Type II error
A Type II error (also known as an error of the second kind) occurs when the stated null hypothesis is false, but is not rejected as false. A type II error may be explained through a false positive/false negative. A false positive, where a 'miss' took place but was marked a 'hit', is a type I error. A false negative, where a 'hit' occurred but was marked a 'miss' is a type II error. This specifically applies to a test that is checking for a single condition with a result of either true or false. In simple terms, a type II error occurs when we fail to believe a truth.
The probability of a type II error occurring is given by the Greek letter Beta (β). Often a type II error occurs because sample sizes are too small.
As an example, consider you are trying to ascertain the natural habitat of Bighorn Sheep in a certain area. The null hypothesis is: 'This area is not a Bighorn Sheep habitat.' Thus, the alternate hypothesis would be: 'This area is a Bighorn Sheep habitat.'
|Null Hypothesis True||Null Hypothesis False|
|Reject Null Hypothesis||Type I error (Not a Big Horn Sheep habitat but marked as a habitat)||Correct Decision|
|Fail to reject Null Hypothesis||Correct Decision||Type II Error (Big Horn Sheep habitat marked as not a habitat)|
Type II Error: The observer failed to see a Bighorn Sheep in a habitat area; thus failing to mark that area a part of its habitat.
- Statistics Glossary, http://www.stats.gla.ac.uk/steps/glossary/hypothesis_testing.html#2err