The Effect of Ignoring Small Measurement Errors in Precision Instrument Calibration
作者:
CarrollRaymond J.,
SpiegelmanClifford H.,
期刊:
Journal of Quality Technology
(Taylor Available online 1986)
卷期:
Volume 18,
issue 3
页码: 170-173
ISSN:0022-4065
年代: 1986
DOI:10.1080/00224065.1986.11979005
出版商: Taylor&Francis
关键词: Calibration;Inverse Regression;Least Squares Regression;Linear Regression;Measurement Error
数据来源: Taylor
摘要:
This paper discusses the effect of measurement errors in both variables when using the simple linear regression model. It is often stated that if the measurement error inxis small, then we can ignore this error and fit the model to data using ordinary least squares. There is some ambiguity in the statistical literature concerning the exact meaning of a small error. For example. Draper and Smith (1981) state that if the measurement error variance inxis small relative to the variability of the truex's, then“errors in thex's can be effectively ignored.”See Montgomery and Peck (1983) for a similar statement. Scheffé(1973) and Mandel (1984) argue for a second criterion, which may be informally summarized that the error inxshould be small relative to (the standard deviation of the observedYabout the line)/(slope of the line). We argue that for calibration experiments, both criteria are useful and important; the former for estimation ofxgivenY, and the latter for the lengths of confidence intervals forxgivenY.
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