Let's assume we have two means with corresponding standard errors.
mean_1 = 3.75, se_1 = 0.64 mean_2 = 2.90, se_2 = 0.94
I would like to average the means and account for the standard error. I would like
mean_1 to contribute more (since the standard error is lower) to the average than
mean_2. A weighted mean if you will.
One way would be to specify weights as the relative magnitude of the standard error like so (I use R's function
weighted.mean found in the base
> weighted.mean(c(3.75, 2.0), w = c((1 -0.64/(0.64+0.94)), (1- 0.94/(0.64+0.94))))  3.041139
Does that make sense? How would one go about this problem? I would be happy to hear your critiques and suggestions.