I doubt there ever was a universal convention. When I was young,
Rsym was calculated from the symmetry related reflections on a
single film. With precession photography there could be a lot of
them, but even the oscillation films often had many mates because
the crystal was aligned with a symmetry axes along the spindle
direction. Rmerge was the agreement of the measurements from
different films from, maybe, multiple crystals. I think the mates
in the Rsym calculation were a subset of those in the Rmerge
calculation. Since there was an Rsym for each film, the average
of all films was reported.
With today's data collection techniques I can't for the life
of me figure out a reason for having both Rsym and Rmerge.
Dale Tronrud
Bart Hazes wrote:
> For what it's worth, I've been told that Rmerge was used originally, in
> the pre-cryo few images per crystal age, to indicate the R-factor for
> merging data collected from multiple crystals. Isym is calculated
> identical but refers to data collected from a single crystal.
>
> To be honest I'm not sure if this reflects history or somebody trying to
> make something out of nothing but I've been using Rsym ever since.
>
> Bart
>
> Phil Evans wrote:
>> I've never been able to discover any difference between Rsym & Rmerge
>> Phil
>>
>> On 21 Jan 2010, at 18:34, james09 pruza wrote:
>>
>>
>>> Dear All CCP4bbers,
>>>
>>> Please help me in finding *R-sym I *(observed), *R-merge I*(obseved),
>>> *R-Free
>>> Error i*n the data provided below. If I am not wrong, Can anyone suggest me
>>> the difference between R-sym and R-merge?
>>>
>>> Thanks in advance for the help.
>>>
>>> James*
>>> *
>>>
>>> R-values of internal consistency :
>>> ======== --------------------
>>> (Anomalous scaling counts I+ and I- as separate hkl.)
>>>
>>> R-merge ( sum |Ij-<I>| / sum |<I>| ) = 23.4 % ( 21.57 % for Fsq > 0)
>>> where <I>=sum(Ij)/N, j=1...N,
>>> calculated from 188629 observations of 60655 /+//-/ reflexions
>>>
>>> - dito within user-defined resolution: 23.4 %
>>> calculated from 188182 observations of 60508 /+//-/ reflexions
>>>
>>>
>>> Sigma-weighted R-merge :
>>> ( sum wj*|Ij-<I>| / sum |<I>| ) = 19.1 %
>>> where <I>=sum(wj*Ij), j=1...N,
>>> with sum(wj)=1,
>>> calculated from 133636 observations of 60655 /+//-/ reflexions
>>>
>>> - dito within user-defined resolution: 19.1 %
>>> calculated from 133323 observations of 60508 /+//-/ reflexions
>>>
>>>
>>> Multiplicity of accepted measurements for unique reflexions, and
>>> completeness C
>>> in equal-volume shells (on average 4161 possible unique reflexions each):
>>> Shell- 1* 2* 3* 4* 5-6* 7-8* 9-12* 13-16* >16* total
>>> C[%]
>>> limits [A] ----- ----- ----- ----- ----- ----- ----- ----- ----- -----
>>> ----
>>> inf. - 30.0 excluded... (but see right below)
>>> 0.0
>>> 30.0 - 6.46 221 878 805 1620 597 0 0 0 0 4121
>>> 95.1
>>> 6.46 - 5.13 73 659 726 1850 840 0 0 0 0 4148
>>> 98.9
>>> 5.13 - 4.48 80 687 841 1823 712 0 0 0 0 4143
>>> 99.1
>>> 4.48 - 4.07 72 673 802 1778 772 0 0 0 0 4097
>>> 99.3
>>> 4.07 - 3.78 94 595 735 1862 831 0 0 0 0 4117
>>> 99.4
>>> 3.78 - 3.56 108 563 738 1883 856 0 0 0 0 4148
>>> 99.7
>>> 3.56 - 3.38 81 519 689 1968 886 0 0 0 0 4143
>>> 99.8
>>> 3.38 - 3.23 49 465 731 1976 877 0 0 0 0 4098
>>> 100.0
>>> 3.23 - 3.11 58 485 772 1950 875 0 0 0 0 4140
>>> 100.0
>>> 3.11 - 3.00 39 457 768 1944 832 0 0 0 0 4040
>>> 98.8
>>> - - - - - - ----- ----- ----- ----- ----- ----- ----- ----- ----- -----
>>> ----
>>> * 30.0 - 3.00 875 5981 7607 18654 8078 0 0 0 0 41195
>>> 99.0
>>> ----------- ----- ----- ----- ----- ----- ----- ----- ----- ----- -----
>>> ----
>>> Below specified lower-resolution limit :
>>> inf. - 30.0 0 1 0 0 0 0 0 0 0 1
>>> Beyond specified high-resolution limit :
>>> 3.00 - 2.99 0 37 25 51 9 0 0 0 0 122
>>>
>>> Same multiplicities as relative percentages [%] and <average multiplicity>
>>> (total measured unique reflexions in each shell = 100.%)
>>> 30.0 - 6.46 5.4 21.3 19.5 39.3 14.5 . . . .
>>> <3.38>
>>> 6.46 - 5.13 1.8 15.9 17.5 44.6 20.3 . . . .
>>> <3.67>
>>> 5.13 - 4.48 1.9 16.6 20.3 44.0 17.2 . . . .
>>> <3.58>
>>> 4.48 - 4.07 1.8 16.4 19.6 43.4 18.8 . . . .
>>> <3.61>
>>> 4.07 - 3.78 2.3 14.5 17.9 45.2 20.2 . . . .
>>> <3.67>
>>> 3.78 - 3.56 2.6 13.6 17.8 45.4 20.6 . . . .
>>> <3.68>
>>> 3.56 - 3.38 2.0 12.5 16.6 47.5 21.4 . . . .
>>> <3.74>
>>> 3.38 - 3.23 1.2 11.3 17.8 48.2 21.4 . . . .
>>> <3.78>
>>> 3.23 - 3.11 1.4 11.7 18.6 47.1 21.1 . . . .
>>> <3.76>
>>> 3.11 - 3.00 1.0 11.3 19.0 48.1 20.6 . . . .
>>> <3.77>
>>> - - - - - - ----- ----- ----- ----- ----- ----- ----- ----- ----- ->>>
>>> * 30.0 - 3.00 2.1 14.5 18.5 45.3 19.6 0.0 0.0 0.0 0.0 100.
>>> <3.66>
>>> ----------- ----- ----- ----- ----- ----- ----- ----- ----- ----- ====
>>> ------
>>> Below specified lower-resolution limit :
>>> inf. - 30.0 . 100.0 . . . . . . .
>>> <2.00>
>>> Beyond specified high-resolution limit :
>>> 3.00 - 2.99 . 30.3 20.5 41.8 7.4 . . . .
>>> <3.27>
>>>
>>>
>>> Multiplicity of centric measurements
>>> Shell- 1* 2* 3* 4* 5-6* 7-8* 9-12* >13* total / poss.
>>> C[%]
>>> limits [A] ----- ----- ----- ----- ----- ----- ----- ----- ----- -----
>>> ----
>>> 30.0 - 6.46 93 354 32 2 0 0 0 0 481 566
>>> 85.0
>>> 6.46 - 5.13 37 251 28 0 0 0 0 0 316 334
>>> 94.6
>>> 5.13 - 4.48 39 209 16 0 0 0 0 0 264 281
>>> 94.0
>>> 4.48 - 4.07 24 193 17 0 0 0 0 0 234 249
>>> 94.0
>>> 4.07 - 3.78 25 169 21 0 0 0 0 0 215 223
>>> 96.4
>>> 3.78 - 3.56 34 161 18 0 0 0 0 0 213 220
>>> 96.8
>>> 3.56 - 3.38 25 157 17 0 0 0 0 0 199 204
>>> 97.5
>>> 3.38 - 3.23 26 145 21 0 0 0 0 0 192 192
>>> 100.0
>>> 3.23 - 3.11 26 138 23 0 0 0 0 0 187 187
>>> 100.0
>>> 3.11 - 3.00 27 129 19 0 0 0 0 0 175 175
>>> 100.0
>>> - - - - - - ----- ----- ----- ----- ----- ----- ----- ----- ----- -----
>>> ----
>>> * 30.0 - 3.00 356 1906 212 2 0 0 0 0 2476 2631
>>> 94.1
>>>
>>>
>>> Multiplicity of acentric measurements for Bijvoet /-/ and /+/ separately :
>>> Shell- 1* 2* 3* 4* 5-6* 7-8* 9-12* >13* total / poss.
>>> C[%]
>>> limits [A] ----- ----- ----- ----- ----- ----- ----- ----- ----- -----
>>> ----
>>> 30.0 - 6.46 1530 4572 790 0 0 0 0 0 6892 7534
>>> 91.5
>>> 6.46 - 5.13 1503 4925 1077 0 0 0 0 0 7505 7720
>>> 97.2
>>> 5.13 - 4.48 1786 4813 974 0 0 0 0 0 7573 7796
>>> 97.1
>>> 4.48 - 4.07 1811 4668 1066 0 0 0 0 0 7545 7754
>>> 97.3
>>> 4.07 - 3.78 1686 4685 1209 0 0 0 0 0 7580 7834
>>> 96.8
>>> 3.78 - 3.56 1756 4595 1308 0 0 0 0 0 7659 7882
>>> 97.2
>>> 3.56 - 3.38 1785 4558 1407 0 0 0 0 0 7750 7896
>>> 98.2
>>> 3.38 - 3.23 1784 4527 1425 0 0 0 0 0 7736 7812
>>> 99.0
>>> 3.23 - 3.11 1833 4549 1415 0 0 0 0 0 7797 7908
>>> 98.6
>>> 3.11 - 3.00 1819 4405 1420 0 0 0 0 0 7644 7826
>>> 97.7
>>> - - - - - - ----- ----- ----- ----- ----- ----- ----- ----- ----- -----
>>> ----
>>> * 30.0 - 3.00 17293 46297 12091 0 0 0 0 0 75681 77962
>>> 97.1
>>>
>>>
>>> Anomalous R-value :
>>> ( sum |<I+>-<I->| / sum |<I+>+<I->| ) = 17.5 %
>>> where <I>=sum(Ij)/N,
>>> calculated from 37074 anomalous pairs (with 143188 measurements:
>>> multiplicity 2.1 <-> 78993 measurements
>>> for I+
>>> multiplicity 1.7 <-> 64195 measurements
>>> for I-
>>> Weighted anomalous R-value :
>>> ( sum |<I+>-<I->| / sum |<I+>+<I->| ) = 18.4 %
>>> where <I>=sum(wj*Ij) with sum(wj)=1,
>>> calculated from 37074 anomalous pairs
>>>
>>>
>>> Table of s-dependent anomalous, and centric, R-factors in equal-volume
>>> shells :
>>> R_ano. = sum { |<I+> - <I->| } / sum { |<I+> + <I->| }
>>> R_cen. = linear R_merge for centric reflexions only.
>>> centric
>>> Resolution s Bijvoet-pairs <I> R_ano. measurements
>>> R_cen.
>>> -----[A]---- ------------- ------- --[%]-- | -------
>>> --[%]--
>>> 30.0 - 6.46 0.000 - 0.077 3252 10168. 12.79 | 806
>>> 29.64
>>> 6.46 - 5.13 0.077 - 0.097 3673 2734. 15.19 | 564
>>> 20.88
>>> 5.13 - 4.48 0.097 - 0.112 3694 4719. 16.01 | 440
>>> 24.88
>>> 4.48 - 4.07 0.112 - 0.123 3682 4326. 17.18 | 418
>>> 23.54
>>> 4.07 - 3.78 0.123 - 0.132 3678 2602. 19.76 | 375
>>> 27.71
>>> 3.78 - 3.56 0.132 - 0.141 3724 1490. 22.87 | 337
>>> 29.09
>>> 3.56 - 3.38 0.141 - 0.148 3806 1032. 26.32 | 317
>>> 34.76
>>> 3.38 - 3.23 0.148 - 0.155 3830 728. 31.24 | 317
>>> 35.64
>>> 3.23 - 3.11 0.155 - 0.161 3844 470. 38.98 | 292
>>> 47.76
>>> 3.11 - 3.00 0.161 - 0.167 3779 358. 48.06 | 250
>>> 59.71
>>> - - - - - - -------- ------- ------- | -------
>>> --[%]--
>>> * 30.0 - 3.00 total : 36962 2745. 17.45% | 4116
>>> 28.09%
>>> -------- ------- ------- -------
>>> Below specified lower-resolution limit :
>>> inf. - 30.0 0.000 - 0.017 1 110. 19.20 |
>>> 0
>>> Beyond specified high-resolution limit :
>>> 3.00 - 2.99 0.167 - 0.167 111 340. 44.46 |
>>> 0
>>>
>>> Summary of neg. <I> : 179 centric reflexions
>>> 2886 /I-/
>>> 2594 /I+/
>>> including 0 pairs with *both* mates <=0
>>>
>>>
>>> Tables of s-dependent R-factors in equal-volume shells :
>>> (Single measurements or negative <I> omitted from all sums.)
>>> R_linear = sum { |I - <I>| } / sum {I}
>>> R_square = SQRT( sum{|I - <I>|**2} / sum{I**2} )
>>>
>>> Resolution s measurements I<0 <I> <I/s> R_squ.
>>> R_lin.
>>> -----[A]---- ------------- -------- ----- ------- ----- --[%]--
>>> --[%]--
>>> 30.0 - 6.46 0.000 - 0.077 12293 119 10081. 5.2 27.28
>>> 18.23
>>> 6.46 - 5.13 0.077 - 0.097 13386 394 2490. 2.7 19.45
>>> 18.50
>>> 5.13 - 4.48 0.097 - 0.112 12787 359 4220. 3.0 21.40
>>> 18.89
>>> 4.48 - 4.07 0.112 - 0.123 12670 452 3638. 2.5 21.79
>>> 21.21
>>> 4.07 - 3.78 0.123 - 0.132 12819 799 2102. 1.6 23.85
>>> 26.60
>>> 3.78 - 3.56 0.132 - 0.141 12820 940 1335. 1.1 26.50
>>> 32.14
>>> 3.56 - 3.38 0.141 - 0.148 12270 1186 958. 0.9 30.64
>>> 37.29
>>> 3.38 - 3.23 0.148 - 0.155 12071 1438 661. 0.6 36.79
>>> 44.73
>>> 3.23 - 3.11 0.155 - 0.161 11613 1619 463. 0.5 43.91
>>> 53.68
>>> 3.11 - 3.00 0.161 - 0.167 10870 1708 376. 0.4 51.01
>>> 61.37
>>> - - - - - - ------ ------ ------- ----- -------
>>> -------
>>> * 30.0 - 3.00 total : 123599 9014 2674. 1.9 26.11%
>>> 22.61%
>>> ------ ------
>>> =======
>>> 4515 non-pos. <I> with 9771 measurements omitted from this table.
>>>
>>> Table of <<I>/sigma(<I>)> for mean values on output file:
>>> ================
>>> Resolution <I> /0/ /+/ /-/
>>> sig<0
>>> -----[A]---- ------------- ------------- ------------- -------------
>>> -----
>>> 30.0 - 6.46 4121 7.7 481 4.5 3551 5.8 3341
>>> 5.7 0
>>> 6.46 - 5.13 4148 4.6 316 2.5 3797 3.5 3708
>>> 3.2 0
>>> 5.13 - 4.48 4143 5.0 264 2.6 3838 3.8 3735
>>> 3.5 0
>>> 4.48 - 4.07 4097 4.3 234 2.1 3835 3.2 3710
>>> 3.0 0
>>> 4.07 - 3.78 4117 3.0 215 1.7 3863 2.2 3717
>>> 2.1 0
>>> 3.78 - 3.56 4148 2.2 213 1.6 3915 1.6 3744
>>> 1.5 0
>>> 3.56 - 3.38 4143 1.6 199 1.3 3938 1.2 3812
>>> 1.1 0
>>> 3.38 - 3.23 4098 1.2 192 0.9 3896 0.8 3840
>>> 0.8 0
>>> 3.23 - 3.11 4140 0.8 187 0.5 3946 0.6 3851
>>> 0.6 0
>>> 3.11 - 3.00 4040 0.6 175 0.4 3853 0.4 3791
>>> 0.4 0
>>> - - - - - - ------------- ------------- ------------- -------------
>>> -----
>>> * 30.0 - 3.00 41195 3.1 2476 2.2 38432 2.3 37249
>>> 2.1 0
>>> ------------- ------------- ------------- -------------
>>> -----
>>> Below specified lower-resolution limit :
>>> inf. - 30.0 1 -1.0 0 ... 1 -0.2 1
>>> -1.0 0
>>> Beyond specified high-resolution limit :
>>> 3.00 - 2.99 122 0.6 10 0.6 112 0.4 111
>>> 0.4 0
>>>
>>> Multiplicity-independent and sigma-weighted R-factors :
>>> PCV = "pooled coefficient of variation"
>>> R_rim = "redundancy-independent merging R-factor" = R_meas.
>>> R_pim = "precision-indicating merging R-factor"
>>> Rw_xxx = sigma-weighted R-factors, where :
>>> <Iw> = sum{ w * I } with sum{ w } = 1
>>> .. defined as:
>>> PCV = sum{ SQRT[ sum{ |Ij - <Ihkl>|**2 }/(n-1) ] } / sum{ <I> }
>>> h j h
>>> R_rim = sum{ SQRT[n/(n-1)] * sum{ |I - <Ihkl>| } } / sum{ I }
>>> R_pim = sum{ SQRT[1/(n-1)] * sum{ |I - <Ihkl>| } } / sum{ I } )
>>> Rw_rim = sum{ SQRT[n/(n-1)] * sum{ w * |I - <Iw>| } } / sum{<Iw>}
>>> Rw_pim = sum{ SQRT[1/(n-1)] * sum{ w * |I - <Iw>| } } / sum{<Iw>}
>>> Rw_squ = SQRT[ sum{ w * |I - <Iw>|**2 } / sum{<Iw>**2} ]
>>> Rw_lin = sum{ w * |I - <Iw>| } / sum{<Iw>}
>>>
>>> Resolution /+//-/ PCV R_rim R_pim Rw_rim Rw_pim Rw_squ.
>>> Rw_lin.
>>> -----[A]---- -------- --[%]-- --[%]-- --[%]-- --[%]-- --[%]-- --[%]--
>>> --[%]--
>>> 30.0 - 6.46 5734 25.53 24.98 16.99 13.73 9.41 11.97
>>> 9.96
>>> 6.46 - 5.13 6143 25.77 25.31 17.18 22.87 15.69 15.44
>>> 16.57
>>> 5.13 - 4.48 5903 26.43 25.94 17.69 21.78 14.98 15.39
>>> 15.75
>>> 4.48 - 4.07 5800 29.69 29.07 19.78 25.73 17.66 18.16
>>> 18.65
>>> 4.07 - 3.78 5810 36.85 36.38 24.69 32.42 22.21 20.15
>>> 23.54
>>> 3.78 - 3.56 5768 44.37 43.66 29.37 40.40 27.53 25.67
>>> 29.44
>>> 3.56 - 3.38 5475 51.15 50.32 33.56 46.70 31.61 30.79
>>> 34.22
>>> 3.38 - 3.23 5375 61.60 60.34 40.23 56.21 38.02 37.98
>>> 41.20
>>> 3.23 - 3.11 5175 73.50 72.31 48.10 66.85 45.19 46.53
>>> 49.03
>>> 3.11 - 3.00 4833 83.97 82.72 55.07 77.06 52.10 57.35
>>> 56.51
>>> --------- ------- ------- ------- ------- ------- -------
>>> -------
>>> * total : 56016 31.39% 30.88% 20.91% 24.72% 16.90% 13.95%
>>> 17.97%
>>>
>>
>>
>
> --
>
> ============================================================================
>
> Bart Hazes (Associate Professor)
> Dept. of Medical Microbiology & Immunology
> University of Alberta
> 1-15 Medical Sciences Building
> Edmonton, Alberta
> Canada, T6G 2H7
> phone: 1-780-492-0042
> fax: 1-780-492-7521
>
> ============================================================================
>
