# Normal probability plot analysis of error in measured and derived quantities and standard deviations

Normal probability plot analysis of error in measured and derived quantities and standard deviations Normal probability plot analysis is applied to independent sets of crystallographic structure factor measurements (F) and the derived coordinates (p). Differences between corresponding pairs of structure factors (F) in the two sets are examined in terms of their pooled standard deviations (F) by plotting the ordered statistic m = F/F against the expected normal distribution. Differences between pairs of coordinates (p) are similarly examined in a p = p/p half-normal probability plot. Both plots result in linear arrays of unit slope and zero intercept, for normal error distribution in the experiment and the model and correctly assigned standard deviations. Analysis of departures from this ideal, especially when both plots are considered together, provides detailed information of the kinds of error in m and in p. By inference, the kinds of error in F and F as well as in p and p can be deduced. The normal probability plot R = |Fmeas| - |Fcalc|/Fmeas should ideally also be linear, with unit slope and zero intercept. Deviations from ideal provide considerably more information than the conventional R values. Analysis of R in combination with m plots allows further specification of the error distribution. Examples using these plots are given and discussed, based both on real and on simulated data. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography International Union of Crystallography

# Normal probability plot analysis of error in measured and derived quantities and standard deviations

, Volume 27 (2): 157 – Mar 1, 1971

## Normal probability plot analysis of error in measured and derived quantities and standard deviations

, Volume 27 (2): 157 – Mar 1, 1971

### Abstract

Normal probability plot analysis is applied to independent sets of crystallographic structure factor measurements (F) and the derived coordinates (p). Differences between corresponding pairs of structure factors (F) in the two sets are examined in terms of their pooled standard deviations (F) by plotting the ordered statistic m = F/F against the expected normal distribution. Differences between pairs of coordinates (p) are similarly examined in a p = p/p half-normal probability plot. Both plots result in linear arrays of unit slope and zero intercept, for normal error distribution in the experiment and the model and correctly assigned standard deviations. Analysis of departures from this ideal, especially when both plots are considered together, provides detailed information of the kinds of error in m and in p. By inference, the kinds of error in F and F as well as in p and p can be deduced. The normal probability plot R = |Fmeas| - |Fcalc|/Fmeas should ideally also be linear, with unit slope and zero intercept. Deviations from ideal provide considerably more information than the conventional R values. Analysis of R in combination with m plots allows further specification of the error distribution. Examples using these plots are given and discussed, based both on real and on simulated data.

/lp/international-union-of-crystallography/normal-probability-plot-analysis-of-error-in-measured-and-derived-Lzb3SmjJgX
Publisher
International Union of Crystallography
Copyright (c) 1971 International Union of Crystallography
ISSN
0567-7394
DOI
10.1107/S0567739471000305
Publisher site
See Article on Publisher Site

### Abstract

Normal probability plot analysis is applied to independent sets of crystallographic structure factor measurements (F) and the derived coordinates (p). Differences between corresponding pairs of structure factors (F) in the two sets are examined in terms of their pooled standard deviations (F) by plotting the ordered statistic m = F/F against the expected normal distribution. Differences between pairs of coordinates (p) are similarly examined in a p = p/p half-normal probability plot. Both plots result in linear arrays of unit slope and zero intercept, for normal error distribution in the experiment and the model and correctly assigned standard deviations. Analysis of departures from this ideal, especially when both plots are considered together, provides detailed information of the kinds of error in m and in p. By inference, the kinds of error in F and F as well as in p and p can be deduced. The normal probability plot R = |Fmeas| - |Fcalc|/Fmeas should ideally also be linear, with unit slope and zero intercept. Deviations from ideal provide considerably more information than the conventional R values. Analysis of R in combination with m plots allows further specification of the error distribution. Examples using these plots are given and discussed, based both on real and on simulated data.

### Journal

Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General CrystallographyInternational Union of Crystallography

Published: Mar 1, 1971