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Errors in Hypothesis Tests

Errors in Hypothesis Tests. When you perform a hypothesis test you make a decision:. reject H 0 or fail to reject H 0. When you make one of these decisions, there is a possibility that you could be wrong! That you made an error!.

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Errors in Hypothesis Tests

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  1. Errors in Hypothesis Tests

  2. When you perform a hypothesis test you make a decision: reject H0or fail to reject H0 When you make one of these decisions, there is a possibility that you could be wrong! That you made an error!

  3. There are two decisions that we make; reject or fail to reject. Each could possibly be a wrong decision; therefore, there are two types of errors.

  4. Type I error • When you reject the null hypothesis that is really true • i.e. Reject when you should have failed to reject • The probability of a type I error is a

  5. Type II error • When you fail to reject the null hypothesis when it is false • i.e. fail to reject when you should have rejected • The probability of a type II error is b

  6. Power The probability of correctly rejecting a false null hypothesis. Power is the probability that the test will do what it is supposed to do i.e. reject the null hypothesis when in fact it should be rejected. Power = 1 – β

  7. Type I error Correct a POWER Suppose H0 is false & we reject it, what type of decision was made? Type II error Correct Suppose H0 is false & we fail to reject it, what type of decision was made? Suppose H0 is true & we reject it, what type of decision was made? Suppose H0 is true & we fail to reject it, what type of decision was made? b

  8. Facts: As a increases, b decreases As a decreases, b increases • Every time you make a decision, you have potentially made an error. • a & b are inversely related Fail to reject H0 Reject H0 a m0 b ma

  9. Facts continued: • The seriousness of the error types is determined by the specific situations. • Depending upon the situation type I or type II may be the more serious. • We often DO NOT know if an error is made in real life. • Except for cases like • Firestone tires • Drugs like: Phen-phen & Vioxx Someone made an error with these products

  10. Let’s look at a jury trial. • State the hypotheses H0 = the defendant is found not guilty Ha = the defendant is found guilty b) What type of error is committed when a guilty person is found not guilty? Type II c) What type of error is committed when an innocent person is found guilty? Type I d) Which of the two type of errors do you believe our justice system considers to be the more serious mistake? Type I – an innocent person is judged guilty This is why we have the appeals process. e) State the power in context of the problem? The probability that we find a guilty person guilty.

  11. Lay’s Chip Company decides to accept a truck load of potatoes based upon the result obtained from a sample of potatoes from the truck load. • State the null and alternative hypotheses in words. H0 = potatoes are good (we keep them) Ha = potatoes are not good (we send them back) b) Identify a Type I error in context of the problem. We determined the potatoes were bad when they were actually good and we sent them back c) Explain a consequence of the Type I error. The supplier could lose money.

  12. Lay’s Chip Company decides to accept a truck load of potatoes based upon the result obtained form a sample of potatoes from the truck load. • State the null and alternative hypotheses in words. H0 = potatoes are good (we keep them) Ha = potatoes are not good (we send them back) d) Identify a Type II error in context of the problem. We failed to identify bad potatoes and kept them e) Explain a consequence of the Type II error. By keeping bad potatoes we could create a bad product

  13. Lay’s Chip Company decides to accept a truck load of potatoes based upon the result obtained form a sample of potatoes from the truck load. • State the null and alternative hypotheses in words. H0 = potatoes are good (we keep them) Ha = potatoes are not good (we send them back) f) Which consequence do you consider the more serious error (if you were the company)? Type II – keeping the bad potatoes g) State the power in context of the problem? The probability that we correctly identified bad potatoes as bad an sent them back.

  14. A doctor is considering a new medication to help fight infections. However, the medication has the possibility of being highly toxic to the patient. You will test the medication to determine toxicity. What are the hypotheses? What are the Type I & II errors? Which is more serious? H0: medicine is not toxic Ha: medicine is toxic Type I: say medicine is toxic when it really isn’t Type II : say medicine isn’t toxic when it really is Most would consider a type II error more serious since people could be harmed.

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