Test questions on how sample size, alpha, and effect size impact test power.

📚 Quick Study Guide

• 🔢 Test Power: The probability of correctly rejecting a false null hypothesis. High power is desirable.
• 📊 Sample Size (n): A larger sample size generally increases test power. More data leads to more accurate results.
• ⚖️ Effect Size: The magnitude of the difference between groups or variables. A larger effect size increases test power.
• 🛡️ Alpha (\(\alpha\)): The significance level. A higher alpha (e.g., 0.05 vs. 0.01) increases test power, but also increases the risk of a Type I error (false positive).
• 💡 Relationship: Power = 1 - \(\beta\), where \(\beta\) is the probability of a Type II error (false negative).
• 📝 Formulas to keep in mind:
  • Power ≈ n * (Effect Size)^2 / Variance
  • Sample Size ≈ (Z\[1-\(\beta\)] + Z\[1-\(\alpha\)/2])^2 * (Standard Deviation)^2 / (Effect Size)^2

🧪 Practice Quiz

1. Which of the following generally increases the power of a statistical test?

   1. Decreasing the sample size.
   2. Decreasing the effect size.
   3. Increasing the alpha level.
   4. Using a one-tailed test when a two-tailed test is more appropriate.

2. What is the relationship between sample size and statistical power, assuming all other factors remain constant?

   1. As sample size increases, statistical power decreases.
   2. As sample size decreases, statistical power increases.
   3. As sample size increases, statistical power increases.
   4. There is no relationship between sample size and statistical power.

3. If you increase the alpha level from 0.01 to 0.05, what happens to the power of the test, assuming all other factors remain constant?

   1. The power decreases.
   2. The power remains the same.
   3. The power increases.
   4. The effect size changes.

4. Which of the following describes the effect of increasing the effect size on statistical power, assuming all other factors remain constant?

   1. Decreases statistical power.
   2. Has no effect on statistical power.
   3. Increases statistical power.
   4. Makes the test invalid.

5. What type of error is most likely to occur if you set a very high alpha level (e.g., 0.10)?

   1. Type II error.
   2. Type III error.
   3. Type I error.
   4. No error.

6. A researcher wants to increase the power of their study without increasing the sample size. Which of the following actions could they take?

   1. Decrease the alpha level.
   2. Use a less precise measurement tool.
   3. Increase the expected effect size (e.g., by refining the intervention).
   4. Use a two-tailed test instead of a one-tailed test.

7. What does a power of 0.80 mean in the context of hypothesis testing?

   1. There is an 80% chance of making a Type I error.
   2. There is a 20% chance of making a Type I error.
   3. There is an 80% chance of correctly rejecting a false null hypothesis.
   4. There is a 20% chance of correctly rejecting a true null hypothesis.