How to calculate the SE for a mean after dividing it in 2?

Question

I want to compare the mean eggs laid per female in two different experiments. The first experiment(control) consist of one females laying eggs in a "box". The second experiement (test) consist of two females laying eggs in the same box. In both experiement, I count the eggs in each box regardless of who laid the eggs.

My results are :

Control females : 1,13 ± 0,35 eggs per female. (n=319)
Test females: 2,07 ± 0,57 eggs for TWO FEMALES. (n=378)

How can I calculate the mean ± SE for each female, in the second experiement, in order to compare the females of both experiments?

Thank you!

Answer 1

The intutitive answer would be to recalculate the second mean & se by dividing all values by 2 (i.e. changing experimental unit from box to hen and uncritically accepting that the estimate per hen would be box/2, which may or may not be an accurate assumption).

Recalculating mean & se, you would find that the mean is exactly your previous mean divided by 2 (by definition of mean). The same would be true for your se (again by definition).

A dummy example in R code would look something like this:

# Generate 50 random values
values=sample(1:10,50,replace=T)
values.5=values/2 # Experimental unit half of the above
# Helper function to calculate se
se <- function(x) sqrt(var(x)/length(x))

# Ratios
> mean(values.5)/mean(values)
[1] 0.5
> se(values.5)/se(values)
[1] 0.5

HTH HAND,
Carl