But in fact, what the study found was a referral rate for blacks and women of 84.7%
I might just be being stupid, but how was this figure derived at all? I understand that the point of the article is that statistics can be presented in non-intuitive and confusing ways, but whenever I’ve seen such examples in the past there has always been some justification, however shaky.
Did the media just outright lie this time, or am I missing something?
Nope: the odds ratio was (.847/(1-.847))/(.906/(1-.906)), which is indeed 57.5%, which could be rounded to 60%. If the starting probability was, say, 1%, rather than 90.6%, then translating the odds ratio statement to “60% as likely” would be legitimate, and approximately correct; probably the journalist learned to interpret odds ratios via examples like that. But when the probabilities are close to 1, it’s more correct to say that the women/blacks were 60% more likely to not be referred.
it’s more correct to say that the women/blacks were 60% more likely to not be referred.
Hmmm. I would have said that white men were 60% as likely to not be referred. (This is the first time I’ve seen the golden ratio show up in a discussion of probability!)
I might just be being stupid, but how was this figure derived at all? I understand that the point of the article is that statistics can be presented in non-intuitive and confusing ways, but whenever I’ve seen such examples in the past there has always been some justification, however shaky.
Did the media just outright lie this time, or am I missing something?
Nope: the odds ratio was (.847/(1-.847))/(.906/(1-.906)), which is indeed 57.5%, which could be rounded to 60%. If the starting probability was, say, 1%, rather than 90.6%, then translating the odds ratio statement to “60% as likely” would be legitimate, and approximately correct; probably the journalist learned to interpret odds ratios via examples like that. But when the probabilities are close to 1, it’s more correct to say that the women/blacks were 60% more likely to not be referred.
Hmmm. I would have said that white men were 60% as likely to not be referred. (This is the first time I’ve seen the golden ratio show up in a discussion of probability!)
I prefer your phrasing.