Early ITU Model

Sensitivity and specificity are statistical measures of the performance of a binary classification test, also known in statistics as classification function. Sensitivity (also called the true positive rate, or the recall rate in some fields) measures the proportion of actual positives which are correctly identified as such (e.g. the percentage of sick people who are correctly identified as having the condition). Specificity (sometimes called the true negative rate) measures the proportion of negatives which are correctly identified as such (e.g. the percentage of healthy people who are correctly identified as not having the condition). These two measures are closely related to the concepts of type I and type II errors. A perfect predictor would be described as 100% sensitive (i.e. predicting all people from the sick group as sick) and 100% specific (i.e. not predicting anyone from the healthy group as sick); however, theoretically any predictor will possess a minimum error bound known as the Bayes error rate.

For any test, there is usually a trade-off between the measures. For example: in an airport security setting in which one is testing for potential threats to safety, scanners may be set to trigger on low-risk items like belt buckles and keys (low specificity), in order to reduce the risk of missing objects that do pose a threat to the aircraft and those aboard (high sensitivity). This trade-off can be represented graphically as a receiver operating characteristic curve.

Definitions

Terminology and derivations
from a confusion matrix

true positive (TP) eqv. with hit true negative (TN) eqv. with correct rejection false positive (FP) eqv. with false alarm, Type I error false negative (FN) eqv. with miss, Type II error sensitivity or true positive rate (TPR) eqv. with hit rate, recall ${\mathit {TPR}}={\mathit {TP}}/P={\mathit {TP}}/({\mathit {TP}}+{\mathit {FN}})$ specificity (SPC) or True Negative Rate ${\mathit {SPC}}={\mathit {TN}}/N={\mathit {TN}}/({\mathit {FP}}+{\mathit {TN}})$ precision or positive predictive value (PPV) ${\mathit {PPV}}={\mathit {TP}}/({\mathit {TP}}+{\mathit {FP}})$ negative predictive value (NPV) ${\mathit {NPV}}={\mathit {TN}}/({\mathit {TN}}+{\mathit {FN}})$ fall-out or false positive rate (FPR) ${\mathit {FPR}}={\mathit {FP}}/N={\mathit {FP}}/({\mathit {FP}}+{\mathit {TN}})=1-{\mathit {SPC}}$ false discovery rate (FDR) ${\mathit {FDR}}={\mathit {FP}}/({\mathit {TP}}+{\mathit {FP}})=1-{\mathit {PPV}}$ accuracy (ACC) ${\mathit {ACC}}=({\mathit {TP}}+{\mathit {TN}})/(P+N)$ F1 score is the harmonic mean of precision and sensitivity ${\mathit {F1}}=2{\mathit {TP}}/(2{\mathit {TP}}+{\mathit {FP}}+{\mathit {FN}})$ Matthews correlation coefficient (MCC) ${\frac {TP\times TN-FP\times FN}{\sqrt {(TP+FP)(TP+FN)(TN+FP)(TN+FN)}}}$ Source: Fawcett (2006).

Imagine a study evaluating a new test that screens people for a disease. Each person taking the test either has or does not have the disease. The test outcome can be positive (predicting that the person has the disease) or negative (predicting that the person does not have the disease). The test results for each subject may or may not match the subject's actual status. In that setting:

• True positive: Sick people correctly diagnosed as sick
• False positive: Healthy people incorrectly identified as sick
• True negative: Healthy people correctly identified as healthy
• False negative: Sick people incorrectly identified as healthy

In general, Positive = identified and negative = rejected. Therefore:

• True positive = correctly identified
• False positive = incorrectly identified
• True negative = correctly rejected
• False negative = incorrectly rejected

Let us define an experiment from P positive instances and N negative instances for some condition. The four outcomes can be formulated in a 2×2 contingency table or confusion matrix, as follows:

Sensitivity

Sensitivity relates to the test's ability to identify positive results.

The sensitivity of a test is the proportion of people that are known to have the disease who test positive for it. This can also be written as:

${\begin{aligned}{\text{sensitivity}}&={\frac {\text{number of true positives}}{{\text{number of true positives}}+{\text{number of false negatives}}}}\\\\&={\frac {\text{number of true positives}}{\text{total number of sick individuals in population}}}\\\\&={\text{probability of a positive test, given that the patient is ill}}\end{aligned}}$

Again, consider the example of the medical test used to identify a disease. A 'bogus' test kit that always indicates positive regardless of the disease status of the patient will achieve, from a theoretical point of view, 100% sensitivity. This is because in this case there are no negatives at all, and false positives are not accounted for in the definition of sensitivity. Therefore, sensitivity alone cannot be used to determine whether a test is useful in practice.

However, a test with high sensitivity can be considered as a reliable indicator when its result is negative, since it rarely misses true positives among those who are actually positive. For example, a sensitivity of 100% means that the test recognizes all actual positives – i.e. all sick people are recognized as being ill. Thus, in contrast to a high specificity test, negative results in a high sensitivity test are used to rule out the disease.

Sensitivity is not the same as the precision or positive predictive value (ratio of true positives to combined true and false positives), which is as much a statement about the proportion of actual positives in the population being tested as it is about the test.

The calculation of sensitivity does not take into account indeterminate test results. If a test cannot be repeated, indeterminate samples either should be excluded from the analysis (the number of exclusions should be stated when quoting sensitivity) or can be treated as false negatives (which gives the worst-case value for sensitivity and may therefore underestimate it).

A test with a high sensitivity has a low type II error rate. In non-medical contexts, sensitivity is sometimes called recall.

Specificity

Specificity relates to the test's ability to identify negative results.

Consider the example of the medical test used to identify a disease. The specificity of a test is defined as the proportion of patients that are known not to have the disease who will test negative for it. This can also be written as:

${\begin{aligned}{\text{specificity}}&={\frac {\text{number of true negatives}}{{\text{number of true negatives}}+{\text{number of false positives}}}}\\\\&={\frac {\text{number of true negatives}}{\text{total number of well individuals in population}}}\\\\&={\text{probability of a negative test given that the patient is well}}\end{aligned}}$

From a theoretical point of view, a 'bogus' test kit which always indicates negative regardless of the disease status of the patient, will achieve 100% specificity, since there are no positive results and false negatives are not accounted for by definition.

However, highly specific tests rarely miss negative outcomes, so they can be considered reliable when their result is positive. Therefore, a positive result from a test with high specificity means a high probability of the presence of disease.

A test with a high specificity has a low type I error rate.

Graphical illustration

• 

  High sensitivity and low specificity

• 

  Low sensitivity and high specificity

Medical examples

In medical diagnostics, test sensitivity is the ability of a test to correctly identify those with the disease (true positive rate), whereas test specificity is the ability of the test to correctly identify those without the disease (true negative rate). If 100 patients known to have a disease were tested, and 43 test positive, then the test has 43% sensitivity. If 100 with no disease are tested and 96 return a negative result, then the test has 96% specificity. Sensitivity and specificity are prevalence-independent test characteristics, as their values are intrinsic to the test and do not depend on the disease prevalence in the population of interest. Positive and negative predictive values, but not sensitivity or specificity, are values influenced by the prevalence of disease in the population that is being tested.

Misconceptions

It is often claimed that a highly specific test is effective at ruling in a disease when positive, while a highly sensitive test is deemed effective at ruling out a disease when negative. This has led to the widely used mnemonics SPIN and SNOUT, according to which a highly SPecific test, when Positive, rules IN disease (SP-P-IN), and a highly 'SeNsitive' test, when Negative rules OUT disease (SN-N-OUT). Both rules of thumb are, howevever, inferentially misleading, as the diagnostic power of any test is determined by both the sensitivity and specificity.

Sensitivity_index

The sensitivity index or d' (pronounced 'dee-prime') is a statistic used in signal detection theory. It provides the separation between the means of the signal and the noise distributions, compared against the standard deviation of the noise distribution. For normally distributed signal and noise with mean and standard deviations $\mu _{S}$ and $\sigma _{S}$, and $\mu _{N}$ and $\sigma _{N}$, respectively, d' is defined as:

$d'={\frac {\mu _{S}-\mu _{N}}{\sqrt {{\frac {1}{2}}(\sigma _{S}^{2}+\sigma _{N}^{2})}}}$

An estimate of d' can be also found from measurements of the hit rate and false-alarm rate. It is calculated as:

d' = Z(hit rate) - Z(false alarm rate),

where function Z(p), p ∈ [0,1], is the inverse of the cumulative Gaussian distribution.

d' is a dimensionless statistic. A higher d' indicates that the signal can be more readily detected.

Estimation of errors in quoted sensitivity or specificity

Sensitivity and specificity values alone may be highly misleading. The 'worst-case' sensitivity or specificity must be calculated in order to avoid reliance on experiments with few results. For example, a particular test may easily show 100% sensitivity if tested against the gold standard four times, but a single additional test against the gold standard that gave a poor result would imply a sensitivity of only 80%. A common way to do this is to state the binomial proportion confidence interval, often calculated using a Wilson score interval.

Confidence intervals for sensitivity and specificity can be calculated, giving the range of values within which the correct value lies at a given confidence level (e.g. 95%).

Terminology in information retrieval

In information retrieval, the positive predictive value is called precision, and sensitivity is called recall.

The F-score can be used as a single measure of performance of the test. The F-score is the harmonic mean of precision and recall:

$F=2\times {\frac {{\text{precision}}\times {\text{recall}}}{{\text{precision}}+{\text{recall}}}}$

In the traditional language of statistical hypothesis testing, the sensitivity of a test is called the statistical power of the test, although the word power in that context has a more general usage that is not applicable in the present context. A sensitive test will have fewer Type II errors.

References

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Further reading

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  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
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  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

External links

• Vassar College's Sensitivity/Specificity Calculator