Consequences
Both types of errors are problems for individuals, corporations, and data analysis. A false positive (with null hypothesis of health) in medicine causes unnecessary worry or treatment, while a false negative gives the patient the dangerous illusion of good health and the patient might not get an available treatment. A false positive in manufacturing quality control (with a null hypothesis of a product being well made) discards a product that is actually well made, while a false negative stamps a broken product as operational. A false positive (with null hypothesis of no effect) in scientific research suggest an effect that is not actually there, while a false negative fails to detect an effect that is there.
Based on the real-life consequences of an error, one type may be more serious than the other. For example, NASA engineers would prefer to waste some money and throw out an electronic circuit that is really fine (null hypothesis H0: not broken; reality: not broken; action: thrown out; error: type I, false positive) than to use one on a spacecraft that is actually broken and throw out less (null hypothesis H0: not broken; reality: broken; action: use it; error: type II, false negative). In that situation a type I error uses more money but increase mission safety, but a type II error would risk the entire mission whilst saving some money.
On the other hand, criminal courts set a high bar for proof and procedure and sometimes acquit someone who is guilty (null hypothesis: innocent; reality: guilty; test find: not guilty; action: acquit; error: type II, false negative) rather than convict someone who is innocent (null hypothesis: innocent; reality: not guilty; test find: guilty; action: convict; error: type I, false positive). In totalitarian states, the opposite may occur, with the preference to jail someone innocent, rather than allow an actual dissident to roam free. Each system makes its own choice regarding where to draw the line.
Minimizing errors of decision is not a simple issue; for any given sample size the effort to reduce one type of error generally results in increasing the other type of error. The only way to minimize both types of error, without just improving the test, is to increase the sample size, and this may not be feasible.
Read more about this topic: Type I And Type II Errors
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