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re: st: Checking reliability of a measurement device

From   David Airey <[email protected]>
To   [email protected]
Subject   re: st: Checking reliability of a measurement device
Date   Fri, 26 Nov 2004 11:55:28 -0600

This package seems to have an aspect of what you want:
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help for concord (STB-43: sg84; STB-45: sg84.1)
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Concordance correlation coefficient

concord var1 var2 [weight] [if exp] [in range]
[ , summary graph(ccc|loa) snd(sndvar[, replace])
noref reg by(byvar) level(level) graph_options ]


concord computes Lin's (1989) concordance correlation coefficient
for agreement on a continuous measure obtained by two persons
or methods. The Lin coefficient combines measures of both precision
and accuracy to determine whether the observed data significantly
deviate from the line of perfect concordance (i.e., the line at 45
degrees). Lin's coefficient increases in value as a function of the
nearness of the data's reduced major axis to the line of perfect
concordance (the accuracy of the data) and of the tightness of the
data about its reduced major axis (the precision of the data). The
Pearson correlation coefficient, r, the bias-correction factor, C_b,
and the equation of the reduced major axis are reported to show these
components. Note that the concordance correlation coefficient, rho_c,
can be expressed as the product of r, the measure of precision,
and C_b, the measure of accuracy. The optional concordance graph
plots the observed data, the reduced major axis of the data, and the
line of perfect concordance as a graphical display of the observed
concordance of the measures.

concord also provides statistics and optional graphics for Bland and
Altman's limits-of-agreement, "loa", procedure (1986). The loa, a
data-scale assessment of the degree of agreement, is a complementary
approach to the relationship-scale approach of Lin.

The user provides the pairs of measurements for a single property as
observations in variables var1 and var2. Frequency weights may
be specified and used. Missing values (if any) are deleted in a
casewise manner.


graph(ccc) requests a graphical display of the data, the line of
perfect concordance and the reduced major axis of the data. The
reduced major axis or SD line goes through the intersection of the
means and has slope given by the sign of Pearson's r and the ratio
of the standard deviations. The SD line serves as a summary of
the center of the data.

graph(loa) requests a graphical display of the loa, the mean
difference, and the data presented as paired differences plotted
against pair-wise means. A Normal plot for the differences is
also shown.

snd(sndvar[, replace]) saves the standard normal deviates
produced for the Normal plot generated by graph(loa). The values
are saved in variable sndvar. If sndvar does not exist, it is
created. If sndvar exists, an error will occur unless replace
is also specified. This option is ignored if graph(loa) is not

noref suppresses the reference line at y=0 in the loa plot.
This option is ignored if graph(loa) is not requested.

reg adds a regression line to the loa plot fitting the paired
differences to the pair-wise means. This option is ignored if
graph(loa) is not requested.

summary requests summary statistics.

by(byvar) produces separate results for groups of observations
defined by byvar.

level sets the confidence level % for the CI; default is 95%.

graph_options are those allowed with graph, twoway. Setting
t1title(.) blanks out the default t1title. The default
graph_options for graph(ccc) are connect(.l) symbol(o.) pen(22)
for the data points and SD line, respectively, along with default
titles and labels. The default graph_options for graph(loa)
include connect(lll.l) symbol(...o.) pen(35324) for the lower
confidence interval limit, the mean difference, the upper confidence
interval limit, the data points, and the regression line (if
requested) respectively, along with default titles and labels.
(The user is not allowed to modify the graph options for the Normal
probability plot.)

Saved values (if by option not used)

S_1 number of observations compared
S_2 concordance correlation coefficient rho_c
S_3 standard error of rho_c
S_4 lower CI limit (asymptotic)
S_5 upper CI limit (asymptotic)
S_6 lower CI limit (z-transform)
S_7 upper CI limit (z-transform)
S_8 bias-correction factor C_b
S_9 mean difference
S_10 standard deviation of mean difference
S_11 lower loa CI limit
S_12 upper loa CI limit


. concord rater1 rater2

. concord rater1 rater2 [fw=freq]

. concord rater1 rater2, s g(c)

. concord rater1 rater2, level(90) by(grp)

. concord rater1 rater2, g(l)


Thomas J. Steichen
[email protected]

Nicholas J. Cox
University of Durham, UK
[email protected]


Bland, J. M., Altman, D. G. 1986. Statistical methods for
assessing agreement between two methods of clinical measurement.
Lancet I, 307-310.

Lin, L. I-K. 1989. A concordance correlation coefficient to
evaluate reproducibility. Biometrics 45: 255-268.

Also see

STB: sg84.1 (STB-45), sg84 (STB-43)

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Hi Statalisters,

a Dentistry PhD student did some measurements on 12
teeth with varying conditions and he asked me how
could he show that the device used for the
measurements is reliable. More specifically each one
of the 12 teeth has been measured by this device by 2
raters (a and b) X 2 time points (week 1 and week 2) X
6 relative positions =   24 measurements. The goal is
to show that the discrepancies among measurements are
not statistically significant.
You might look at Stata's "kappa" and "alpha" commands...


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