The definition of "risk reduction" as used by StatMate.

If you use StatMate to compute sample size to compare two proportions, you can choose to ask StatMate to present the results as the difference between two proportions or ratios. Understanding the differences is no problem. The ratios are a bit trickier to understand, and easy to misunderstand. 

When you are looking at an increase in risk, there is no ambiguity. A relative risk of 3.0 means that the risk is three times higher with the treatment.

When you are looking at a reduction in risk, it gets a big confusing. StatMate does not simply report the relative risk, but rather the risk reduction. 

Consider this example.  The risk in the controls is 0.93. You are looking for a change down to a risk of 0.36. If you ask StatMate to tabulate differences, then of course the difference StatMate would report is 0.57.  What is the equivalent risk reduction? Divide that value 0.57 by the baseline risk of 0.93 to get a relative risk reduction of 0.62, which is what StatMate tabulates. An alternative way to report these results would be to simply report the relative risk, which would be 0.36/0.93 which equals 0.39. StatMate does not report the results this way, where a smaller number would mean a larger effect. Instead, it reports the risk reduction computed as explained above, where a larger value means a larger effect.

If you find this confusing, we suggest you ask StatMate to tabulate differences, which are easier to think about.