# Should I make equally sized samples for the Mann-Whitney U test if originally I have unequal sample sizes

I have 2 groups with unequal sizes (control 70% and test 30%) and need to find out if there is a significant difference between these groups. I've read that MW test works fine with unequal sized samples, but the statistical power will diminish as the group sizes become more unequal. Hence I was adviced to make groupes of equal sizes (by multiplying by coefficient). I worry that in this case the stat power will diminish as well, however couldn't find published references to prove that.

Could anyone help me with advice what I should do : leave it as it is or try making the groups equally sized.

Appreciate all the help)

• I would rather see you used your data as is, rather than multiplying by some arbitrary coefficient. Nov 23 '21 at 6:55
• The loss for unequal (compared to equal) sample sizes is under the situation of a fixed total sample size. If you are making them equal by losing data, you're losing power. Nov 23 '21 at 9:25

Claims about losing power when groups have unequal sizes make more sense in the context of designing the experiment. If you have enough resources to make $$100$$ observations, the greatest power will be when you allocate $$50$$ to the control group and the other $$50$$ to the treatment group. However, $$150$$ in the control group with $$50$$ in the treatment group will be more powerful than the test with $$100$$ observations, even if it is not the most powerful allocation of the $$200$$ observations.
(It can be defended to do uneven allocation, however. Maybe the treatment is expensive, but you still get adequate power with $$50$$ treatment subjects and $$150$$ control subjects.)