![]() They next set their sights a bit lower, with α = 0.05 and β = 0.10, and find that n is still ‘too large’. But in that case experimenters are usually quite disappointed to see what large values of n are required, especially in trials with binomial (success/failure) outcomes. Often the sample-size calculation is first made with β = α = 0.05. No one is satisfied to report that ‘the new treatment is statistically significantly better than the old ( p ≤ 0.20)’. ![]() But sometimes the opposite is true, and we never see studies proposed with α = 0.20 and β = 0.05. if the new treatment is much more expensive, or if it entails greater discomfort). Why is such a large value of β acceptable? Why the severe asymmetry in favor of α? Sometimes, of course, a Type I error would be much more costly than a Type II error would be (e.g. The specific alternative value chosen might be suggested by pilot studies or uncontrolled trials that preceded the experiment that is now being planned, and the sample size is determined with α = 0.05 and β = 0.20. In trials that compare a new treatment to an old one, the ‘null’ hypothesis usually states that the new treatment is not better than the old, while the alternative states that it is. We begin with a mild peculiarity - why is it that the Type I error rate α is ordinarily required to be 0.05 or 0.01, but a Type II error rate as large as 0.20 is regularly adopted? This often occurs when the sample size for a clinical trial is being determined. Isn’t 80% power just as arbitrary as p-value thresholds? And why should we settle for such a large probability of error before we even start an experiment?įrom Royall (1997, pp. It’s a question we’ve probably all thought about at some point. The following example comes from Royall’s book (you really should read it), and questions why we settle for a power of only 80%. Coming back to the topic of my previous post, about how we must draw distinct conclusions from different hypothesis test procedures, I’d like to show an example of how these confusions might actually arise in practice.
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