Chapter VII_part 3_errors in Hypoth testing_II (1).docx

# Probability 1 type ii error probability a missletting

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probability = (1 - ) Type II error probability = ( a “miss”—letting a guilty person go free) ^ ^ JURY’s Decision Now if reject the null when it is true, we have wrongfully convicted an innocent person (like calling mary a Xenon when she is a human). This is type I error. If we set them free when they are innocent (fail to reject the null when it is true), we have done the right thing. Nothing happened, and we realized it. (Mary’s not a Xenon, and we realize that she’s not a Xenon). 1

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A Practical Guide to Basic Statistics Chapter VII IF we fail to reject the null when it is FALSE, we set them free when they are GUILTY. They get away with it (like Mary might get away with being a Xenon, but fooling us into thinking she’s a human). This is a type II error. If we reject the null when it is false, however, we have convicted a guilty person--- something really happened, and we caught them. (Mary is a Xenon, and we have caught her). This is “power”. There is NO WAY for a jury to be 100% certain of the truth—they can only judge based on the evidence (just like a researcher). It is not possible to avoid the risk of all mistakes —you must decide which mistake is “worse”, and minimize that one (which makes the other more likely). In our justice system, we have decided that it is better to free a guilty person ( type II error --β) than to convict and punish an innocent person ( type I error -- α). So we set our alpha level very low (we make it VERY HARD TO CONVICT someone) in order to avoid falsely convicting innocent people. It takes a lot of evidence, gathered just the right way, etc. As a result, lots of guilty people end up going free due to “technicalities”, etc (in other words, our β, or type II error, is high). 2
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• Spring '17
• Vera Davis
• Type I and type II errors

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