Power is the probability that the study will detect a difference or effect if there is one to be detected (i.e., the probability of avoiding a Type II error).
The power of a study is typically set at 0.80 or 80%, meaning there is an 80% chance of detecting a statistically significant effect if one exists.
The power of a study depends on:
1. Sample Size:
Larger sample sizes increase the power of a study because they reduce the standard error and make it easier to detect a difference.
2. Effect Size:
Larger effects are easier to detect, so the power increases with the effect size.
3. Variability:
Less variability in the data increases the power because the effect stands out more clearly against the background noise.
4. Significance Level (α):
Decreasing the significance level (making it more stringent, like moving from 0.05 to 0.01) decreases the power for the same sample size, because the criteria for detecting an effect are stricter.
Reason to Run Power Analysis:
1. Ensure Adequacy:
To make sure the study is adequately powered to detect an effect if one exists, avoiding waste of resources and unethical underpowered studies.
2. Optimize Resources:
To balance the trade-off between statistical precision and the use of resources (time, money, participants).
3. Guide Design Choices:
To influence decisions about study design, including the choice of significance level and the estimation of necessary resources.
Factors Affecting Power of a Study:
1. Sample Size:
Larger sample sizes increase power by reducing the standard error of the estimated effect, making it easier to distinguish the effect from random noise.
2. Effect Size:
Larger effect sizes are easier to detect, increasing the power.
The expected difference or association should be scientifically meaningful and estimated based on prior research or pilot studies.
3. Variability in Data:
Lower variability (standard deviation) within groups increases the power, as the signal-to-noise ratio improves.
4. Significance Level (α):
A higher α (less stringent, e.g., 0.05 vs. 0.01) increases power since the criterion for detecting an effect is less strict. However, this also increases the risk of Type I errors.
5. Measurement Precision:
Better measurement tools or more precise data collection methods reduce random error and can increase the power.
6. Study Design:
Certain designs, such as crossover designs or matched case-control studies, can be more efficient and thus more powerful for a given sample size compared to simpler designs.