# Statistical power/Self-check assessment

Use the following quiz questions to check your understanding of statistical power. Note that as soon as you have indicated your response, the question is scored and feedback is provided. As feedback is provided for each option, you may find it useful to try all of the responses (both correct and incorrect) to read the feedback, as a way to better understand the concept.

Understanding power
• Power is:
• The probability that the null hypothesis is true.
• That's not quite right. The null hypothesis is either true or false; there is no probability involved.
• The probability that the null hypothesis is false.
• That's not quite right. The null hypothesis is either true or false; there is no probability involved.
• The probability a false null hypothesis will be rejected.
• That's correct. Power relates to a study's ability to reject, correctly, a null hypothesis which is in fact false. A type II error is the failure to reject a false null hypothesis.
• The probability a true null hypothesis will be rejected.
• That's not quite right. The probability of rejecting a true null hypothesis is the probability of a type 1 error.
• If the power of a research study is low then
• The experiment will likely be inconclusive.
• That's correct. With low power, the null hypothesis is unlikely to be rejected. When the null hypothesis is not rejected, the experiment is inconclusive.
• Any significant findings obtained are suspect.
• That's not quite right. Significant findings are much less likely when power is low, but not out of the question.
• The results are skewed.
• That's not quite right. When a study has low power, the significance test is more likely to result in failing to reject the null hypothesis.
• Power is the probability of accepting the null hypothesis given that the null hypothesis is true.
• True
• That's not quite right. Remember that power is related to a type II error, which can only occur if the null hypothesis is false.
• False
• That's correct. Power is the probability of rejecting a false null hypothesis.

The following questions are multiple selection multiple choice. Choose all that apply to both questions before clicking on Submit.

# Factors affecting power

1. Which of the following increase power?

 Increasing the standard deviation → That's not quite right. A large standard deviation means we are less sure about $\bar x$ (or other sample estimate). Increasing the sample size → That's correct. With more data, we have more information about $\bar x$ (or other sample estimate), and a better chance of detecting that the population μ is in fact different from the value specified in the null hypothesis. Increasing the significance level → That's correct. A larger significance level, α, increases the chance of rejecting the null hypothesis (i.e. obtaining a statistically significant result) when the null hypothesis is in fact false, that is, it reduces the risk of a Type II error, and increases power. Increasing the size of the difference between means → That's correct. The larger the effect size (e.g., a difference in means) the easier it will be to detect, resulting in a study with more power.

2. Which of the following decreases the probability of a type I error?

 Increasing the standard deviation → That's not quite right. The size of the standard deviation has no effect. (Given a true null hypothesis, the probability of a type I error = α.) Increasing the sample size → That's not quite right. The size of the sample has no effect. (Given a true null hypothesis, the probability of a type I error = α.) Decreasing the significance level → That's correct. Given a true null hypothesis, the probability of a type I error is equal to α.

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## Acknowledgements

The questions included in this quiz were adapted from