What is the motivation of introducing an additional level of indirection from the descriptive 'false positive' to the integer '1'? Is 'false positive' really too long?
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13$\begingroup$ I'm with you, it's an awful name. I take every opportunity to not use it. $\endgroup$– Matthew DruryJun 20, 2018 at 13:49
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7$\begingroup$ Same. I could never remember which was which, until I heard this incredibly helpful way to tell them apart... In the story The Boy Who Cried Wolf, the villagers first make a type 1 error, and the second time make a type 2 error. $\endgroup$– samJun 20, 2018 at 22:49
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1$\begingroup$ @Sam I remember them as in "The first thing a researcher does after discovering an effect is publish." But on the right pane there is a link to a question with 84 upvotes on how to remember them. $\endgroup$– VoracJun 21, 2018 at 8:13
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$\begingroup$ I always find 'false positive' and 'false negative' very confusing. In medicine 'positive' refers to 'having the condition' (which is already confusing and source of many jokes) but what kind of (statistical) test is used to determine you got the condition? Is positive, having the condition, equal to a rejected $H_0$ testing for healthiness (e.g. tests for healthy levels of some component, e.g. iron in the blood), or is it equal to a non-rejected $H_0$ testing for sickness (e.g. tests for markers that indicate the disease, condition, or something else like pregnancy)? $\endgroup$– Sextus EmpiricusJun 28, 2018 at 8:35
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Great question, motivated me to Google it :) Per Wikipedia (with minor formatting edits):
A type I error (or error of the first kind) is the incorrect rejection of a true null hypothesis.
A type II error (or error of the second kind) is the failure to reject a false null hypothesis.
Further down the page it discusses the etymology:
In 1928, Jerzy Neyman (1894–1981) and Egon Pearson (1895–1980), both eminent statisticians, discussed the problems associated with "deciding whether or not a particular sample may be judged as likely to have been randomly drawn from a certain population" ...
"...in testing hypotheses two considerations must be kept in view, (1) we must be able to reduce the chance of rejecting a true hypothesis to as low a value as desired; (2) the test must be so devised that it will reject the hypothesis tested when it is likely to be false."
They also noted that, in deciding whether to fail to reject, or reject a particular hypothesis amongst a "set of alternative hypotheses", $H_1$, $H_2$, . . ., it was easy to make an error:
"...[and] these errors will be of two kinds:
(I) we reject $H_0$ [i.e., the hypothesis to be tested] when it is true (II) we fail to reject $H_0$ when some alternative hypothesis $H_A$ or $H_1$ is true." In the same paper they call these two sources of error, errors of type I and errors of type II respectively.
So it looks like the first type of error was based on Fisher's original work on significance testing. The second type of error was based on Neyman and Pearson's extension of Fisher's work, namely the introduction of the alternative hypothesis and hence hypothesis testing. See here for more detail.
It appears that the order in which these types of errors were identified correspond to their number, as given by Neyman and Pearson.
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1$\begingroup$ Historical reasons - unsurprising. Just like R's
<-and C++'s text substitution macros. Thank you for replying to my poorly researched question. And thanks to @gung for the nice question edit. $\endgroup$– VoracJun 20, 2018 at 15:39 -
3$\begingroup$ Wasn't "the order in which they thought about it" strongly influenced by the prior work of Fisher though? i.e. until Neyman and Pearson introduced the idea of an alternate hypothesis there was only one "type" of error (rejecting H_0 when it is true). Along with H_A comes the possibility of an error "of the second type". $\endgroup$ Jun 20, 2018 at 18:35
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$\begingroup$ One small point which might be good to add is that the 1928 article "On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference" does not yet define the different sources of error as 'type I' and 'type II' errors (instead is does speak of ordered type when relating to Pearson distribution's). It is in 1933 that Neyman and Pearson defined it as type I and type II. $\endgroup$ Jun 28, 2018 at 8:17
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$\begingroup$ It would be also good to straighten the quote with correct references. Or at least the first quote "...in testing hypotheses two considerations..." is not literally from the 1928 article. $\endgroup$ Jun 28, 2018 at 8:19