POWER OF A TEST
Power and Type 2 Error
Power and Type 2 Error
Type 1 error is rejecting H0 when you shouldn't have, and the
probability of doing so is α (significance level)
Power and Type 2 Error
Type 1 error is rejecting H0 when you shouldn't have, and the
probability of doing so is α (significance level).
Power and Type 2 Error
▶
Type 1 error is rejecting H0 when you shouldn't have, and the
probability of doing so is α (significance level)
▶
Type 2 error is failing to reject H0 when you should have, and
the probability of doing so is β (a little more complicated to
calculate)
Power and Type 2 Error
▶ Type 1 error is rejecting H0 when you shouldn't have, and the
probability is α (significance level).
▶ Type 2 error is failing to reject H0 when you should have, and
the probability is β.
Power of a test is 1 – β, and is the probability
of correctly rejecting H0
Keep α and β low, but there are inherent trade-offs.
Example:
Given:
Explain its meaning.
What is the power of the test? Explain.
Example:
Given:
Explain its meaning.
This is the probability of failing to reject the null
hypothesis when it is false.
What is the power of the test? Explain.
The power of the test is
The probability of correctly rejecting
the false null hypothesis is .85.
The probability of Type I error:
The probability of Type II error:
The power of the test (probability of
correctly rejecting null):
To increase the power of a test
▶
Increase sample size
▶
Increase alpha (but,Type 1 error more likely)
▶
Decrease standard deviation
Putting it all together
True value
Hypothesized
132
The End