Which statement correctly describes the relationship between Type II error and statistical power?

Which statement correctly describes the relationship between Type II error and statistical power?

• A. Higher Type II error corresponds to higher power.
• B. Higher Type II error corresponds to lower power.
• C. Type II error and power are unrelated.
• D. Power is the square of Type II error.

Answer: (B)

The key idea is that beta and power move in opposite directions. Type II error is the probability of failing to detect a real effect when one exists, while power is the probability of detecting that effect. For a fixed test setup, power equals 1 minus beta. So if the Type II error increases, power decreases. This is why larger beta means weaker ability to detect true differences, and conversely, reducing beta (through larger samples, bigger effects, or lower variability) increases power. The other statements don’t fit because beta and power are not independent, power isn’t the square of beta, and higher beta does not imply higher power.

The key idea is that beta and power move in opposite directions. Type II error is the probability of failing to detect a real effect when one exists, while power is the probability of detecting that effect. For a fixed test setup, power equals 1 minus beta. So if the Type II error increases, power decreases. This is why larger beta means weaker ability to detect true differences, and conversely, reducing beta (through larger samples, bigger effects, or lower variability) increases power. The other statements don’t fit because beta and power are not independent, power isn’t the square of beta, and higher beta does not imply higher power.