Differences between independent groups when all you have are Mean +95% CI

I seem to recall a method where one could compare and look for differences between independent samples when you only have the mean for each sample and their 95% Confidence Intervals. You are unable to recover any other information about each group. Am I off my rocker and this is not possible? I know the ‘rule of thumb’ about 83% CI overlap between groups, but that isn’t universal enough for my needs.

Is anyone else out there smarter than me able to help?


Someone has published this and I hope others can point us to it. You take the two intervals and sample sizes, backtrack to get standard deviations, estimate SD of the difference from the quadratic mean of the two SDs, and get an approximation of the confidence interval for the difference from that. Don’t need to spend much time on interpreting the two intervals or looking to see if they overlap.


Essentially, with a bit of algebra, you are reverse engineering the 2 samples T test; that was my thought. If you don’t have sample sizes, you are forced to use the Z table. Is this correct?

That was my thought, generally. The sample size is not recoverable in this case. Perhaps it is because it’s late on a Friday but I’m having trouble working through the steps that are are Z-table or Chi-square based. I swear I’ve seen it worked out and published but my Google search terms are failing me.

Try this paper by Douglas Altman – if you can recover the p values you should figure out the rest. You are essentially solving for the pooled variance. If you can’t use sample sizes, maybe inverse variance weighing could be used?

1 Like

Check this paper by Altman and Bland: Interaction revisited: the difference between two estimates - PubMed


Perfect. That Altman paper spells things out perfectly and easily. I don’t love that I have to assume the 95% CIs are parametric or symmetrical, but it’s the best I’m going to get, I think. I appreciate the input everyone!

1 Like