# Deming regression

Command: | Statistics Method comparison & evaluation Deming regression |

## Description

Allows to perform method comparison using the Deming regresson model (Cornbleet & Gochman, 1979).

Whereas the ordinary linear regression method assumes that only the Y measurements are associated with random measurement errors, the Deming method takes measurement errors for both methods into account.

## Required input

Select the variables for the two techniques you want to compare.

For each of both techniques you can either enter 2 variables (which contain repeated measurements) or you can enter only one variable, in which case you will have to enter an already established Coefficient of Variation (CV, expressed as a percentage).

As an option, you can create 2 graphs:

- A scatter diagram with the regression line
- The residuals plot.

Use the Subgroups button if you want to identify subgroups in the scatter diagram and residuals plot. A new dialog box is displayed in which you can select a categorical variable. The graph will display different markers for the different categories in this variable.

## Results

The results are displayed in the following text window:

- Mean and Coefficient of Variation (%) for both methods
- Sample size: the number of (selected) data pairs
- Variance ratio: this is the ratio of the measurement errors of X and Y.
- The regression equation, Intercept and Slope with 95% confidence interval
- The Intercept and Slope are calculated according to Combleet & Gochman, 1979. The standard errors and confidence intervals are estimated using the jackknife method (Armitage et al., 2002).

The 95% confidence interval for the Intercept can be used to test the hypothesis that A=0. This hypothesis is accepted if the confidence interval for A contains the value 0. If the hypothesis is rejected, then it is concluded that A is significantly different from 0 and both methods differ at least by a constant amount.

The 95% confidence interval for the Slope can be used to test the hypothesis that B=1. This hypothesis is accepted if the confidence interval for B contains the value 1. If the hypothesis is rejected, then it is concluded that B is significantly different from 1 and there is at least a proportional difference between the two methods.

## Graphs

The first graph window displays the scatter diagram with regression line (solid line) and identity line (x=y, dotted line)

The second graph windows displays the residuals:

## Literature

- Cornbleet PJ, Gochman N (1979) Incorrect least-squares regression coefficients in method-comparison analysis. Clinical Chemistry 25:432-438. [Abstract]
- Armitage P, Berry G, Matthews JNS (2002) Statistical methods in medical research. 4
^{th}ed. Blackwell Science.

## See also

## External links

- Deming regression on Wikipedia.