Standard Deviation from IPSLA values

Answered Question
Apr 15th, 2010

I have a question about some of the values that can be pulled from IPSLA.  We would like to calculate the standard deviation for the mean jitter values.  I see several references to using values provided by ip sla (ie Sum2) to calculate this but the way it reads that doesn't seem quite right to me.  Does the Sum2 value = the sum of each (value - mean) squared?  The way it reads to me is that it is the sum of the each value squared.  I'm not sure how the latter would be useful.

If the first case is true then I should be able to just calculate the square root of Sum2/Number and I'm good but I want to confirm that this is accurate.

Correct Answer by Joe Clarke about 6 years 10 months ago

It depends on the sample size.  The formula:

Sum/sqrt(2(Num))

Will give you an estimation of the closeness of the sample stddev to the actual.  A sample size of 10,000 gives you a 1% margin of error.

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Joe Clarke Thu, 04/15/2010 - 23:50

The Sum2 value is the sum of the squares of the jitter values.  So, if say the first positive SD jitter value is 1, number would be 1, sum would be 1, and sum2 would be 1.  If the second value is 2, number would be 2, sum would be 3, and sum2 would be 5.  If the third value was 6, then number would be 3, sum would be 9, and sum2 would be 41.

That would put the mean at 3, and the list of deviations at -2, -1, and 3.  The squares of the deviations are 4, 1, and 9.  The sum of squares is 14, which puts the std. deviation at ~ 2.65.

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David Williams Fri, 04/16/2010 - 07:37

So I guess this goes back to my original concern.  How is the Sum2 value helpful at all in calculating the standard deviation or anything for that matter?  Since we can't pull the exact jitter values from the entire operation we can't calculate Standard Deviation using the standard formula.  All we get here is the number of samples exhibiting jitter,  the sum of those the values, and apparently the sum of the squares of those values.  The values themselves are still a mystery.

Joe Clarke Fri, 04/16/2010 - 10:16

You're right.  Given that you do not have discrete values, you cannot calculate the standard deviation from the statistics output.  However, the Sum2 value will allow you to get the population standard deviation (estimated stddev).  The formula for that is:

s = sqrt((Sum2/Num) - ((Sum/Num)^2))

So, in my example, that would be ~ 2.16.

David Williams Fri, 04/16/2010 - 11:46

Ok, so I think I see where you took this.  Since there is no way to calculate the actual standard deviation due to the lack of discrete values you are doing the next best thing, which is getting us close.  I did replicate this math on my own sample population and compared it to the actual standard deviation and it is definitely close.

I guess I was hoping to get the actual value but this could work.  Do you happen to have any idea what the margin for error is on the results from calculating it this way?  I could do my own analysis, but if you happen to know that would be great!

Thanks for all your help on this!  It is much appreciated.

Dave

Correct Answer
Joe Clarke Fri, 04/16/2010 - 16:11

It depends on the sample size.  The formula:

Sum/sqrt(2(Num))

Will give you an estimation of the closeness of the sample stddev to the actual.  A sample size of 10,000 gives you a 1% margin of error.

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