Measurement Error Example (Supplemental)
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Page 1
Measurement Error Example (Supplemental)
Here we give a hypothetical example that illustrates the properties shown in the measurement
handout. We create a data set where the true measures (Yt and Xt) have a correlation of .7 with
each other
–
but the observed measures (Y and X) both have some degree of random
measurement error, and the reliability of both is .64. The way I am constructing the data set,
using the
corr2data
command, there will be no sampling variability, i.e. we can act as though
we have the entire population.
. matrix input corr = (1,.7,0,0\.7 ,1,0,0\0,0,1,0\0,0,0,1)
. matrix input sd = (4,8,3,6)
. matrix input mean = (10,7,0,0)
. corr2data Yt Xt ey ex, corr(corr) sd(sd) mean(mean) n(500)
(obs 500)
. * Create flawed measures with random measurement error
. gen Y = Yt + ey
. gen X = Xt + ex
A & B.
We see that the flawed, observed measures have the same means as the true measures
–
but their variances & standard deviations are larger:
. sum
Yt Y Xt X
Variable 
Obs
Mean
Std. Dev.
Min
Max
+
Yt 
500
10
4
2.639851
22.83863
Y 
500
10
5
3.706503
26.55569
Xt 
500
7
8
16.16331
28.80884
X 
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 Spring '11
 RichardWilliams
 Errors and residuals in statistics, Observational error, Xt, measurement error

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