What is the difference between stdev.p and stdev.s & which should I use?

JenniferMurphy

Well-known Member
Joined
Jul 23, 2011
Messages
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Office Version
  1. 365
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  1. Windows
The stdev.p function returns the std dev for a population, whereas the stdev.s does so for a sample, presumably less than the entire population.

These 2 pages from Microsoft appear identical except for the denominator. It's n for stdev.p and n-1 for stdev.s, so stdev.p will always be slightly larger than stdev.s.
But it doesn't say anything about when to use one or the other.


Based on this example, where I am using the std dev to calculate z scores, it doesn't really matter which I use. The z scores based on stdev.s are slightly more spread out, but the order doesn't change. The raw data is prices and Amazon-style 5-star ratings. If these were selected products, they would clearly be a sample, not the entire population.

Cell Formulas
RangeFormula
C2:D2D2=AVERAGE(MrExcel[Price])
F2:G2G2=AVERAGE(MrExcel[Rtg])
C3C3=STDEV.S(MrExcel[Price])
F3F3=STDEV.S(MrExcel[Rtg])
D4D4=STDEV.P(MrExcel[Price])
G4G4=STDEV.P(MrExcel[Rtg])
C7:C21C7=ZScore([@Price],@Mean,@StdDevP,FALSE)
D7:D21D7=ZScore([@Price],@Mean,@StdDevS,FALSE)
F7:F21F7=ZScore([@Rtg],@Mean,@StdDevP)
G7:G21G7=ZScore([@Rtg],@Mean,@StdDevS)
H7:H21H7=[@[Price Z(P)]]+[@[Rtg Z(P)]]
I7:I21I7=[@[Price Z(S)]]+[@[Rtg Z(S)]]
J7:J21J7=RANK.EQ([@[Sum Z(P)]],[Sum Z(P)])
K7:K21K7=RANK.EQ([@[Sum Z(S)]],[Sum Z(S)])
L7:L21L7=[@[Rank X(S)]]-[@[Rank X(P)]]
 

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Hello,

Use STDEV.P if you need to calculate the standard deviation for a whole population. If you just need to calculate the standard deviation of a sample of a population, use the STDEV.S function.

So, are you looking at the whole Population, or just at some part (a sample) of it?

Hint: In case you look at all your games with your grand kids so far, it's the whole population, so use STDEV.P.

Regards,
Bernd
 
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Hello,

Use STDEV.P if you need to calculate the standard deviation for a whole population. If you just need to calculate the standard deviation of a sample of a population, use the STDEV.S function.

So, are you looking at the whole Population, or just at some part (a sample) of it?

Hint: In case you look at all your games with your grand kids so far, it's the whole population, so use STDEV.P.

Regards,
Bernd
Yes, I understand the difference between a sample of a pop[u;ation and the whole population.

Perhaps I wasn't clear enough in my question. I would like to know why STDEV.S is more accurate than STDEV.P when applied to a sample? Why is dividing the terms by n+1 more accurate than by just n?
 
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The link took me to the editing version, maybe the below is a bit better

Yes, that is a better description. The difference mathematically is that for the population std dev, the denominator is N, whereas for the sample std dev it's N-1.

Now why this correction is necessary is a little more complicated than I have time to study right now. But I am convinced that I should use stdev.s if I don't have the entire population, which I will rarely have.

Thanks
 
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The link took me to the editing version, maybe the below is a bit better

 
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The link takes me to a more readable version today probably due to note at the bottom of the Wikipedia page
1666697118950.png


but it still only gives me the option to go to the edit pages (on a laptop)
1666697366514.png
 
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