In other words if we are looking for a big difference between treatments we might be able to accept a wide probability distribution, if we want to detect a small difference we will need great precision and small probability distributions. This example shows that the initial comparison between groups 1 and 3 showed no statistical difference as the confidence intervals overlapped. Since the width of probability distributions is largely determined by how many subjects we study it is clear that the difference sought affects sample size calculations. If there truly is a difference between the interventions we express the probability of getting a type II error and how likely are we to find it. For example, the principle outcome measures for many diagnostic studies will be the sensitivity and specificity for a particular test, typically reported with confidence intervals for these values.


A study with a small sample size will have large confidence intervals and will only show up as statistically abnormal if there is a large difference between the two groups. Conversely, if we find, or are looking for, a large difference a fairly wide probability distribution may be acceptable. The size of the confidence interval is inversely proportional to the number of subjects studied. Figure 2 demonstrates how increasing the number of subjects can give a more precise estimate of differences.
We see that the confidence intervals no longer overlap indicating that the difference in means is unlikely to have occurred by chance.


By performing a sample size calculation for a diagnostic study we can specify the precision with which we would like to report the confidence intervals for the sensitivity and specificity.



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