Type I and type II errors

In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (also known as a "false positive" finding), while a type II error is incorrectly retaining a false null hypothesis (also known as a "false negative" finding).^[1] More simply stated, a type I error is to falsely infer the existence of something that is not there, while a type II error is to falsely infer the absence of something that is.

In statistical test theory, the notion of statistical error is an integral part of hypothesis testing. The test requires an unambiguous statement of a null hypothesis, which usually corresponds to a default "state of nature", for example "this person is healthy", "this accused is not guilty" or "this product is not broken". An alternative hypothesis is the negation of null hypothesis, for example, "this person is not healthy", "this accused is guilty" or "this product is broken". The result of the test may be negative, relative to the null hypothesis (not healthy, guilty, broken) or positive (healthy, not guilty, not broken). 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. Due to the statistical nature of a test, the result is never, except in very rare cases, free of error. Two types of error are distinguished: type I error and type II error.

Type I error

A type I error occurs when the null hypothesis (H₀) is true, but is rejected. It is asserting something that is absent, a false hit. A type I error may be likened to a so-called false positive (a result that indicates that a given condition is present when it actually is not present).

The type I error rate or significance level is the probability of rejecting the null hypothesis given that it is true.^[5][6] It is denoted by the Greek letter α (alpha) and is also called the alpha level. Often, the significance level is set to 0.05 (5%), implying that it is acceptable to have a 5% probability of incorrectly rejecting the null hypothesis.^[5]

Type II error

A type II error occurs when the null hypothesis is false, but erroneously fails to be rejected. It is failing to assert what is present, a miss. A type II error may be compared with a so-called false negative (where an actual 'hit' was disregarded by the test and seen as a 'miss') in a test checking for a single condition with a definitive result of true or false. A Type II error is committed when we fail to believe a true alternative hypothesis.^[7] In terms of folk tales, an investigator may fail to see the wolf ("failing to raise an alarm"). Again, H₀: no wolf.

The rate of the type II error is denoted by the Greek letter β (beta) and related to the power of a test (which equals 1−β).

Table of error types

Tabularised relations between truth/falseness of the null hypothesis and outcomes of the test:^[2]

Reference  https://en.wikipedia.org/wiki/Type_I_and_type_II_errors 

Table of error types		Null hypothesis (H0) is
		True	False
Decision About Null Hypothesis (H0)	Reject	Type I error (False Positive)	Correct inference (True Positive)
	Accept (not rejected)	Correct inference (True Negative)	Type II error (False Negative)