# FOUR. Variance Matrices and Linear Transformations

Published Online: 11 AUG 2003

DOI: 10.1002/0471467979.ch4

Copyright © 2003 John Wiley & Sons, Inc.

Book Title

## Quantitative Methods in Population Health: Extensions of Ordinary Regression

Additional Information

#### How to Cite

Palta, M. (2003) Variance Matrices and Linear Transformations, in Quantitative Methods in Population Health: Extensions of Ordinary Regression, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471467979.ch4

#### Publication History

- Published Online: 11 AUG 2003
- Published Print: 15 AUG 2003

#### Book Series:

#### Book Series Editors:

- Walter A. Shewhart and
- Samuel S. Wilks

#### ISBN Information

Print ISBN: 9780471455059

Online ISBN: 9780471467977

- Summary
- Chapter

### Keywords:

- variance matrix;
- correlation matrix;
- linear transformation;
- variance of difference;
- variance of mean;
- paired t-test;
- matching;
- interaction effect;
- standard error;
- PROC TTEST

### Summary

We define the variance matrix including covariance elements. Correlation matrix. Definition of linear transformation. Variance matrix of a linear transformation. Application of variance formula to obtain the variance of means and difference of correlated observations. Implications for study design Example of comparing the variance used for paired and unpaired t-test. Obtaining the standard error of the regression coefficient of a main effect in the presence of interaction two ways, applied to the regression of systolic blood pressure on age, BMI and their interaction. PROC REG with the COVB feature to obtain the variance matrix of the regression coefficients. Paired and unpaired t-tests by PROC TTEST illustrated by comparison of glycosylated hemoglobin between first two years of type 1 diabetes.