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Wilmington, North Carolina once had a thriving Black middle class and an elected interracial government. In 1898 white supremacists used violence to overthrow that government, kill Black residents and drive many others from the city.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
) within the green area ( ) represent false positives (negative samples that were classified as positive). Conversely, the green circle (
) within the pink area ( ) represents false negatives (positive samples that were classified as negative).A false positive is an error in binary classification in which a test result incorrectly indicates the presence of a condition (such as a disease when the disease is not present), while a false negative is the opposite error, where the test result incorrectly indicates the absence of a condition when it is actually present. These are the two kinds of errors in a binary test, in contrast to the two kinds of correct result (a true positive and a true negative). They are also known in medicine as a false positive (or false negative) diagnosis, and in statistical classification as a false positive (or false negative) error.[1]
In statistical hypothesis testing, the analogous concepts are known as type I and type II errors, where a positive result corresponds to rejecting the null hypothesis, and a negative result corresponds to not rejecting the null hypothesis. The terms are often used interchangeably, but there are differences in detail and interpretation due to the differences between medical testing and statistical hypothesis testing.
A false positive error, or false positive, is a result that indicates a given condition exists when it objectively does not. For example, a pregnancy test which indicates someone is pregnant when they are not, or the conviction of an innocent person.
A false positive error is a type I error where the test is checking a single condition, and wrongly gives an affirmative (positive) decision. However it is important to distinguish between the type 1 error rate and the probability of a positive result being false. The latter is known as the false positive risk (see Ambiguity in the definition of false positive rate, below).[2]
A false negative error, or false negative, is a test result which wrongly indicates that a condition does not hold. For example, when a pregnancy test indicates a woman is not pregnant, but she is, or when a person guilty of a crime is acquitted, these are false negatives. The condition "the woman is pregnant", or "the person is guilty" holds, but the test (the pregnancy test or the trial in a court of law) fails to realize this condition, and wrongly decides that the person is not pregnant or not guilty.
A false negative error is a type II error occurring in a test where a single condition is checked for, and the result of the test is erroneous, that the condition is absent.[3]
The false positive rate (FPR) is the proportion of all negatives that still yield positive test outcomes, i.e., the conditional probability of a positive test result given an event that was not present.
The false positive rate is equal to the significance level. The specificity of the test is equal to 1 minus the false positive rate.
In statistical hypothesis testing, this fraction is given the Greek letter α, and 1 − α is defined as the specificity of the test. Increasing the specificity of the test lowers the probability of type I errors, but may raise the probability of type II errors (false negatives that reject the alternative hypothesis when it is true).[a]
Complementarily, the false negative rate (FNR) is the proportion of positives which yield negative test outcomes with the test, i.e., the conditional probability of a negative test result given that the condition being looked for is present.
In statistical hypothesis testing, this fraction is given the letter β. The "power" (or the "sensitivity") of the test is equal to 1 − β.
The term false discovery rate (FDR) was used by Colquhoun (2014)[4] to mean the probability that a "significant" result was a false positive. Later Colquhoun (2017)[2] used the term false positive risk (FPR) for the same quantity, to avoid confusion with the term FDR as used by people who work on multiple comparisons. Corrections for multiple comparisons aim only to correct the type I error rate, so the result is a (corrected) p-value. Thus they are susceptible to the same misinterpretation as any other p-value. The false positive risk is always higher, often much higher, than the p-value.[4][2]
Confusion of these two ideas, the error of the transposed conditional, has caused much mischief.[5] Because of the ambiguity of notation in this field, it is essential to look at the definition in every paper. The hazards of reliance on p-values was emphasized in Colquhoun (2017)[2] by pointing out that even an observation of p = 0.001 was not necessarily strong evidence against the null hypothesis. Despite the fact that the likelihood ratio in favor of the alternative hypothesis over the null is close to 100, if the hypothesis was implausible, with a prior probability of a real effect being 0.1, even the observation of p = 0.001 would have a false positive rate of 8 percent. It wouldn't even reach the 5 percent level. As a consequence, it has been recommended[2][6] that every p-value should be accompanied by the prior probability of there being a real effect that it would be necessary to assume in order to achieve a false positive risk of 5%. For example, if we observe p = 0.05 in a single experiment, we would have to be 87% certain that there as a real effect before the experiment was done to achieve a false positive risk of 5%.
The article "Receiver operating characteristic" discusses parameters in statistical signal processing based on ratios of errors of various types.
Source: Wikipedia. Article content is retrieved live through the MediaWiki API.
Negative testing is a method of testing an application or system to improve the likelihood that an application works as intended/specified and can handle unexpected input and user behavior. Invalid data is inserted to compare the output against the given input. Negative testing is also known as failure testing or error path testing. When performing negative testing exceptions are expected. This shows that the application is able to handle improper user behavior. Users input values that do not work in the system to test its ability to handle incorrect values or system failure.
A negative test can relate to: Negative diagnostic test, a medical test in which the target parameter that was evaluated was not present Negative test variation, a software stress test designed to determine the response of the system outside of normal parameters Negative testing
In medicine, statistics, and epidemiology, sensitivity and specificity mathematically describe the accuracy of a test that reports the presence or absence of a medical condition. If individuals who have the condition are considered "positive" and those who do not are considered "negative", then sensitivity is a measure of how well a test can identify true positives and specificity is a measure of how well a test can identify true negatives: Sensitivity (true-positive ratio) is the probability of a positive test result, conditioned on the individual truly being positive. Specificity (true-negative ratio) is the probability of a negative test result, conditioned on the individual truly being negative. If the true status of the condition has been difficult to determine without testing, but the existing test is invasive, costly, or otherwise difficult to access, a candidate test’s sensitivity and specificity can be defined relative to a "gold standard test" that is assumed to always produce the truly correct outcome. In all testing, in both medical diagnosis and screening, there is usually a trade-off between sensitivity and specificity: higher sensitivity usually means lower specificity, and vice versa. A test that reliably detects the presence of a condition, resulting in a high number of true positives and a low number of false negatives, will have high sensitivity. This is especially important when the consequences of failing to treat the condition are serious and/or the treatment is highly effective with minimal side effects. A test that reliably excludes individuals who do not have the condition, resulting in many true negatives and few false positives, will have high specificity. This is especially important when people who are identified as having a condition may be subjected to more testing, expense, stigma, anxiety, etc. American biostatistician Jacob Yerushalmy introduced the terms "sensitivity" and "specificity" in 1947. There are different definitions within laboratory quality control, wherein "analytical sensitivity" is defined as the smallest amount of substance in a sample that can accurately be measured by an assay (synonymously to detection limit), and "analytical specificity" is defined as the ability of an assay to measure one particular organism or substance, rather than others. However, this article deals with diagnostic sensitivity and specificity as defined above.
A false positive is an error in binary classification in which a test result incorrectly indicates the presence of a condition (such as a disease when the disease is not present), while a false negative is the opposite error, where the test result incorrectly indicates the absence of a condition when it is actually present. These are the two kinds of errors in a binary test, in contrast to the two kinds of correct result (a true positive and a true negative). They are also known in medicine as a false positive (or false negative) diagnosis, and in statistical classification as a false positive (or false negative) error. In statistical hypothesis testing, the analogous concepts are known as type I and type II errors, where a positive result corresponds to rejecting the null hypothesis, and a negative result corresponds to not rejecting the null hypothesis. The terms are often used interchangeably, but there are differences in detail and interpretation due to the differences between medical testing and statistical hypothesis testing.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Joe Louis.