# Differences Between Sensitivity, Specificity, False positive, False negative

In many domains, including medicine, statistics, and machine learning, it is vital to comprehend the complexities of diagnostic tests and their outcomes. There are four key principles that come into play when assessing a diagnostic test’s efficacy: sensitivity, specificity, false positives, and false negatives. Confusion and incorrect interpretation of test results can result from the casual usage of these terms interchangeably. To better understand the accuracy and reliability of diagnostic tests, this article will look into the distinctions between sensitivity, specificity, false positives, and false negatives. Readers will be better able to evaluate test results, make educated judgments, and recognize the benefits and drawbacks of different diagnostic techniques if they have a firm grasp of these ideas.

## What is Sensitivity?

• Sensitivity is a concept that is fundamental to diagnostic testing. It measures a test’s ability to accurately identify individuals with a specific condition or attribute. It quantifies the proportions of true positives, or individuals with the condition that are correctly identified as positive, among all the people who have the condition.
• Mathematically speaking, sensitivity can be calculated by multiplying the number of positives by the total of positives and negatives. The result is then multiplied by 100 in order to convert it into a percentage. A high sensitivity means that the test is accurate in detecting the condition for most people who have it.
• Consider, for example, a medical test that is designed to detect a specific disease. If the sensitivity is 95%, the test will correctly detect 95 out of 100 people who have the disease. The remaining 5% are false negatives. This means that the test did not detect the disease for a small number of people who were actually infected.
• Sensitivity can be a critical measure, particularly in situations where a missed positive case could have serious consequences. For example, in medical screenings and disease diagnosis. It is important to note that high sensitivity doesn’t guarantee the absence false positives or negatives. These aspects are evaluated separately by specificity and other factors.

## What is Specificity?

• The concept of specificity is a crucial aspect of diagnostic testing that serves to complement the notion of sensitivity. Sensitivity and specificity are two important parameters used to evaluate the performance of a diagnostic test. Sensitivity refers to the proportion of individuals with a particular condition who are correctly identified by the test, while specificity refers to the proportion of individuals without the condition who are correctly identified as negative by the test, also known as true negatives.
• The concept of specificity pertains to the ratio of individuals who are correctly identified as negative for a particular condition, i.e., true negatives, to the total number of individuals who do not have the condition. The computation involves the division of the count of true negatives by the sum of true negatives and false positives, followed by multiplication of the quotient by 100 to denote the value as a percentage. A high level of specificity denotes a low incidence of false positives in the test, implying its precision in identifying individuals without the ailment.
• For the purpose of illustration, let us contemplate the aforementioned medical examination for a particular ailment. When the specificity of a test is 90%, it indicates that the test has the ability to accurately detect 90% of individuals who are not afflicted with the disease, out of a total of 100 individuals. The residual 10% denotes instances of false positives, wherein the test erroneously detects a minor fraction of individuals as afflicted with the ailment despite their being in good health.
• The attribute of specificity holds significant importance in scenarios where a positive outcome that is erroneous can result in superfluous treatments, interventions, or psychological distress for individuals who are, in reality, free of the disease. The comprehensive evaluation of a diagnostic test’s accuracy and reliability can be obtained by assessing both sensitivity and specificity simultaneously.
• It is noteworthy that sensitivity and specificity frequently exhibit an inverse relationship, whereby enhancing one metric may result in a decline in the other. The optimal balance between the two measures is contingent upon the particular context and objectives of the diagnostic examination.

## Sensitivity vs Specificity mnemonic

To help remember the difference between sensitivity and specificity, you can use the mnemonic “SnNOut” for sensitivity and “SpPin” for specificity.

1. SnNOut: Sensitivity rules out the condition.
• “Sn” stands for Sensitivity.
• “NOut” reminds you that a negative result on a sensitive test rules out the condition.
• Sensitivity focuses on minimizing false negatives, ensuring that individuals with the condition are not missed by the test.
2. SpPin: Specificity pins down the diagnosis.
• “Sp” stands for Specificity.
• “Pin” signifies that a positive result on a specific test pins down the diagnosis.
• Specificity aims to minimize false positives, ensuring that individuals without the condition are not mistakenly identified as positive.

By associating the terms “SnNOut” and “SpPin” with their respective meanings, you can quickly recall which measure relates to ruling out the condition (sensitivity) and which one relates to confirming the diagnosis (specificity).

## What is False positive and False negative?

Diagnostic testing mistakes or inaccuracies are referred to as false positive and false negative. They reflect circumstances in which the test findings do not match the real state or characteristic of the person being examined.

• False Positive: A false positive happens when a diagnostic test mistakenly declares that a person has a certain ailment or quality when, in fact, they do not. In other words, even though the test result is positive and shows that the condition is present, it is only a misleading sign. False positives may result in unneeded therapies, follow-up exams, or worry and anxiety for the patient.
• False Negative: On the other hand, a false negative happens when a diagnostic test fails to recognize a person as having a certain ailment or quality even if they do. In this instance, the test result is negative, indicating that the condition is not present, yet this is an incorrect conclusion. False negative results can be troublesome since they could lead to missed diagnoses, put off treatments, or give the patient a false feeling of security.

Diagnostic testing can suffer from false positives and false negatives, which can affect the test’s precision and dependability. Although sensitivity and specificity should be balanced, there is frequently a trade-off between the two in actual use. To correctly understand test findings and make choices on them, it is important to comprehend false positives and false negatives.

## Sensitivity and specificityExamples

To further comprehend sensitivity and specificity in the context of a disease test, let’s look at an example.

Let’s say there is a diagnostic procedure that can identify a certain virus in a patient. Positive or negative test findings might be classed.

1. Sensitivity:

• Sensitivity gauges how well a test can identify people who actually have the virus (true positives).
• Assume that the test properly identifies 90 of the 100 people who actually have the virus as positive (true positives) out of the 100 total. False negatives are those 10 people who were mistakenly categorized as negative.
• It is possible to calculate sensitivity as follows:
• True Positives / (True Positives + False Negatives) * 100 is the formula for sensitivity.
• Sensitivity is equal to (90/(90+10)) * 100 = 90%

The test’s sensitivity in this instance is 90%. This indicates that in 90% of those who genuinely have the virus, the test correctly identifies it. The 10% of false negatives are instances where people who do have the virus go undetected by the test.

2. Specificity:

• The ability of a test to correctly identify people who do not have the virus (true negatives) is known as specificity.
• Let’s say the test accurately detects 80 of the 100 people who are actually virus-free as negative (true negatives). 20 people who don’t have the virus are mistakenly labeled as positives (false positives), nonetheless.
• One way to determine specificity is as follows:
• (True Negatives / (True Negatives + False Positives)) * 100 is the formula for specificity.
• Specificity is equal to (80/(80 + 20)). * 100 = 80%

The test’s specificity in this instance is 80%. It implies that 80% of people who are virus-free are correctly classified as negative by the test. The 20% of false positives are instances where the test falsely indicates that those who are virus-free actually have the virus.

Achieving high numbers for both sensitivity and specificity might be difficult because they are independent of one another. In order to accurately assess the overall effectiveness of a diagnostic test, these metrics must be balanced.

Test Results for a Diagnostic Test

## Tabulated Results

In this example, let’s calculate sensitivity and specificity based on the provided test results:

1. Sensitivity:
• Sensitivity = (True Positives / (True Positives + False Negatives)) * 100
• Sensitivity = (90 / (90 + 10)) * 100 = 90%
2. Specificity:
• Specificity = (True Negatives / (True Negatives + False Positives)) * 100
• Specificity = (80 / (80 + 20)) * 100 = 80%

So, in this case, the sensitivity of the test is 90%, indicating that it correctly identifies 90% of individuals who actually have the condition. The specificity of the test is 80%, indicating that it correctly identifies 80% of individuals who do not have the condition.

These tabulated results provide a clear overview of the true positives, false positives, false negatives, and true negatives, allowing for the calculation of sensitivity and specificity to assess the performance of the diagnostic test.

## Positive Predictive Value (PPV) and Negative Predictive Value (NPV)

Positive Predictive Value (PPV) and Negative Predictive Value (NPV) are additional measures used to assess the reliability of a diagnostic test. They provide insights into the probability that a positive or negative test result is truly indicative of the presence or absence of a condition, respectively, within a given population.

1. Positive Predictive Value (PPV):
• PPV represents the proportion of individuals with a positive test result who truly have the condition or attribute being tested.
• It helps answer the question: “Given a positive test result, how likely is it that the individual actually has the condition?”
• PPV can be calculated as follows: PPV = (True Positives / (True Positives + False Positives)) * 100
2. Negative Predictive Value (NPV):
• NPV represents the proportion of individuals with a negative test result who are truly free of the condition or attribute being tested.
• It helps answer the question: “Given a negative test result, how likely is it that the individual is actually free of the condition?”
• NPV can be calculated as follows: NPV = (True Negatives / (True Negatives + False Negatives)) * 100

Both PPV and NPV are influenced by factors such as the prevalence of the condition in the tested population and the accuracy of the test itself. It’s important to note that PPV and NPV are dependent on the sensitivity and specificity of the test, as well as the prevalence of the condition being tested for.

These values are useful in clinical decision-making, as they provide an estimate of the probability that a positive or negative test result is accurate and can guide the next steps, such as further diagnostic procedures or treatments.

By considering sensitivity, specificity, PPV, and NPV together, a more comprehensive understanding of the performance and utility of a diagnostic test can be gained.

## Calculation

Positive Predictive Value (PPV) is calculated by dividing the number of true positives by the sum of true positives and false positives. Alternatively, it can be calculated by dividing the number of true positives by the total number of positive results. In the provided table, we can determine the PPV as follows: PPV = 480 / (480 + 15) = 0.97… or 97%.

Negative Predictive Value (NPV) is calculated by dividing the number of true negatives by the sum of true negatives and false negatives. Alternatively, it can be calculated by dividing the number of true negatives by the total number of negative results. Using the given table, we can calculate the NPV as follows: NPV = 100 / (100 + 5) = 0.95… or 95%.

Therefore, if a test yields a positive result, there is a 97% chance that it is correct, and if the result is negative, there is a 95% chance it is correct. It’s important to note that the opposite values of PPV and NPV are False Discovery Rate (FPV) for PPV and False Omission Rate (FOR) for NPV.