Imagine that two researchers independently carry out clinical trials to test the same null hypothesis, that cox-2 selective inhibitors (which are used to treat arthritis) have no effect on the risk of cardiac arrest. they use the same population for their study, but one experimenter uses a sample size of 60, and the other uses a sample size of 100. assume that all other aspects of the studies, including significance levels are the same between the two studies. which study has higher power?

The study with the higher power is the second study using a sample size of 100.

The power of an experiment refers to the probability that the statistical analysis can detect a treatment effect if this is present. The size of the sample population determines whether our statistical analysis and conclusions are accurate and reliable.

When conducting an experiment like the one in this example, we set a null hypothesis, which states that there is no difference between the two means that we compare. The aim of every experiment is to prove that the null hypothesis is wrong. The statistical analysis can conclude in two errors, type I and II. Type I (or false positive) happens when we conclude that there is a statistically significant difference between the means of our tested populations, when in fact there is not and the difference we observe is due to chance sampling variation. Type II (false negative) is when we fail to detect the statistically significant difference. By definition, the smaller the sample size, the higher the probability of a type II error, since smaller populations have less chance of detecting a statistically significant difference. The power of the analysis equals to 1-probability for type II error. The 100-subject population has lower probability of type II error and therefore higher power.