# Combining single-point estimates and two-point (range) estimates

I'm looking at capital costs of different battery technologies, with the aim of conducting a meta-analysis of both the published literature and known commercial installations. It's quite common for a range to be quoted, though some authors provide a single-point estimate, and installations provide one value. My task is to provide a single-point descriptor of the population with an associated measure of uncertainty. This will be an input into later modelling work.

One option is to collapse the ranges to mid-ranges and treat them as additional single-points, but it seems a shame to throw away information on spread. On the other hand, the number of samples used to produce the ranges aren't quoted, so perhaps I can't do any better. Is this the case, and if not, what methods should I consider?

I'm open to both Bayesian and frequentist approaches. I appreciate it's far from ideal conditions for rigorous statistics, and there are a number of other factors working against me (sparse data, nuisance parameters, outliers) but some insights into this aspect alone would be great.

• Most forms of meta-analysis require some measure of variability so the problem is likely to be the studies which just provide a single estimate. Can you give us more details? – mdewey Jul 28 '16 at 16:41
• Yes, that's definitely a challenge. I'm dealing with new technologies for the most part, so a lot of academic reviews and public reports just quote values without quantifying uncertainty. It could be that meta-analysis is the wrong term, and I'm looking at more of a primary analysis. I could impute a (subjective) weighting by the credibility of the source and the level of detail considered and rigour in the study, but it's a bit of a poor substitute. – MikeSimpson Jul 28 '16 at 17:04
• The simplest approach to combining data is vote counting... The American Congress is a good example, with the Senate being composed by two senators for each state irrespective of population and the House of Representatives being composed by a number of representatives proportional for each state population. Meta-analysis should be ideally conducted in keeping with the House of Representatives rationale, but nobody would say the Senate has no democratic legitimacy. – Joe_74 Jul 29 '16 at 11:04