# Run Deming regression to compare methods in Excel

This tutorial will show you how to set up and interpret a Deming regression to compare methods in Excel using the XLSTAT statistical software.

## Method comparison with the Deming regression

When developing a new method to measure the concentration or the quantity of an element (molecule, micro organism, …) you might want to check whether it gives results that are similar to a reference or comparative method or not.

Deming (1943) developed a regression method, that allows comparing two measurement methods (for example, two techniques for measuring concentration of an analyte), which supposes that measurement error are present in both X and Y. It overcomes the assumptions of the classical linear regression that are inappropriate for this application. XLSTAT provides the Deming regression to evaluate the performance of a method compared to another.

XLSTAT includes both simple and weighted Deming regression. Weighted Deming regression suppose that errors are proportionnal and simple Deming regression suppose that errors are constant.

## Dataset for method comparison with the Deming regression

The data correspond to a medical experiment during which the concentration of an antibody is measured for 8 mice submitted to 8 different doses of a new molecule being tested. For each mouse, a blood sample has been taken and divided into four homogeneous sub-samples. Two methods are being tested each on 2 of the 4 sub-samples. The first method is currently considered as the reference, but it is much more expensive than the second and new method.

Our goal is to check if it is possible to use the new method instead of the reference one.

## Setting up a Deming regression

Once XLSTAT has been started, select the Method validation / Deming regression function, or click on the corresponding button of the Method validation toolbar (see below).

When you click on the button, a dialog box appears. Select the data that correspond to the first method, then to the second method.

When you click OK, computations are launched and results are displayed.

## Interpreting the results of a Deming regression

The first table displays the descriptive statistics for the two methods. The new method has a larger mean but a larger variance as well.

Then, model coefficients are displayed.

The intercept value is -1.909 with a confidence interval including 0. We may thus say that the systematic difference between the two methods is not significantly different from 0.

The slope coefficient is equal to 1.21 with a confidence interval including 1. This means that the proportional difference between the two methods is equal to 1. If 1 is included in the confidence interval, then the hypothesis that the slope is equal to 1 is not rejected.

The confidence intervals are obtained using the jackknife method.

We can say that there are no systematic nor proportional differences between the two methods.

This is confirmed by the regression plot:

We can say that both methods are equivalent and that the new less expensive method can be used to replace the old one.