# Linearity (method comparison)

Linearity is the assumption that the relationship between the methods is linear.

The regression procedures used in method comparison studies assume the relationship between the methods is linear. A CUSUM is a measure of the linearity, defined as a running sum of the number of observations above and below the fitted regression line. When the relationship is linear it is expected the points above and below the line are randomly scattered, and the CUSUM statistic is small. Clusters of points on one side of the regression line produce a large CUSUM statistic.

A formal hypothesis test for linearity is based on the largest CUSUM statistic and the Kolmogorov-Smirnov test. The null hypothesis states that the relationship is linear, against the alternative hypothesis that it is not linear. When the test p-value is small, you can reject the null hypothesis and conclude that the relationship is nonlinear.

- What is Analyse-it?
- What's new?
- Administrator's Guide
- User's Guide
- Statistical Reference Guide
- Distribution
- Compare groups
- Compare pairs
- Contingency tables
- Correlation and association
- Principal component analysis (PCA)
- Factor analysis (FA)
- Item reliability
- Fit model
- Method comparison / Agreement
- Correlation coefficient
- Scatter plot
- Fit Y on X
- Fitting ordinary linear regression
- Fitting Deming regression
- Fitting Passing-Bablok regression
- Linearity
- Residual plot
- Checking the assumptions of the fit
- Average bias
- Estimating the bias between methods at a decision level
- Testing commutability of other materials
- Difference plot (Bland-Altman plot)
- Fit differences
- Plotting a difference plot and estimating the average bias
- Limits of agreement (LoA)
- Plotting the Bland-Altman limits of agreement
- Mountain plot (folded CDF plot)
- Plotting a mountain plot
- Partitioning and reducing the measuring interval
- Agreement measures for binary and semi-quantitative data
- Chance corrected agreement measures for binary and semi-quantitative data
- Agreement plot
- Estimating agreement between two binary or semi-quantitative methods
- Study design
- Study design for qualitative methods
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Survival/Reliability
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 6.15

Published 18-Apr-2023