Type I and Type II Errors

The Pregnancy Test Example H0: You are not pregnant. HA: You ARE pregnant. The test can be ACCURATE, and say that: 1) you’re pregnant when you actually are, OR 2) you’re not pregnant when you actually AREN’T Or it can be INACCURATE, and say that: 3) you’re pregnant when you’re NOT (a FALSE ALARM), OR 4) you’re not pregnant when you actually ARE…. (a FAILURE TO DETECT) Reality What the Pregnancy Test Said H0 True (Really Are Pregnant) H0 False (Really NOT pregnant) POS (Reject H0) NEG (Fail to Reject H0) (Really ARE pregnant)

Consequences of Pregnancy Test Errors Type I Error – The test raised a false alarm and got you either very worried or excited. You may have already run to the store to buy baby supplies, incurring unnecessary costs. You may have spent days or weeks panicking until you realized that the test was faulty. Type II Error - The test failed to detect your pregnancy and you didn’t stop drinking or smoking, therefore potentially harming a life. You didn’t seek prenatal medical attention. In a case like this, the test designers need to think about how to minimize BOTH Type I and Type II Errors. There are psychological and cost ramifications if either kind happens.

(Really NOT Guilty; it was a SKUNK) Getting Picked Up By the Cops The scenario: A cop pulls you over and says he smells pot in your car. He is trying to figure out whether or not to take you to jail. The cop needs to do a little hypothesis test in his head to figure out whether to bring you in. H0: You are not guilty. HA: You ARE guilty. You have been smoking pot in your car. The cop can be ACCURATE, and say that: 1) you’re guilty when you actually are, OR 2) you’re not guilty and you haven’t been smoking pot Or he can be INACCURATE, and say that: 3) you’re guilty when you’re NOT (a FALSE ARREST), OR 4) you’re not guilty when you actually ARE…. (a FAILURE TO DETECT and a GET OUT OF JAIL FREE card) Reality What the Cop Decided H0 True (Really NOT Guilty; it was a SKUNK) H0 False (Really ARE Guilty) I’m Taking You to Jail (Reject H0) I’m Letting You Go (Fail to Reject H0)

Consequences of Cop Errors Type I Error – The test raised a false alarm and got you sent to jail even though you didn’t deserve it. It cost you time and maybe even cost you money – bailing yourself out, or fighting court fees!! Type II Error - The cop let you go when he had reason to send you to jail! Probably good for you, bad for the cop (who may be trying to make his arrest quota for the month). Possibly bad for society, but other factors would have to be considered. Probably best to focus on keeping the Type I Error as low as possible in these cases – it’s more problematic to have a lot of false alarms than to let a few pot smokers off free here and there.

(Really NOT Guilty; you just look sketchy) Getting Picked Up By the Cops #2 The scenario: A cop pulls you over and suspects that you have just committed a murder. He is trying to figure out whether or not to take you to jail. The cop needs to do a little hypothesis test in his head to figure out whether to bring you in. H0: You are not guilty. HA: You ARE guilty. You are hiding evidence and a body in your trunk. The cop can be ACCURATE, and say that: 1) you’re guilty when you actually are, OR 2) you’re not guilty - you haven’t just killed someone Or he can be INACCURATE, and say that: 3) you’re guilty when you’re NOT (a FALSE ARREST), OR 4) you’re not guilty when you actually ARE…. (a FAILURE TO DETECT the murder and eluding the law) Reality What the Cop Decided H0 True (Really NOT Guilty; you just look sketchy) H0 False (Really ARE Guilty) I’m Taking You to Jail (Reject H0) I’m Letting You Go (Fail to Reject H0)

Consequences of Cop Errors (#2) Type I Error – The test raised a false alarm and got you sent to jail and into a HUGE legal mess even though you didn’t deserve it. It costs you time and will probably cost you tons of money – bailing yourself out, court fees, lawyers… a trial!! Type II Error - The cop let you go when you had a body in the trunk! Probably good for you, bad for the cop, and VERY BAD for society. I’d want to keep the Type II Error as low as possible in this case, and risk some false alarms to AVOID letting killers go. Would you??