Understanding Statistical Power and Type I and Type II Errors
When conducting statistical hypothesis testing, it is important to understand concepts like statistical power, Type I errors, and Type II errors. These ideas help researchers design studies that can detect meaningful effects while controlling for erroneous conclusions.
In this blog post, we will define these key terms and discuss how adjusting the threshold for statistical significance, called the alpha (α) level, can impact the risks of different types of errors. Real-life examples will be used to illustrate these concepts in a clear and accessible way.
Let’s imagine we want to know if a new medicine is effective at lowering blood pressure. We conduct a study comparing blood pressure readings in a group taking the medicine versus a placebo group.
Our null hypothesis (H0) is that the medicine has no effect — both groups have the same average blood pressure. The alternative hypothesis (H1) is that the medicine lowers blood pressure compared to placebo.
A Type I error occurs when we wrongly reject the null hypothesis that is actually true. In our study, this would be concluding the medicine works when it really doesn’t.
A Type II error is failing to reject a null hypothesis that is actually false. In our study, this would be saying the medicine does nothing when it truly does lower blood pressure on average.
We want to control both types of errors, but they cannot be fully eliminated. The choice of α level balances this risk.
Statistical Power
Statistical power refers to the probability we will correctly reject the null hypothesis when it is false. Higher power means we are less likely to make a Type II error.
Power depends on:
- The actual effect size in the population
- Our sample size
- Our choice of α level threshold
For a given effect size and sample, power increases as we raise α because it’s easier to reject the null. But this also raises the Type I error risk.
Choosing the Alpha Level
By convention, most fields use α=0.05, meaning we reject H0 if our p-value is ≤ 0.05. This controls the Type I error risk at 5% or less.
A lower α like 0.01 controls Type I errors more strictly but risks missing real effects. Meanwhile, an α of 0.1 is more lenient and powerful, but risks false positives.
The appropriate α balances these risks given our research question. For example, medical studies often use α=0.05 to safely identify effective treatments. But in exploratory disciplines like psychology, α=0.1 may be used to better detect interesting relationships for further study.
Real-World Implications
Let’s return to our blood pressure medication study. Say the drug truly lowers it by 5 points on average. With α=0.05 and sample of 100 in each group, we have only 60% power to detect this effect.
We might miss discovering an actually effective drug one-fifth of the time with this study, committing a Type II error. By raising α to 0.1, power improves to 75%, reducing but not eliminating that risk.
Statistical thinking helps researchers design ethical, effective studies and evaluate findings appropriately — neither falsely concluding too much nor missing meaningful discoveries. With a nuanced understanding of concepts like statistical power, Type I and Type II errors, and the role of α, we can gain useful insights from data.
