Statistical power is the probability that a statistical test will correctly reject a false null hypothesis (H0) when a specific alternative hypothesis (H1) is true. H0 is the null hypothesis, which states there is no effect or no difference. H1 is the alternative hypothesis, which states there is a real effect or difference. Alpha (α) is the probability of a Type I error (a false positive), which is the risk of incorrectly rejecting the H0 when it is actually true. You set this value before the experiment, commonly at 0.05. Beta (β) is the probability of a Type II error (a false negative), which is the risk of failing to reject the H0 when it is actually false.
Power is calculated as 1−β. Increasing power means you are decreasing the probability of making a Type II error.
Several factors can be adjusted to increase the power of a statistical test:
Effect Size: This is the magnitude of the difference you are trying to detect. A larger effect size is easier to detect, thus increasing power.
Sample Size: The number of observations in a study. A larger sample size provides more information about the population, reducing the margin of error and increasing the power to detect a true effect.
Variation: Refers to the spread or standard deviation of the data within the population. Less variation makes it easier to distinguish a real effect from random noise, thereby increasing power.
Alpha (): Increasing the alpha level (e.g., from 0.05 to 0.10) also increases power, but at the cost of a higher risk of a Type I error. This trade-off is often undesirable.
