**Introduction to Analysis of Variance (ANOVA)**

*
David J. Lilja, Ph.D., P.E.
*

**
Course Overview**

Analysis of variance
(ANOVA) is a general technique for separating the total variation in a set of
measurements into the variation due to measurement noise and the variation due
to real differences among the alternatives being compared. This course provides
a gentle introduction to comparing a set of alternatives using the ANOVA technique.

This course includes
a multiple-choice quiz at the end, which is designed to enhance the understanding
of the course materials.

**
**

Learning Objective

After completing this 3-hour course, you will be able to:

- Use the ANOVA
technique to determine whether there is a statistically significant difference
in the performance of
*k*different systems; - Compute the effects of the different alternatives;
- Compute the mean square values of the effects and the alternatives;
- Use the F-test to determine if two variances are statistically different; and
- Use contrasts to determine where the differences in the alternatives occur.

Reading Assignment

The reading assignment
for this course is **Chapter 5.2** of *Measuring
Computer Performance: A Practitioner's Guide,* David J. Lilja, Cambridge
University Press, 2000.

If you don't have
this book, you can purchase Chapter 1 in PDF format online at **eBooks.com**
for a modest cost. **The price for this course listed on this website does
not include the cost of purchasing the chapter through eBooks.com.
However, the price has been reduced to compensate for the cost of purchasing
the chapter required.** If you plan to take all 6 courses (E132 to E137) based
on this book, you may consider to purchase a hard copy of the book or the entire
book in PDF format online through **eBooks.com**.

**Key
Terms**

- ANOVA
- Analysis of Variance
- One-factor experiment
- Variation
- Effects
- Mean square value
- F-test
- Contrasts

**Study
Notes**

Consider a situation
in which you are trying to compare *k* different computer systems. You
make *n* measurements of the execution time of a benchmark program on
each of the systems for a total of *kn* unique measurements. Due to measurement
noise, it is likely that none of the measurements will be the same. However,
it appears that there could be some differences between the systems in spite
of the noise in your measurements. How can you sort through all of these measurements
to determine whether there actually are real differences between the systems,
or whether the differences you see are due simply to measurement noise (errors)?

Analysis of variance (ANOVA) is a very general statistical technique developed precisely for sorting through these types of measurement experiments.

The basic idea behind ANOVA is to begin by determining the total variation observed in all of the measurements. This variation then is partitioned into two components. The first component is the variation within a single system. This variation is assumed to be caused by measurement noise only. The second component is the variation in the measured values between the systems being compared. This second component of the variation is due to both measurement error and, potentially, due to real differences between the systems.

ANOVA provides us with a technique for comparing these two components of the variation in all of the measurements to determine if the variation between systems is statistically larger than the variation due to the measurement noise within a system. If the variation due to actual differences among the alternatives is enough larger than the variation due to measurement noise, then we can say that there is a statistically significant difference in the performance of the systems tested. The key is determining how much is "enough larger" to be statistically significant.

The ANOVA technique
can be extended to more than one input (factor), as discussed in Chapter 9 of
the course text. However, the basic idea as described in this course remains
the same.

**Quiz**

**Once
you finish studying ****the
above course content,****
you need to
take a quiz
to obtain the PDH credits**.

DISCLAIMER: The materials contained in the online course are not intended as a representation or warranty on the part of PDH Center or any other person/organization named herein. The materials are for general information only. They are not a substitute for competent professional advice. Application of this information to a specific project should be reviewed by a registered architect and/or professional engineer/surveyor. Anyone making use of the information set forth herein does so at their own risk and assumes any and all resulting liability arising therefrom.