Solved – How to interpret the overlap or non-overlap of two related confidence intervals

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?

As the comments outline, you can't simply look for overlapping CI's, because it can be misleading. The better way, as you will soon learn in your classes, is to conduct a statistical hypothesis test:

You make a null hypothesis, $H_0$, which in this case would be the mean birth weight of males and females is the same, and you calculate the probability, if $H_0$ were true, of the means of your two samples not being closer than they actually are. That is the mythical p-value, which, if small enough, allows you to more or less confidently reject the null hypothesis (and get your paper published).

Notice that you can never prove $H_0$, only fail to disprove it, which is not the same. In your case, you cannot say that males and females have the same mean birth weight, only that there is not enough evidence to say they are different…

For your case, you would probably use a Student's t test, for two independent samples.

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