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Statistical Decision Making: Understanding Type I and Type II Errors

Learn how to make informed decisions in statistical inference, including when to accept or reject null hypotheses, using examples like the Potato Chips Scenario. Understand significance levels, confidence intervals, and how to decrease Type II errors. Improve your statistical decision-making skills with these essential concepts.

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Statistical Decision Making: Understanding Type I and Type II Errors

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  1. Section 10.4.1Inference as Decision AP Statistics March 4, 2010 CASA

  2. When inference is used to make a decision… • Either you reject H0 or you fail to reject H0. • You can reject H0 correctly • You can fail to reject H0 correctly • You reject H0 incorrectly • (Type I error) • You can fail to reject H0 incorrectly • (Type II error)

  3. Potato Chips Example • The salt content of the chips should have a mean of 2 mg with a standard deviation of .1 mg. • When deciding whether to accept or reject a batch of potato chips, a company looks at the salt content of 50 chips. • If the salt content is too far away from the mean, it will reject the batch.

  4. What range values are acceptable? • The company will check a 50 chip sample. • If our alpha is .05, the acceptable range is the same as the 95% confidence interval:

  5. We understand with normal variation and everything working normally, we will get a sodium value between 1.9723 mg and 2.0277 mg 95% of the time. Accept or reject?

  6. We understand with normal variation and everything working normally, we will get a sodium value between 1.9723 mg and 2.0277 mg 95% of the time. This means the 5% of the time you will reject a batch of chips that are fine. When we reject the batch (and H0) incorrectly we have committed a Type I error. Accept or reject?

  7. Accept H0 Reject H0 Reject H0 95% Confidence Interval 1.9723 2.0277

  8. Significance and Type I Error • The significance level α of any fixed level test is the probability of a Type I error. That is, α is the probability that the test will reject the null hypothesis H0 when H0 is in fact true.

  9. Probability of reject H0 correctly • The probability that we correctly reject H0 (that is, we say there is a difference when the difference really exists) is called the “Power”. • The probability of the Type II error is 1- “Power” • We increase the “Power” by either increasing • the sample size • Alpha • Remember, when we increase alpha, we increase the probability of the Type I error

  10. Assignment • 10.66-10.69 all

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