6.3: Errors & Power (Statistics)
Presentation
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
David HS)
Used 10+ times
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47 Slides • 0 Questions
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6.3: Errors & Power
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Innocent person goes to
jail.
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Correct Decision!
Innocent person goes to
jail.
5
Correct Decision!
Innocent person goes to
jail.
Correct Decision!
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Correct Decision!
Innocent person goes to
jail.
Correct Decision!
Guilty person goes free.
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Correct Decision!
Innocent person goes to
jail.
Correct Decision!
Guilty person goes free.
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Will we reject or fail to reject the null hypothesis?
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Will we reject or fail to reject the null hypothesis?
Assume the claim Ho is true.
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Will we reject or fail to reject the null hypothesis?
Assume the claim Ho is true.
Find the p-value from the sample data.
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Will we reject or fail to reject the null hypothesis?
Assume the claim Ho is true.
Find the p-value from the sample data.
Ha
Ho
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Will we reject or fail to reject the null hypothesis?
Assume the claim Ho is true.
Find the p-value from the sample data.
Ho Ha
Ha
Ho
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Will we reject or fail to reject the null hypothesis?
Assume the claim Ho is true.
Find the p-value from the sample data.
Ho Ha
Ha
Ho
Type I
Error
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Will we reject or fail to reject the null hypothesis?
Assume the claim Ho is true.
Find the p-value from the sample data.
Ho Ha
Ha
Ho
Type I
Error
Correct!
"Power"
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Will we reject or fail to reject the null hypothesis?
Assume the claim Ho is true.
Find the p-value from the sample data.
Ho Ha
Ha
Ho
Type I
Error
Correct!
"Power"
Correct!
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Will we reject or fail to reject the null hypothesis?
Assume the claim Ho is true.
Find the p-value from the sample data.
Ho Ha
Ha
Ho
Type I
Error
Correct!
"Power"
Correct!
Type II
Error
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reject Ho
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reject Ho
failed to reject Ho
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reject Ho
failed to reject Ho
significance level
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reject Ho
failed to reject Ho
significance level
P(Type I error) = alpha level (α)
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power
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power
The probability we reject Ho correctly.
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power
The probability we reject Ho correctly.
reject Ho correctly.
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fail to reject Ho
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fail to reject Ho
β
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fail to reject Ho
β
P(Type II error) = β
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fail to reject Ho
β
P(Type II error) = β
power = 1 - β
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Type1: We say the patient does not have arthritis, when they really don't.
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Type I: We say the patient does not have arthritis, when they really don't.
Consequence: The patient gets unnecessary treatment.
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Type I: We say the patient does have arthritis, when they really don't.
Consequence: The patient gets unnecessary treatment.
Type II: We say the patient does not have arthritis, when they really do.
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Type I: We say the patient does have arthritis, when they really don't.
Consequence: The patient gets unnecessary treatment.
Type II: We say the patient does not have arthritis, when they really do.
Consequence: The patient does not get the necessary treatment they need.
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Type I error (α)
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Type I error (α)
Power
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Type I error (α)
Power (1 - β)
Correct
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Type I error (α)
Power (1 - β)
Correct
Type II error (β)
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Type I error (α)
Power (1 - β)
Correct
Type II error (β)
significance level
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Type I error (α)
Power (1 - β)
Correct
Type II error (β)
significance level
The more likely we are to reject the null hypothesis (Ho), the more likely we are going to do it correctly.
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Type I error (α)
Power (1 - β)
Correct
Type II error (β)
significance level
The more likely we are to reject the null hypothesis (Ho), the more likely we are going to do it correctly.
Reject Ho correctly
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lower
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lower
They increase/decrease together
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lower
They increase/decrease together
When the others increase/decrease, Type II does the opposite.
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lower
They increase/decrease together
When the others increase/decrease, Type II does the opposite.
6.3: Errors & Power
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