6.3: Errors & Power (Statistics)

6.3: Errors & Power

​Innocent person goes to

jail.

​Correct Decision!

​Innocent person goes to

jail.

​Correct Decision!

​Innocent person goes to

jail.

​Correct Decision!

​Correct Decision!

​Innocent person goes to

jail.

​Correct Decision!

Guilty person goes free.

​Correct Decision!

​Innocent person goes to

jail.

​Correct Decision!

Guilty person goes free.

Will we reject or fail to reject the null hypothesis?

Will we reject or fail to reject the null hypothesis?

Assume the claim Ho is true.

Will we reject or fail to reject the null hypothesis?

Assume the claim Ho is true.

Find the p-value from the sample data.

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

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

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

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"

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!

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

reject Ho

reject Ho

failed to reject Ho

reject Ho

failed to reject Ho

significance level

reject Ho

failed to reject Ho

significance level

P(Type I error) = alpha level (α)

power

power

The probability we reject Ho correctly.

power

The probability we reject Ho correctly.

reject Ho correctly.

​

​fail to reject Ho

​fail to reject Ho

β

​fail to reject Ho

β

P(Type II error) = β

​fail to reject Ho

β

P(Type II error) = β

power = 1 - β

​Type1: We say the patient does not have arthritis, when they really don't.

​Type I: We say the patient does not have arthritis, when they really don't.

Consequence: The patient gets unnecessary treatment.

​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.

​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.

​Type I error (α)

​Type I error (α)

Power

​Type I error (α)

Power (1 - β)

Correct

​Type I error (α)

Power (1 - β)

Correct

Type II error (β)

​Type I error (α)

Power (1 - β)

Correct

Type II error (β)

significance level

​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.

​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

​lower

​lower

They increase/decrease together

​lower

They increase/decrease together

When the others increase/decrease, Type II does the opposite.

​lower

They increase/decrease together

When the others increase/decrease, Type II does the opposite.