Percentages in research results
Let's say we have a news headline "Eggplant reduces impotence risk by 50%!". Sounds great, you immediately want to run and eat eggplants, or give them to your boyfriend. But deceptive relative numbers are often used here.
Let's say 2000 people participated in this study:
- 1000 ate eggplants
- 1000 didn't eat them
In the first group, impotence developed in 5 people, and in the second in 10. The relative risk reduction (RRR) will be 50%.
Now a bit of math for those interested. The formula for calculating RRR is:
\[ \text{RRR} = \frac{R_c - R_t}{R_c} \times 100\% \]
Where \(R_c\) is the risk in the control group, \(R_t\) is the risk in the treatment group. In our case \(R_c = \frac{10}{1000} \times 100 = 1\%\), \(R_t = \frac{5}{1000} \times 100 = 0.5\%\). Plugging in: \(\text{RRR} = \frac{1 - 0.5}{1} \times 100 = 50\%\).
But there's also the concept of absolute risk reduction (ARR), and in our case it equals 0.5%. Completely different numbers now. For the mathematicians:
\[ \text{ARR} = R_c - R_t \]
There's also a metric showing how many need to be treated for an effect (NNT — Number Needed to Treat). Formula:
\[ \text{NNT} = \frac{1}{\text{ARR}} \]
In our case this will be 200, meaning conditionally 200 men must eat eggplants so that one lucky guy doesn't get impotence.
And now the same news can be described in different ways:
- 🎉 RRR — eggplant reduces impotence risk by 50%
- 🤏 ARR — eggplant reduces impotence risk by 0.5%
- 👬 NNT — if a group of 200 men eats eggplants for a long time, then possibly one will have impotence instead of two
After the last two headlines, you're not as eager to run for eggplants anymore.