All entries for Tuesday 23 December 2014
December 23, 2014
You know, the one at the bottom of your meta-analysis that summarises the pooled result? This one:
Well, I don't like it. Why not? I think it's misleading, because the diamond shape (to me at least) suggests it is representing a probability distribution. It puts you in mind of something like this:
And that seems to make sense - the thick bit of the diamond, where your point estimate is, ought to be the area where the (unknown) true treatment effect would be most likely to be, and the thin points of the diamond are like the tails of the distribution, where the probability of the true value is getting smaller and smaller. That would be absolutely right, if the analysis was giving you a Bayesian credible interval - but it isn't.
It's a frequentist confidence interval, and as lots of people have been showing recently, frequentist confidence intervals do not represent probability distributions. They are just an interval constructed by an algorithm so that, if the experiment were repeated many times, 95% of the intervals would include the true value. They are NOT a distribution of the probability of any value of the treatment effect, conditional on the data, althought that is the way they are almost always interpreted. They don't say anything about the probability of the location of the true value, or even whether it is inside or outside any particular interval.
I think a solid bar would be a more reasonable way to represent the 95% confidence interval.
For more info:
Hoekstra R, Morey, RD, Rouder JN, Wagenmakers EJ. Robust misinterpretation of confidence intervals. Psychon Bull Rev. 2014, DOI 10.3758/s13423-013-0572-3