What formula is used for std in vertex_average and edge_average?
I am curious what is being used to calculate the standard deviation of the average in gt.vertex_average and gt.edge_average
t2=gt.Graph() t2.add_vertex(2) t2.add_edge(t2.vertex(0), t2.vertex(1)) gt.vertex_average(t2, "in") (0.5, 0.35355339059327373)
Now, shouldn't std be σ(n)=sqrt(((0-0.5)^2+(1-0.5)^2)/2)=0.5 ? also q(n-1)=sqrt((0.5^2+0.5^2)/(2-1))~=0.70710 0.3535 is sqrt(2)/4 which happens to be σ(n-1)/2, so it seems there is some relation to that. A little bigger graph.
t3=gt.Graph() t3.add_vertex(5) t3.add_edge(t3.vertex(0), t3.vertex(1)) gt.vertex_average(t3, "in") (0.2, 0.17888543819998318)
Now, we should have 0,1,0,0,0 series for vertex incoming degree. So Windows calc gives σ(n)=0.4 and σ(n-1)~=0.44721, so where does 0.1788854 come from ? Reason, I am asking because, I have a large graph, where the average looks quite alright but the std makes no sense, as going by the histogram, degree values are quite a bit more distributed than the std would indicate. -- View this message in context: http://main-discussion-list-for-the-graph-tool-project.982480.n3.nabble.com/... Sent from the Main discussion list for the graph-tool project mailing list archive at Nabble.com.
Hi there, On 05/21/2013 01:37 PM, VaSa wrote:
I am curious what is being used to calculate the standard deviation of the average in gt.vertex_average and gt.edge_average
These functions return the standard deviation of *the mean* not the standard deviation of the distribution, which is given by, \sigma_a = \sigma / sqrt(N) where \sigma is the standard deviation of the distribution, and N is the number of samples.
t2=gt.Graph() t2.add_vertex(2) t2.add_edge(t2.vertex(0), t2.vertex(1)) gt.vertex_average(t2, "in") (0.5, 0.35355339059327373)
Now, shouldn't std be σ(n)=sqrt(((0-0.5)^2+(1-0.5)^2)/2)=0.5 ? also q(n-1)=sqrt((0.5^2+0.5^2)/(2-1))~=0.70710
The standard deviation of the mean is therefore: 0.5 / sqrt(2) = 0.35355339059327373... which is what you see.
A little bigger graph.
t3=gt.Graph() t3.add_vertex(5) t3.add_edge(t3.vertex(0), t3.vertex(1)) gt.vertex_average(t3, "in") (0.2, 0.17888543819998318)
Now, we should have 0,1,0,0,0 series for vertex incoming degree. So Windows calc gives σ(n)=0.4 and σ(n-1)~=0.44721, so where does 0.1788854 come from ?
Again, 0.4 / sqrt(5) = 0.17888543819998318...
Reason, I am asking because, I have a large graph, where the average looks quite alright but the std makes no sense, as going by the histogram, degree values are quite a bit more distributed than the std would indicate.
If you want the deviation of the distribution to compare with the histogram, just multiply by sqrt(N). Cheers, Tiago -- Tiago de Paula Peixoto <tiago@skewed.de>
Hi, there I had the same problem. This topic answered me what I wanted, but I have a doubt: Why this calculation is more importante/often then just standard deviation of the distribution? It is just a curiosity because I never saw that measurement :) Thanks, Éverton -- Sent from: https://nabble.skewed.de/
Am 16.07.20 um 21:45 schrieb Éverton Fernandes da Cunha:
Hi, there
I had the same problem. This topic answered me what I wanted, but I have a doubt: Why this calculation is more importante/often then just standard deviation of the distribution?
Because we want to express the uncertainty of the mean, not of the distribution.
It is just a curiosity because I never saw that measurement :)
https://en.wikipedia.org/wiki/Standard_deviation#Standard_deviation_of_the_m... -- Tiago de Paula Peixoto <tiago@skewed.de>
participants (3)
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Tiago de Paula Peixoto -
VaSa -
Éverton Fernandes da Cunha