Q: Which formula correctly represents Cohen's $$d$$ for effect size?

$$d = \frac{\text{Mean difference between } \overline{X}_1 \text{ and } \overline{X}_2}{\text{Mean standard deviation}}$$

Question 1

Which of the following best defines statistical power in hypothesis testing?

Accepted Answer

The probability of correctly rejecting a false null hypothesis.

Question 2

A researcher wants to detect a 15% decrease in cancer cell proliferation rate between Drug A and a control. Which type of power analysis should be performed before data collection?

Accepted Answer

A priori power analysis

Question 3

If the probability of a Type II error is $$\beta = 0.2$$, what is the statistical power of the test?

Accepted Answer

$$0.8$$

Question 4

Which of the following changes will increase the statistical power of a test?

Accepted Answer

Increasing the significance level $$\alpha$$

Question 5

In a clinical trial, the null hypothesis $$H_0$$ states that the average fasting blood glucose is $$85 mg/dL. If $$the true mean is $$90 mg/dL$$, what does the blue area under the curve represent in a power analysis diagram?

Accepted Answer

Statistical power ($$1-\beta)$$

Question 6

Which formula correctly represents Cohen's $$d$$ for effect size?

Accepted Answer

$$d = \frac{	ext{Mean difference between } \overline{X}_1 	ext{ and } \overline{X}_2}{	ext{Mean standard deviation}}$$

Question 7

A hospital has only 80 breast cancer patients, split evenly between Drug A and control. After the trial, the null hypothesis is rejected. What can post hoc power analysis help determine?

Accepted Answer

If the lack of effect is associated with high $$\beta$$ value

Question 8

Which of the following is NOT a benefit of conducting a power analysis before an experiment?

Accepted Answer

Guarantees a statistically significant result

Question 9

If a researcher increases the sample size while keeping $$\alpha$$ and effect size constant, what happens to the statistical power?

Accepted Answer

It increases

Question 10

Which scenario is most likely to require a larger sample size to achieve 80% power?

Accepted Answer

Detecting a small effect size ($$d = 0.2)$$

Question 11

A researcher sets $$\alpha = 0.05$$ and $$\beta = 0.2$$ for a study. What is the probability of making a Type I error?

Accepted Answer

$$0.05$$

Question 12

Which of the following statements about effect size is TRUE?

Accepted Answer

A smaller effect size requires a larger sample size to detect a significant difference.

Question 13

In the context of hypothesis testing, what does the red area under the curve typically represent?

Accepted Answer

Type I error ($$\alpha)$$

Question 14

Which of the following is a correct interpretation of $$1-\alpha$$?

Accepted Answer

Probability of retaining the null hypothesis when it is true

Question 15

A researcher uses G Power software to calculate the required sample size for a study. Which input is NOT necessary for this calculation?

Accepted Answer

The actual data collected

Question 16

Which of the following is an ethical reason for conducting power analysis before starting a clinical trial?

Accepted Answer

To minimize unnecessary patient involvement

Question 17

If a study is underpowered, which of the following is most likely to occur?

Accepted Answer

Type II error increases

Question 18

Which equation is used to calculate the $$z-$$score for a sample mean in hypothesis testing?

Accepted Answer

$$z = \frac{\overline{X} - \mu}{\sigma / \sqrt{n}}$$

Question 19

Which of the following is NOT a factor that affects statistical power?

Accepted Answer

The color of the data points in a graph

Question 20

A study finds Cohen's $$d = 1.472$$ for the difference in blood glucose after two treatments. What does this indicate?

Accepted Answer

A large effect; the means are very likely to be different

Statistical Power and Sample Size Determination

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