False positives & False negatives (practice problem)

False positives and false negatives “False Positive“ redirects here. For other uses, see False Positive (disambiguation). 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. False positive error A false positive error, or false positive, is a result that indicates a given condition exists when it does not. For example, a pregnancy test which indicates a woman is pregnant when she is 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). False negative error 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. Problem: At the Krispie Foods factory, cookies are tested for crispness with the following results: • For cookies that are really crispy, the test says “Yes“ 90% of the time • For cookies that are not crispy, the test says “Yes“ 15% of the time (“false positive“) If 95% of all cookies are crispy, and for a randomly selected cookie the Krispie Food’s test says “Yes“, what are the chances that the cookie really is crispy? A) 85.5% B) % C) % D) 100% #bayesian #bayes #bayestheorem #falsepositive #Bayersrule #falsepositive #probability #statistics #Genetics #bayestheorem #Bayeslaw #Bayes rule Nikolay’s genetics lessons #Calculus #Education #Math #Solution #conditionalprobability #Probability #bayestheorem #BayesianInference #veritasium #bayes #probability #thomas #bayes #bayes #bayesian #inference #math #mathematics #treediagrams #venndiagrams #bayestheorem #Statistics #lawofprobability #BayesRuleFalsePositiveParadox #BayesRule #FalsePositiveParadox #Probability #Statistics #Genetics #BayesTheorem #BayesLaw #NikolaysGeneticsLessons #Calculus #Education #math #Solution #Conditional #bayes #Theorem #BayesianInference #veritasium #BayesTheorem #rule #prior #conditionProbability #thomasBayes #bayesRule #bayesian #inference #mathematics #treeDiagrams #vennDiagrams #lawOfProbability