Combining Estimates with Actual Values I am exploring stature (living height), calculated from arm and leg bones, from an archaeological sample. Unfortunately, there are very few complete bones that can be measured and entered into the stature reconstruction formulae (e.g., stature = 44.8 + .267 * LengthOfUpperArmBone).
To increase the sample size, I estimated total bone length from additional bone fragments (there are accepted standards for doing this) present in the sample, which I then entered into the stature formulae. My results are: mean male stature from actual bone lengths = 1694 mm vs. from estimated bone length = 1681 mm; mean female statue from actual bone lengths = 1573 mm vs. from estimated bone length = 1531 mm.
My question is: are there any guidelines for when estimates are too deviant from actual to be used (e.g. combined) with actual values. In my case, I feel fairly good that I can combine the male data since the means only differ by 13 mm (ca. 1/2 inch), which seems too small to worry about, but the female means deviate by 42 mm (ca. 1 & 3/4 inch), which seems too much. Any ideas what I should do? Is it reasonable to use the male estimated data, but not the female estimates?
Here are the statistics for the four groups:
Male stature from actual bone length: mean=1694, std dev=79, n=8
Male stature from estimated bone length: mean=1681, std dev=109, n=18
Female stature from actual bone length: mean=1573, std dev=40, n=15
Female stature from estimated bone length: mean=1531, std dev=130, n=19
 A: It appears that the bone length estimation method may introduce a downward bias compared to direct measurement. The best way forward depends on your research question and objectives. If there’s a concrete guideline here, it’s that you should report measures of variance (i.e. standard deviation, standard error, confidence intervals, etc.) with your mean stature estimates. But the decision of whether to pool the estimated and actual bone lengths is really up to you.
Regardless of whether these results will be published in peer-reviewed literature, it might be useful to adopt the posture of a peer reviewer from your discipline. Perhaps such a reviewer would be convinced by statistical significance testing. So you could test for statistical differences between the actual and estimated lengths for males and females and let the outcome of the statistical tests determine whether or not to pool (i.e. pool if there are no significant differences, and keep separate if you detect a significant difference). In this case it’s entirely possible that the outcome could lead you to pool the male data but not the female data.
Another option is to use your own expert knowledge of the context. It sounds like you regard an effect size of 0.5 inches as not very meaningful, whereas 1.75 inches is quite meaningful. Following this values judgment, pooling the males but not the females seems credible as long as you clearly document your decision process.
Personally I would advocate for reporting two sets of estimates: one set of means and standard errors of each of the 4 groups, and one set of means and standard errors of the two pooled groups.  When described clearly, this would provide your readers with the richest context.
