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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)

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    $\begingroup$ I would rather see you used your data as is, rather than multiplying by some arbitrary coefficient. $\endgroup$ Nov 23 '21 at 6:55
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    $\begingroup$ 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. $\endgroup$
    – Glen_b
    Nov 23 '21 at 9:25
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Use your original data.

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.)

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