I am estimating an evolutionary metric for various genes. Each estimate has an associated standard error. Typically, I'll have a set of genes for which I want to compare its mean to the mean of the rest of the genes. The size of the sets are typically in the 10 to 100 range. What I have been doing is using the (1 / estimated standard error) of each value within the set to weight each value, and using the weighted Welch's t-test in R to compare the weighted means.
However, if I want to compare the value of a single gene to the rest, I'm not quite sure what the best way to do that is. I could just ask if the single value is significantly different than the mean of the other set, but I would like to incorporate the estimated standard error of the single value to make the test more conservative. I could use this standard error (with N=1) in conjunction with the weighted standard deviation of the set to calculate the Welch's t statistic and degrees of freedom estimate. However, N=1 here seems wrong because this N should refer to the sampling used to derive the standard error estimate. This standard error is calculated by the curvature method from an optimization algorithm, so there isn't really an N associated with it. Would it still be fair (conservative) to just use N=1 here to calculate the t statistic and degrees of freedom? Are there other options/tests for incorporating this standard error of this single value to compare to a set of multiple values?