**Errors and Confidence Intervals**

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

**
Course Overview**

All measurements
of real computer systems are subject to both random and systematic errors. These
errors introduce uncertainty and imprecision into your measurements, which can
make it difficult to interpret your results. In this course, you will learn
how an appropriate model of these errors can be used to quantify the precision
of your measurements using confidence intervals.

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:

- Understand why errors are typically modeled using the Gaussian (normal) distribution;
- Understand the differences between the accuracy, precision, and resolution of your measuring tools;
- Calculate confidence intervals for the mean value of a collection of measurements;
- Calculate confidence intervals for proportions; and
- Estimate the number of measurements required to obtain a given level of precision in computing a sample mean.

Reading Assignment

The reading assignment
for this course is **Chapter 4** 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**

- Accuracy
- Precision
- Resolution
- Random errors
- Systematic errors
- Gaussian error distribution
- Confidence interval
- Confidence level
- Significance level
- Central limit theorem

**Study
Notes**

All measurements of real computer systems, such as those made using interval timers, for example, will include errors. These errors introduce some uncertainty into your measurements, which can make it difficult to interpret your final results. These errors are due to perturbations in the system being measured from time-sharing, interrupts, real-time processing, non-deterministic cache and memory replacement policies, and so forth. Additionally, the inherent accuracy, precision, and resolution limitations of your measuring tool will add errors to your final measured values.

You will learn
in this course why the *Gaussian* probability distribution is typically
used to model errors in most types of measurements that you are likely to make
of computer systems. This distribution also is known as a *normal* distribution
and is what we more casually refer to as the traditional *bell curve*.

If the distribution
of errors in a set of measurements actually is Gaussian distributed, we can
use the unique properties of this distribution to quantify the precision of
the measurements. In particular, when we make a series of measurements, we compute
the *sample mean* as our best estimate of the actual mean of the event
being measured. We then compute a *confidence interval* for this sample
mean. This confidence interval allows us to say how likely it is that the real
mean is between the two end-points of the computed interval.

In this course, you will learn how to compute confidence intervals for both continuous values and for proportions. You also will learn how to use confidence intervals to estimate how many measurements you will have to make of a given system to obtain a desired level of precision in your estimate of the mean value.

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.