power Flashcards
What is statistical power?
Statistical power is the probability of correctly rejecting the null hypothesis when it is false, i.e., detecting an effect when one truly exists.
How is statistical power mathematically defined?
Statistical power = 1 − Type II error (𝛽)
Why is statistical power important in study planning?
It helps determine the required sample size to detect a given effect or the smallest effect detectable with a given sample size.
What factors influence statistical power? (4)
Sample size
effect size
variability in the system
the significance level (𝛼).
What is a Type I error?
A Type I error (false positive) occurs when the null hypothesis is incorrectly rejected.
What is a Type II error?
A Type II error (false negative) occurs when the null hypothesis is not rejected despite being false.
What is the significance level (𝛼) in hypothesis testing?
The probability of making a Type I error, commonly set at 0.05 (5%).
How is statistical power related to Type II errors?
Higher power means a lower probability of Type II errors (𝛽), reducing the risk of failing to detect a true effect.
What is the null hypothesis (𝐻0) in hypothesis testing?
The assumption that there is no effect or difference in the population being studied.
What is an alternative hypothesis (𝐻1)?
The hypothesis that there is a real effect or difference in the population.
How does sample size affect statistical power?
Larger sample sizes generally increase power, making it easier to detect true effects.
How does effect size impact power?
Larger effect sizes make it easier to detect differences, increasing power.
What is the formula for the test statistic in a one-sample z-test?
Zstat = (data estimate - hypothesised value)/standard error
In a hypothesis test, when do we reject 𝐻0?
When the test statistic exceeds the critical value (𝑧𝑐𝑟𝑖𝑡) based on the significance level (𝛼).
What are the main ways to increase statistical power?
Increase sample size, reduce variability, accept a higher Type I error rate, or detect a larger effect size.
How does increasing sample size affect power?
Larger sample sizes reduce the standard error, making it easier to detect true effects and increasing power.
How does reducing variability increase power?
Controlling variability (e.g., testing under standard conditions) reduces noise in the data, making effects easier to detect.
How does accepting a higher Type I error rate (𝛼) affect power?
A higher 𝛼 lowers the decision boundary, reducing Type II error and increasing power.
What is the trade-off when increasing power by raising 𝛼?
It reduces Type II errors but increases the likelihood of false positives (Type I errors).
What is the advantage of using simulations to estimate power?
Simulations provide an intuitive and flexible way to estimate power, especially for complex designs.
How does simulation-based power estimation work?
Generate many random samples under 𝐻1, compute test statistics, and estimate power based on rejection rates.
What happens to Type I and Type II errors when adjusting for multiple comparisons?
Decreasing Type I error (false positives) increases Type II error (false negatives), reducing power.
How does adjusting the family-wise error rate (FWER) affect power?
It makes Type I error thresholds more stringent, increasing the likelihood of Type II errors and lowering power.
Why is power important in planning a statistical study?
It ensures a high probability of detecting a real effect if one exists, reducing the risk of false negatives.
What is the commonly accepted minimum power level for a study?
80%, meaning there is a 20% chance of failing to detect a true effect.
What factors decrease statistical power?
Small sample sizes, small effect sizes, and high variability in measurements.
Why is post-hoc power analysis considered meaningless?
If 𝐻0 is not rejected, power will always be low by definition, making post-hoc calculations misleading.
What is the problem with conducting a post-hoc power analysis after failing to reject 𝐻0?
It falsely suggests that low power justifies a negative result, which is statistically invalid.
What is an example of scientific misconduct related to power?
Designing a study with low power to deliberately fail to reject 𝐻0.
