# Negative effect size?

#### statn00b

##### New Member
Hi,

I calculated the effect size for the results of Mann-Whitney U tests but some of them are negative. I was double checking the formula and how to do it and I noticed that some of them reported a positive effect size despite the formula (by doing it myself) gave a negative effect size.

So, my question is, when you do the formula for the effect size, should you use a negatize/positive Z or should I just use the positive value?

The formula I found is Z/sq of N.

Thank you,

Statn00b

#### noetsi

##### Fortran must die
You can't have a negative effect size, it is a physical impossibility. It would mean that there was less than no difference between groups which can not happen. One group could be less or higher than the other and depending on which group you make the reference group the sign of the effect might show as plus or minus - but the effect size is the absolute value of what you find. In other words the effect is the difference between one group and the other.

If A has a mean of 5 and B of 2 then you would get a value of 3 or -3 depending on which you subtracted from which. But the effect is 3.

#### trinker

##### ggplot2orBust
Dason I disagree but maybe I don't understand.

Cohen's d is an effect size and you can have a negative effect. If product B is worse than product A it will have a negative effect on the outcome of Y in comparison to A.

#### jpkelley

##### TS Contributor
As trinker says, a negative effect is entirely possible. For the Mann-Whitney effect size, you typically take the absolute value of the formula you mentioned (like noetsi mentioned). That simply gives you the magnitude of the effect, but you could also look at the sign of the effect. Most people just report the magnitude, but it's often just as important to understand the direction of the effect.

#### noetsi

##### Fortran must die
Dason I disagree but maybe I don't understand.

Cohen's d is an effect size and you can have a negative effect. If product B is worse than product A it will have a negative effect on the outcome of Y in comparison to A.
I think you meant me as Dason did not post here (although its pretty complmentary of course to be mistaken for Dason)

Right, as I noted it is negative (or positive) relative to the reference group. The effect of B on Y relative to A will generate a negative effect, the reverse would be true if you compare A on Y relative to B. It is an artificial number, the magnitude of the effect is the same. If you want to know how powerful an effect is (and thus how substantively important) there is no sign and indeed Cohen's D is usually discussed in terms of the absolute value.

#### Dason

Dason I disagree but maybe I don't understand.
Ok. I'm sorry I said something. Oh wait I'm not cause I didn't.

But I had the same objection to noetsi too.

#### noetsi

##### Fortran must die
*sob*

I guess it depends on what is important. When I have seen effect size discussed they wanted to know how substantively important an effect size was which is tied entirely to its magnitude.

#### trinker

##### ggplot2orBust
Yeah I meant noetsi, I said dason. Sorry this whole bot thing has really got me on edge.

#### jpkelley

##### TS Contributor
*sob*
I guess it depends on what is important. When I have seen effect size discussed they wanted to know how substantively important an effect size was which is tied entirely to its magnitude.
Exactly right. Usually, I think authors have already shown graphs to indicate the direction, so it's only necessary to indicate the magnitude.