Reporting effects as relative differences...with a confidence interval
Researchers frequently report results as relative effects, for example,
“Male flies from selected lines had 50% larger upwind flight ability than male flies from control lines (Control mean: 117.5 cm/s; Selected mean 176.5 cm/s).”
where a relative effect is
\[\begin{equation} 100 \frac{\bar{y}_B - \bar{y}_A}{\bar{y}_A} \end{equation}\]If we are to follow best practices, we should present this effect with a measure of uncertainty, such as a confidence interval. The absolute effect is 59.0 cm/s and the 95% CI of this effect is (48.7, 69.3 cm/s). But if we present the result as a relative effect, or percent difference from some reference value, how do we compute a “relative CI”?
