We are performing an inter-comparison experiment for three devices that can measure concentration (cells/mL). We take one solution and run it through each device, and we compute mean concentration and variance on that device. I would like to find the average of the means and weight it according to sample size and variance.
I found an example applet which illustrates calculation, but cannot determine the source code formula:
Given sample size, variance, and mean what is the formula for pooling these measurements to obtain an ensemble mean?
Is there a better approach?