# Accession Number:

## ADA159104

# Title:

## A Note on the Effect of Ignoring Small Measurement Errors in Precision Instrument Calibration.

# Descriptive Note:

## Technical rept. Sep 84-Sep 85,

# Corporate Author:

## NORTH CAROLINA UNIV AT CHAPEL HILL INST OF STATISTICS

# Personal Author(s):

# Report Date:

## 1985-06-01

# Pagination or Media Count:

## 17.0

# Abstract:

The authors focus is the simple linear regression model with measurement errors in both variables. It is often stated that if the measurement error in x is 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 in x is small relative to the variability of the true xs, then errors in the xs can be effectively ignored, see Montgomery Peck 1983 for a similar statement. Scheffe 1983 and Mandel 1984 argue for a second criterion, which may be informally summarized that the error in x should be small relative to the standard deviation of the observed Y about the lineslope of the line. We argue that for calibration experiments both criteria are useful and important, the former for estimation of x given Y and the latter for confidence intervals for x given Y. Keywords Confidence intervals. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability
- Test Facilities, Equipment and Methods