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!)
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.