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UIUC CHLH 410 - type_i_and_ii_errors

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Name: ______________________________________________ Official Class: __________ Date: ________________Teacher: ___________________________________________Period: ___________ Class: _____________________To Err is Human: What are Type I and II ErrorsAs much as researchers, journals, and newspapers might like to think otherwise, statistics isdefinitely not a fool-proof science. Statistics is a game of probability, and we can never know forcertain whether our statistical conclusions are correct. Whenever there is uncertainty, there isthe possibility of making an error. In statistics, there are two types of statistical conclusion errorspossible when you are testing hypotheses: Type I and Type II.Type I error occurs when you incorrectly reject a true null hypothesis. If you got tripped up onthat definition, do not worry—a shorthand way to remember just what the heck that means isthat a Type I error is a “false positive.” Say you did a study comparing happiness levels betweenpeople who were given a puppy to hold versus a puppy to merely look at. Your null hypotheseswould be that there is no statistically significant difference in happiness levels between thosewho held and those who looked at a puppy.However, suppose that there was no real difference in happiness between groups—which is tosay, people are actually just as happy when holding a puppy or looking at one. If your statisticaltest was significant, you would have then committed a Type I error, as the null hypothesis isactually true. In other words, you found a significant result merely due to chance.The flipside of this issue is committing a Type II error: failing to reject a false null hypothesis. Thiswould be a “false negative.” Using our puppy example, suppose that you found there was nostatistically significant difference between your groups, but in reality, people who hold puppiesare much, much happier. In this case, you incorrectly failed to reject the null hypothesis, becauseyou said there was not a difference when one actually exists.The chances of committing thesetwo types of errors are inverselyproportional—that is, decreasingType I error rate increases Type IIerror rate, and vice versa. Yourrisk of committing a Type I erroris represented by your alphalevel (the p value below whichyou reject the null hypothesis).The commonly accepted α = .05means that you will incorrectlyreject the null hypothesis approximately 5% of the time. To decrease your chance of committinga Type I error, simply make your alpha (p) value more stringent. Chances of committing a Type IIerror are related to your analyses’ statistical power. To reduce your chance of committing a TypeII error, increase your analyses’ power by either increasing your sample size or relaxing youralpha level!Depending on your field and your specific study, one type of error may be costlier than the other.Suppose you conducted a study looking at whether a plant derivative could prevent deaths fromcertain cancers. If you falsely concluded that it could not prevent cancer-related deaths when itreally could (Type II error), you could potentially cost people their lives! If you were looking atwhether people’s happiness levels were higher when they held versus looked at a puppy, eithertype of error might not be so importantName: ______________________________________________ Official Class: __________ Date: ________________Teacher: ___________________________________________Period: ___________ Class: _____________________Truth About the PopulationHO True HA TrueDecision Based onSampleReject HOFail to Reject HORamifications: - A Type I error is made when the null hypothesis HO is actually true but the alternative hypothesis HA is chosen. - A Type II error is made when the alternative hypothesis HA conservative step of accepting the null hypothesis HO is actually made. Example 1: Conjecture: The defendant is guilty of the crime. - HO : The defendant is not guilty - HA : The defendant is guiltyBecause we are seeking evidence for guilt, it becomes the alternative hypothesis. The trial is the process whereby information (sample data) is obtained. The jury then deliberates about the evidence (the data analysis). Finally, the jury either convicts the defendant (rejects the null hypothesis) or declares the defendant not guilty (fails to reject the null hypothesis). The two correct decisions are to conclude that an innocent man is not guilty or conclude that a guilty person is guilty. The two incorrect decisions are to convict an innocent person or to let a guilty man free.Truth About the DefendantHO True HA TrueDecisionBased onEvidenceReject HOType 1 Error – come to theconclusion that the defendantis guilty when his is notCorrect Decision Fail toReject HOCorrect DecisionType II Error – come to theconclusion that the defendant isnot guilty when he really is guiltyWhich is worse?If you want to reduce the possibility of a type I error, you must lower your alpha value - you want to be as sure as possible that a person did it. Circumstantial evidence is not enough. We don't have an innocent person punished. But if we do that, there are certainly going to be more peoplewho get away with crimes because in that process of being crystal sure of the person's guilt, we will be letting more people go for whom we have strong suspicion but not positive proof. That means we are increasing the possibility of a type II error. If we want to reduce the possibility of a type II error, (we don't want criminals getting away with it), we need to take anyone we strongly have suspicions about crimes and punish them. But if wedo that, there are bound to be people who get caught by the circumstantial evidence against them and possibility gets punished for crimes when they didn't do it. Hence more type I errors. Ramifications:- Type I error – punishing a person who is truly innocent and putting them wrongly in jail. - Type II error – criminals gets away with crimes and perhaps thinks he always can. Later in life, this can lead to larger or continued crimes. Type I and II Error Practice1. The USDA limit for salmonella contamination for chicken is 20%. A meat inspector reports that the chicken produced by a company exceeds the USDA limit. You perform a hypothesis test to determine whether the meat inspector’s claim is true. a. What are the null and alternative hypotheses?b. Make the table like the one above to show what and where your type


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