# Mann Whitney U - P Value of 0.0000

#### n1477

##### New Member
Good Afternoon all,

I am using a Mann Whitney U to compare two populations the data ranges from (-2 to 2).
I have already done this on 4 different variables however for one of them I have repeatedly got a p=value of 0.0000 (Using mini-tab).

C2 461 2.0000
C1 503 1.0000

Point estimate for ETA1-ETA2 is -0.0000
95.0 Percent CI for ETA1-ETA2 is (-0.0001,-0.0000)
W = 238940.5
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.0001
The test is significant at 0.0000 (adjusted for ties)

I have explored the forums and my ol pal Google and there has been nothing helpful. If anyone could shed some light on this, it would be much appreciated.

Niall

#### Dason

You didn't actually ask a question.

#### n1477

##### New Member
My apologies, from what I gather the p value shouldnt be 0.000 therefore I am assuming that there is something going wrong somewhere along the way. I was wondering whether anyone could suggest what might be happening.

#### Dason

This happens with software quite a bit. Your p-value most likely isn't exactly 0 but it's small enough that the program either 1) can't distinguish between your p-value and 0 (we only have limited accuracy using computers) or 2) your program doesn't care to bother you with the true p-value (which could be something like .0000000000000000000000000000000000000001) and opts to just say 0 instead.

#### rogojel

##### TS Contributor
This is quite baffling at first sight because the p value being this small says that we have to reject the Null Hypothesis which is that the two medians are the same - so the test tells us that the two medians are different. However the difference seems to be zero - which is the same as saying that the the two are the same. This isnthebreally interesting point here not the p-value in itself.

the solution is the same, Minitab is giving the numbers with a finite precision, so the difference is not exactly zero, but very small (-0'0000 means that it is negative but less then 0,0001)'

#### rogojel

##### TS Contributor
[/QUOTE]

2. A P value of 0.000049 is still quite sufficient to reject your null hypothesis, so I don't understand why it baffled you in the first place?[/QUOTE]

The fact that the p-value AND THE diference were both zero at first sight.

#### rogojel

##### TS Contributor
To be more clear, you seem to completely misunderstand my argument. What I mean is that one would never see the combination of a p-value of near zero and a difference of EXACTLY zero. This would not make sense, not because the p-value is the difference but because the null hypothesis is generally that the difference is zero.

#### rogojel

##### TS Contributor
Nope. You are mixing me up with the author of the post probably. I was relieved, if you may call it that, because I saw thatbthe upper limit of the confidence interval is not EXACTLY zero but a very small number. This way the zero p-value could make sense.

#### victorxstc

##### Pirate
Yes the P values being reported by different software are like any other calculated numbers with decimal places: They are actually rounded values, not real values. In some software packages, you can configure the level of rounding the P value (to three, four, or sometimes to more than four decimal places), but in some, it is not possible. Anyway, a P = 0.0000 can be actually P = 0.0004888888, = 0.0000000002, or = 0.0000000000000000000000000000000000000000001. All of these are reported as 0.0000 (as the rounded P value). In SPSS it is possible to check the "real" not-rounded P value, but in Minitab it is not possible.

However, another point here is that Mann-Whitney does not compare medians, actually (although it is widely believed so). It actually compares the dispersions around medians. A search within this forum, especially in posts sent by CowboyBear would give you more details.

Two other points: 1. as far as I know, Minitab reports only three places of decimal, so I wonder which version of Minitab you use which shows 4 decimal places in P value?

2. A P value of 0.000049 is still quite sufficient to reject your null hypothesis, so I don't understand why it baffled you in the first place?

However the difference seems to be zero - which is the same as saying that the the two are the same.
I think you are thinking that the P value refers to the difference between medians, no? So you were baffled since you saw the difference (that you though is shown by P value) is zero, but you are now relieved since you see the difference between the medians (shown by P values) is not actually zero (and is something like 0.00004 for example).

If I am right and you think P value is the difference between medians, you should study the notion of P value first, since you seem to be on a wrong path right now. But fear not! That is an interesting matter and there are many high-quality threads already available on P value (as well as experts willing to help you). --------------------------------

The fact that the p-value AND THE diference were both zero at first sight.
Aha I see but then you saw that P is not actually zero, and was relieved to see that a zero difference between medians led to a P significant at that level? Didn't you think that a difference as small as 0.0000 is least likely to accompany a P value not about 1.0?

And let me ask again, which Minitab version reports four decimal places? Could you please let me know how you managed to extract four decimal places out of that software, because I could use your method. Yeah I found it, thanks. --------------------------------

lol yeah I was thinking you are the original poster lol Nice to meet you!