I just stumbled across Language Log: Thou shalt not report odds ratios (2007-07-30), HT reddit/statistics:

(…) this finding was widely reported in the media:(…)

“Doctors are only 60% as likely to order cardiac catheterization for women and blacks as for men and whites.”

Now let't try a little test of reading comprehension. The study found that the referral rate for white men was 90.6%. What was the referral rate for blacks and women?

If you're like most literate and numerate people, you'll calculate 60% of 90.6%, and come up with .6*.906 = .5436. So, you'll reason, the referral rate for blacks and women was about 54.4 %.

But in fact, what the study found was a referral rate for blacks and women of 84.7%.

This was a failure mode of pop-sci journalism which I was not aware of (if I would happen to know enough to understand real papers, I’d definitely value pop-sci at minus-whatever in the meantime…)

On a related note this article got me remembering Understanding Uncertainty: 2845 ways to spin the Risk, which argues that certain presentations bias the understanding of probabilities:

Similarly people confronted with the statement “Cancer kills 2,414 people out of 10,000” rated cancer as more risky than those told “Cancer kills 24.14 people out of 100”. The potential influence of the size of the numerator and denominator is known as the 'ratio bias'.

I’d be quite interested if anybody could point me to further resources on good presentation of statistical facts (beside the normalization on one type of presentation), or on further pop-sci journalism failure modes.