Power of a Test Math Example 3
Follow the full solution, then compare it with the other examples linked below.
Example 3
easyList four factors that increase the power of a hypothesis test, and explain the direction of each effect.
Solution
- 1 1. Larger sample size (): reduces SE, making it easier to detect real effects → Power
- 2 2. Larger significance level (): easier to reject (more liberal) → Power (but Type I error also increases)
- 3 3. Larger true effect size (bigger difference from null): more signal → Power
- 4 4. Smaller population variability (): less noise → Power
Answer
Power increases with: larger n, larger α, larger effect size, smaller σ.
Power depends on the signal-to-noise ratio in the testing context. More signal (larger true effect) or less noise (smaller σ, larger n) both increase power. Increasing α is the least preferred method since it inflates Type I errors.
About Power of a Test
The probability that a hypothesis test correctly rejects a false null hypothesis. Power , where is the probability of a Type II error.
Learn more about Power of a Test →More Power of a Test Examples
Example 1 medium
A test has [formula] and [formula]. Calculate the power and interpret it. If the researcher wants Po
Example 2 hardFor testing [formula] vs [formula], with [formula], [formula], [formula]: calculate the rejection re
Example 4 hardA study fails to reject [formula] and concludes 'there is no effect.' Critique this conclusion using