goals… define what is meant by a type i error. define what is meant by a type ii error. define...
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Goals…Define what is meant by a Type I error. Define what is meant by a Type II error. Define what is meant by the power of a
test. Identify the relationship between the
power of a test and a Type II error. List four ways to increase the power of a
test.
Errors in Statistical Inferene
Type I ErrorWe make a “Type I Error” when we
incorrectly reject H0.
We make a “Type II Error” when we incorrectly fail to reject Ho.
TYPE I ERRORInform the EPA that the
water is safe to drink when it is actually UNSAFE!
TYPE II ERRORInform the EPA that the water is not safe to drink even though it really WAS
safe.
Consequence?
Consequence?
People drink unsafe water and could get
sick
People are unable to use this
valuable water source and the
government imposes water restrictions
• Which error do you believe is more serious? Why?
• If you had to choose and alpha level of α = 0.1, 0.05, or 0.01 which would you choose? Why?
TYPE I ERROR
Inform the EPA that the water is safe to drink when it is actually UNSAFE!
TYPE II ERRORInform the EPA that the water is not safe to drink even though it
really WAS safe.
People drink unsafe water and could get
sick
People are unable to use this valuable water source
and the government imposes water restrictions
Mel•Mel N. Colly is interested in whether or not his new treatment for depressed patients is decreasing his patients’ rating of depression. Suppose all of his depressed patients have a mean depression score of 8 with a standard deviation of 4. Mel chooses a random sample of 30 depressed patients treated with his innovative approach and determines that the mean depression score for these individuals is 7.5. Does the treatment decrease depression?
•H0: μ = 8•Ha: μ < 8
Mel •H0: μ = 8•Ha: μ < 8
•Describe and give the consequences of a Type I error and a Type II error.
•TYPE I ERROR• Description: Mel concludes that the mean depression score post-treatment is less than 8 even through it this is not the case. • Consequence: Mel uses the treatment on depressed patients even though it has no effect on them (or it could increase depression!) rather than researching a better treatment that could really help. Patients waste time and money on a useless (or harmful) treatment.
Mel •H0: μ = 8•Ha: μ < 8
•Describe and give the consequences of a Type I error and a Type II error.
•TYPE II ERROR• Description: Mel concludes that the mean
depression score post-treatment is still 8 (or higher), but in reality post-treatment scores are less than 8.
• Consequence: Mel does not use the effective treatment on his patients and these individual miss out on the opportunity to decrease their level of depression and improve their lives.
Mel
•Which error do you believe is more serious? Why?
•If you had to choose and alpha level of α = 0.1, 0.05, or 0.01 which would you choose? Why?
•TYPE I ERROR• Description: Mel concludes that the mean depression score post-treatment is less than 8 even through it this is not the case. • Consequence: Mel uses the treatment on depressed patients even though it has no effect on them rather than researching a better treatment that could really help. Patients waste time and money on a useless (or harmful) treatment.
•TYPE II ERROR• Description: Mel concludes that the mean depression score post-treatment is still 8 (or higher), but in reality post- treatment scores are less than 8.• Consequence: Mel does not use the
effective treatment on his patients and these individual miss out on the opportunity to decrease their level of depression and improve their lives.
Error Probabilities
H0 is true Ha is true
Reject H0
α (0.05)TYPE I ERROR
Correct Decision
Fail to reject H0Correct Decision
TYPE II ERROR
• We decide to use α = 0.05• What does that mean?
• The probability of a Type I error = α
Error ProbabilitiesH0 is true Ha is true
Reject H0
α
TYPE I ERROR
Correct Decision
Fail to reject H0Correct Decision
βTYPE II ERROR
• The probability of a Type II error is β
Error Probabilities
H0 is true Ha is true
Reject H0
α TYPE I ERROR
1-βCorrect Decision
Fail to reject H0Correct Decision
(1-α)
βTYPE II ERROR
• Which box do we WANT to fall in?
Error Probabilities
H0 is true Ha is true
Reject H0
α TYPE I ERROR
1-βCorrect Decision
Fail to reject H0Correct Decision
(1-α)
βTYPE II ERROR
• 1-β is called the POWER of the test
Error Probabilities
μ = 8(H0 is true)
μ < 8(Ha is true)
Reject H0
α =0.05TYPE I ERROR
Power = 1-β = 0.166
Correct Decision
Fail to reject H0Correct Decision
(1-α)
β = 0.834TYPE II ERROR
• Mel wants to use an alpha level of 0.05. • Find the probability of a Type I error• The probability of a Type II error is 0.834. What
is the Power of the test?
Power: You do NOT need to calculate β or Power by
hand (except in the way we just did in the chart). You just need to understand the concept.
Power is the probability that you will CORRECTLY reject the null hypothesis.
A perfect study would have VERY high powerThere are a few ways to increase power…http://bcs.whfreeman.com/tps3e/
HOMEWORK!!!
Classwork: Error and Power WorksheetHomework: 11.59, 11.62, 11.64, 11.69 (full test)