[email protected] wrote:

Hi All,

I am wondering why f/sigf is always about twice of i/sigi. Is there any mathematics behind this relation? Maybe it is not directly related to phenix, but i sincerely hope someone could help me with it.

I'm not sure if that is exactly the case, and it may depend on the the distribution of errors and the size of the error, but in the limit of small errors it should be a good approximatin. Start with some calculus: d/dx(x^2) = 2x or dx^2 = 2xdx (the change in x^2 is 2*x times the change in x but we like to express as a fraction, or percent error, so divide both sides by x^2 dx^2/x^2 = 2 dx/x the percentage change in x^2 is twice the percentage change in x (for small dx) Now say <F> is X, and dX is the distance from that to one of the measurements. each of the measurements will be twice as far from the mean values when expressed as I as when expressed as F. Then run that through the root-mean-square math for calculating sigma, and see if it doesn't come out twice as large for I as for F. Or take an example: F is 100, which was derived from I=10000 a second measure is F=101 (1% different), which was derived form I=101^2 = 10201 (2.01% different)

Thank you in advance! Fengyun

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Thanks for asking! not often I can come up with the answer to a math question. Of course I answered the inverse- why sigmaI/I is 2 x sigmaF/F but close enough. eab Edward A. Berry wrote:

Edward A. Berry wrote:

...

[email protected] wrote:

...

Hi All,

I am wondering why f/sigf is always about twice of i/sigi. Is there any mathematics behind this relation? Maybe it is not directly related to phenix, but i sincerely hope someone could help me with it.

I'm not sure if that is exactly the case, and it may depend on the the distribution of errors and the size of the error, but in the limit of small errors it should be a good approximatin.

Start with some calculus: d/dx(x^2) = 2x or dx^2 = 2xdx (the change in x^2 is 2*x times the change in x

but we like to express as a fraction, or percent error, so divide both sides by x^2

dx^2/x^2 = 2 dx/x the percentage change in x^2 is twice the percentage change in x (for small dx)

Now say <F> is X, and dX is the distance from that to one of the measurements. each of the measurements will be twice as far from the mean values when expressed as I as when expressed as F. Then run that through the root-mean-square math for calculating sigma, and see if it doesn't come out twice as large for I as for F.

Better, use chain rule for propagation of error- sigma(F(I)) = Sigma(I)*dF/dI

...

Or take an example: F is 100, which was derived from I=10000 a second measure is F=101 (1% different), which was derived form I=101^2 = 10201 (2.01% different)

...

Thank you in advance! Fengyun

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thank you! Quoting Nathaniel Echols :

On Fri, Jul 13, 2012 at 2:25 PM, wrote:

...

I am wondering why f/sigf is always about twice of i/sigi. Is there any mathematics behind this relation? Maybe it is not directly related to phenix, but i sincerely hope someone could help me with it.

I don't know the logic behind this, but from notes in our code, the default implementation appears to be this one:

http://www.iucr.org/__data/iucr/cif/software/xtal/xtal372htmlman/html/addref...

specifically, section 4.5.2.4.

-Nat

Hi all, Sorry to post here. I tried to post to CCP4BB, but it takes me one day to subscribe, confirm and doing again and again, but i still could not email to the list. Hope someone could help me. Thanks! I have to merge several datasets from different crystals because the crystals suffer from severe radiation damage. I read some previous posts and follow the protocol as described, 1) individually process the data; 2) scaleit to compare the Rfactors between different datasets; 3) renumber the batch number; 4) for those with low R-factor files (below 0.25), sort them; 5) scala the sorted file. the script i used for the SCALA is, scales batch brotaion spacing 5 which is the one in CCP4 example script that recommended for synchrontron data. For the first four dataset that are all cutoff to about 3.0A based on I/sigI, and the statistics are like this, N 1/d^2 Dmin(A) Rmrg Rfull Rcum Av_I SIGMA I/sigma $$ 1 0.0111 9.49 0.038 0.030 0.038 1934 125.2 15.5 2 0.0222 6.71 0.050 0.009 0.044 1182 92.4 12.8 3 0.0333 5.48 0.086 0.018 0.055 565 71.0 8.0 4 0.0444 4.74 0.093 0.166 0.065 724 100.2 7.2 5 0.0556 4.24 0.105 0.139 0.074 746 116.9 6.4 6 0.0667 3.87 0.143 0.058 0.085 522 105.4 5.0 7 0.0778 3.59 0.217 0.142 0.098 358 107.8 3.3 8 0.0889 3.35 0.365 0.265 0.115 216 109.5 2.0 9 0.1000 3.16 0.634 2.509 0.134 126 110.0 1.1 10 0.1111 3.00 0.965 10.157 0.154 81 109.8 0.7 For the fifth data cutoff to 2.76A, the stastics for the single data is like this, N 1/d^2 Dmin(A) Rmrg Rfull Rcum Av_I SIGMA I/sigma $$ 1 0.0131 8.73 0.031 0.036 0.031 6866 416.2 16.5 2 0.0263 6.17 0.034 0.036 0.032 2994 185.5 16.1 3 0.0394 5.04 0.039 0.040 0.034 2327 185.5 12.5 4 0.0525 4.36 0.039 0.045 0.036 3358 249.6 13.5 5 0.0656 3.90 0.047 0.048 0.038 2226 184.2 12.1 6 0.0788 3.56 0.064 0.059 0.041 1390 151.7 9.2 7 0.0919 3.30 0.101 0.084 0.045 787 118.0 6.7 8 0.1050 3.09 0.145 0.114 0.048 482 98.8 4.9 9 0.1181 2.91 0.271 0.234 0.053 259 96.5 2.7 10 0.1313 2.76 0.398 0.333 0.058 183 102.8 1.8 Then i merge this fifth data with the other four and get the stastics like this, N 1/d^2 Dmin(A) Rmrg Rfull Rcum Av_I SIGMA I/sigma $$ 1 0.0131 8.73 0.072 0.048 0.072 7545 954.4 7.9 2 0.0263 6.17 0.100 0.057 0.085 3417 528.8 6.5 3 0.0394 5.04 0.145 0.072 0.103 2497 543.6 4.6 4 0.0525 4.36 0.158 0.089 0.121 3308 790.6 4.2 5 0.0656 3.90 0.200 0.091 0.138 2374 710.3 3.3 6 0.0788 3.56 0.299 0.128 0.158 1496 663.8 2.3 7 0.0919 3.30 0.462 0.173 0.177 848 644.7 1.3 8 0.1050 3.09 0.577 0.144 0.187 483 414.7 1.2 9 0.1181 2.91 0.720 0.265 0.192 311 358.2 0.9 10 0.1312 2.76 0.392 0.342 0.192 217 122.7 1.8 My question is that after why the SIG_I becomes very large at different resolution shells merging the five data. Say, at 8.73A, merging the four low-resolution files give about SIG_I of 125; the single high-resolution file give 416, but after merging, they give up to 954, is this normal? or i made something wrong? Thank you very much in advance! Fengyun