I'm working on a paper and one of the texts states "On average, inmates who participated in correctional education programs had 43% lower odds of recidivating than those who did not...this translates into a reduction in the risk of recidivating of 13% for those who participate in correctional education programs versus those who do not"
Does this mean, an inmate who participates in an education program has a 13% percent chance to end up back in prison, and that for an inmate who does not participate in an educational program they would have a 66% chance of ending up back in prison (43% higher than someone in an educational program)?
I interpret the article as follows:
The chance of an inmate re-offending, who does not receive correctional education programs is $~X : 0 < X < 1.$
The chance of an inmate re-offending, who does receive correctional education programs is $~(1 - 0.43) \times X.$
$X - \left[(1 - 0.43) \times X\right] = 0.13.$
Assuming that I have interpreted the article correctly, this implies that
$\displaystyle (0.43) \times X = 0.13 \implies X = \frac{13}{43}.$
This is the fraction of inmates who will re-offend if they do not receive correctional education programs.
Then, the fraction of inmates who will re-offend if they do receive correctional education programs is
$\displaystyle (0.57) \times X = \frac{57 \times 13}{100 \times 43}.$
Edit
Is it just me, or does the $\displaystyle X = \frac{13}{43}$ fraction seem significantly too low.