Type I and type II errors

In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (a "false positive"), while a type II error is the failure to reject a false null hypothesis (a "false negative"). More simply stated, a type I error is detecting an effect that is not present, while a type II error is failing to detect an effect that is present. The terms "type I error" and "type II error" are often used interchangeably with the general notion of false positives and false negatives in binary classification, such as medical testing, but narrowly speaking refer specifically to statistical hypothesis testing in the Neyman–Pearson framework, as discussed in this article.

Definition

In statistics, a null hypothesis is a statement that one seeks to nullify with evidence to the contrary. Most commonly it is a statement that the phenomenon being studied produces no effect or makes no difference. An example of a null hypothesis is the statement "This diet has no effect on people's weight." Usually an experimenter frames a null hypothesis with the intent of rejecting it: that is, intending to run an experiment which produces data that shows that the phenomenon under study does make a difference. In some cases there is a specific alternative hypothesis that is opposed to the null hypothesis, in other cases the alternative hypothesis is not explicitly stated, or is simply "the null hypothesis is false" – in either event this is a binary judgment, but the interpretation differs and is a matter of significant dispute in statistics.

False positives and false negatives

In medical testing, and more generally in binary classification, a false positive is an error in data reporting in which a test result improperly indicates presence of a condition, such as a disease (the result is positive), when in reality it is not, while a false negative is an error in which a test result improperly indicates no presence of a condition (the result is negative), when in reality it is present. These are the two kinds of errors in a binary test (and are contrasted with a correct result, either a true positive or a true negative.) They are also known in medicine as a false positive (respectively negative) diagnosis, and in statistical classification as a false positive (respectively 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 (How I Met Your Mother)

"False Positive" is the 12th episode of the sixth season of the CBS sitcom How I Met Your Mother, and the 124th episode overall. It aired on December 13, 2010. It features guest star Alex Trebek.

Plot

Ted is outside a movie theater showing It's a Wonderful Life, waiting for the rest of the gang and carrying a gingerbread house as their Christmas-themed movie snack. Future Ted backtracks to two days before, when Marshall and Lily eagerly await the results of her latest pregnancy test. The test is positive and they tell Ted, Barney, and Robin the news, but the doctor later says it's a false alarm and Future Ted tells the story of what happened while the gang thought Lily was pregnant.

Prior to the test, Ted and Punchy begin talking about Punchy's wedding. After hanging up, Ted argues with Robin about his ability to be an effective best man, especially in the event that Punchy gets cold feet. Robin reveals that she auditioned as a "currency rotation specialist" (coin-flip bimbo) in the game show Million Dollar Heads or Tails, hosted by Alex Trebek. Ted rebukes her for bailing on her New Year's Resolution to be working for the Worldwide News Network by the end of the year. Robin admits that she applied for the Network, but only an associate researcher position is available. When Marshall and Lily break the news of the pregnancy, Robin becomes aware of how her own life is stalling, and resolves to take the research position, but when they reveal the false positive, she changes her mind once more, deciding that she is content to be a "coin-flip bimbo".