Wilcoxon test for sample n=3 I have a dataset of male and female bats. Male bats comprise 3 evening and 3 morning trips. Female bats 5 evening and 3 morning trips. 
Trips consist of parameters like trip duration, covered distance, farthest point from roost, speed, home range and flying height. 
I actually wanted to perform a Wilcoxon test separately for male and female bats to see if differences between evening and morning trips arose by chance or not. Now I was surprised to hear, that Wilcoxon only works with a minimum of n=6. That means I can not do the test with none of my bats. Is that really correct? If not, pleas I would be so grateful if you could refer to a reference, since i am writing my bachelors thesis about that issue.
Also when comparing evening trips between male and female bats using the Mann Withney U test, the sample size requieres to be of a ratio minimum of 4:2. So I can not perform that test for male bats neither?

There is individual bat making a trip in the evening and in the morning. This is called paired. Please correct me if I am wrong. I want to test e.g. the speed of the evening trip with the speed of the same bat during morning trips. I have three individuals. 
 A: Well, I can answer part of the question:
The Wilcoxon rank sum test (Mann Whitney U) works for a comparison of $n_1=3$ vs $n_2=3$ just fine.
However for a two-tailed test you can't reasonably set your significance level smaller than 10%, since that's the smallest achievable p-value.
Here's an example done in R:
> x
[1] 0.21 1.70 2.55
> y
[1] 2.58 4.25 3.21
> wilcox.test(x,y)

        Wilcoxon rank sum test

data:  x and y
W = 0, p-value = 0.1
alternative hypothesis: true location shift is not equal to 0

A Wilcoxon signed rank test of 3 pairs also works just fine, but the significance level issue is worse; now your lowest possible two-tailed significance level is 25%. Here's an example:
> wilcox.test(y-x)

        Wilcoxon signed rank test

data:  y - x
V = 6, p-value = 0.25
alternative hypothesis: true location is not equal to 0

So the claim that one or the other test doesn't "work" at those sample sizes isn't true -- but if you want a smaller significance level, that would be a problem for you.
[Whether what you're trying to do/have been advised to do makes sense is less clear from your discussion. More details would help.]
