Say I want to determine if there is a relation/association between birth weights in male and female populations.
Hence I calculate the mean for birth weights in males and females and a calculate 95% CI for each using this formula:
CI = mean +/- 1.96 x SE
I then see if the female group birth weight mean lies within the male CI and vice versa.
If, in the typical scenario, both genders lie within their opposite genders CI then gender is associated/related with birth weight.
However, if not, then gender and birth weight are not associated but are significantly different.
My question is what happens if, e.g., the female population lies in the male CI, but the male population does not lie in the female CI, is it possible?
Is it due to a statistical error?