Asymptotics
3060:Sufficiency
2827:Interaction
2739:Replication
2719:Effect size
2676:Violin plot
2656:Radar chart
2636:Forest plot
2626:Correlogram
2576:Kendall's Ï
1821:14 December
1573:false alarm
1467:mammography
1448:blood tests
1446:The simple
1250:we reject H
670:or accept H
467:Not reject
4584:Categories
4435:Demography
4153:ARMA model
3958:Regression
3535:(Friedman)
3496:(Wilcoxon)
3434:Normality
3424:Lilliefors
3371:Student's
3247:Resampling
3121:Robustness
3109:divergence
3099:Efficiency
3037:(monotone)
3032:Likelihood
2949:Population
2782:Stratified
2734:Population
2553:Dependence
2509:Count data
2440:Percentile
2417:Dispersion
2350:Arithmetic
2285:Statistics
2227:Datamation
2163:Health Day
2149:Biometrika
1974:Biometrika
1900:1584884401
1798:References
1534:Biometrics
1401:Pap smears
1313:hypothesis
1290:See also:
871:should be
609:See also:
605:Error rate
432:about null
159:Definition
150:errors of
142:commission
140:errors of
129:biometrics
70:April 2019
3816:Logistic
3583:posterior
3509:Rank sum
3257:Jackknife
3252:Bootstrap
3070:Bootstrap
3005:Parameter
2954:Statistic
2749:Statistic
2661:Run chart
2646:Pie chart
2641:Histogram
2631:Fan chart
2606:Bar chart
2488:L-moments
2375:Geometric
2104:119855116
2096:0305-0041
2029:0020-269X
1994:0006-3444
1866:cite book
1858:262680588
1632:Computers
1460:hepatitis
1385:screening
1195:In 1928,
1191:Etymology
1156:−
1150:ϕ
1123:−
1095:−
1066:μ
1005:⇒
980:−
919:−
910:⩾
810:¯
725:¯
585:β
582:−
550:α
517:β
489:α
486:−
4530:Category
4223:Survival
4100:Johansen
3823:Binomial
3778:Isotonic
3365:(normal)
3010:location
2817:Blocking
2772:Sampling
2651:QâQ plot
2616:Box plot
2598:Graphics
2493:Skewness
2483:Kurtosis
2455:Variance
2385:Heronian
2380:Harmonic
2169:Archived
2054:original
1959:65216357
1677:See also
1528:stenosis
1379:Medicine
1366:â
430:Decision
152:omission
4556:Commons
4503:Kriging
4388:Process
4345:studies
4204:Wavelet
4037:General
3204:Plug-in
2998:L space
2777:Cluster
2478:Moments
2296:Outline
2076:Bibcode
1646:malware
1389:testing
962:Z-table
676:p-value
662:Example
534:Reject
115:, or a
100:, or a
56:Please
4425:Census
4015:Normal
3963:Manova
3783:Robust
3533:2-way
3525:1-way
3363:-test
3034:
2611:Biplot
2402:Median
2395:Lehmer
2337:Center
2102:
2094:
2027:
1992:
1957:
1947:
1922:
1897:
1856:
1846:
1228:false.
1168:0.0036
425:False
4595:Error
4049:Trend
3578:prior
3520:anova
3409:-test
3383:-test
3375:-test
3282:Power
3227:Pivot
3020:shape
3015:scale
2465:Shape
2445:Range
2390:Heinz
2365:Cubic
2301:Index
2100:S2CID
1309:tests
1120:121.9
1058:121.9
1014:121.9
1002:1.645
422:True
417:) is
4282:Test
3482:Sign
3334:Wald
2407:Mode
2345:Mean
2092:ISSN
2050:null
2025:ISSN
1990:ISSN
1955:OCLC
1945:ISBN
1920:ISBN
1895:ISBN
1872:link
1854:OCLC
1844:ISBN
1823:2019
1587:and
1458:and
1454:for
1414:and
1387:and
1321:this
1265:or H
1159:2.68
1114:<
1055:<
946:0.05
613:and
211:and
131:and
96:, a
3462:BIC
3457:AIC
2084:doi
2017:doi
1982:doi
1978:20A
1546:or
1456:HIV
1403:).
1237:, H
1126:125
1098:125
1072:125
983:120
922:120
835:, X
831:, X
707:, X
703:, X
678:or
168:In
92:In
60:to
4586::
2098:.
2090:.
2082:.
2072:29
2070:.
2056:).
2023:.
2013:10
2011:.
1988:.
1976:.
1953:.
1893:.
1891:54
1868:}}
1864:{{
1852:.
1831:^
1814:.
1648:,
1644:,
1640:,
1542:,
1530:.
1511:.
1485:.
1422:.
597:)
563:)
529:)
501:)
463:)
135:.
127:,
111:A
3407:G
3381:F
3373:t
3361:Z
3080:V
3075:U
2277:e
2270:t
2263:v
2215:k
2106:.
2086::
2078::
2045:0
2043:H
2031:.
2019::
1996:.
1984::
1961:.
1928:.
1903:.
1874:)
1860:.
1825:.
1494:0
1431:0
1332:0
1329:H
1277:0
1267:1
1263:A
1259:0
1252:0
1239:2
1235:1
1233:H
1165:=
1162:)
1153:(
1147:=
1143:)
1135:3
1131:2
1107:3
1103:2
1092:T
1085:(
1081:P
1078:=
1075:)
1069:=
1062:|
1052:T
1049:(
1046:=
1043:P
1011:=
1008:c
999:=
992:3
988:2
977:c
943:=
939:)
931:3
927:2
916:c
907:Z
903:(
899:P
880:1
876:0
874:H
869:1
865:0
849:3
837:3
833:2
829:1
807:X
801:=
796:3
790:3
786:X
782:+
777:2
773:X
769:+
764:1
760:X
753:=
750:T
722:X
709:3
705:2
701:1
699:X
688:0
684:0
672:0
668:0
579:1
483:1
448:0
444:H
402:0
398:H
313:0
309:H
286:1
282:H
259:0
255:H
228:1
224:H
197:0
193:H
83:)
77:(
72:)
68:(
54:.
34:.
20:)
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