# INTRODUCTION

These web documents contain supplementary material for laboratory work in the introductory (first year) physics course. They provide an emphasis and point of view which some laboratory manuals lack.

A large part of this material commonly goes by the name "error analysis," a name that often strikes fear into the tender heart of freshmen. Some physics teachers also fear to tackle the subject; and laboratory manuals vary greatly in the extent and character of their treatments. Some ignore it entirely. Some include it in the introduction, then never refer to it again. Some manuals include exhaustive treatments of error theory far beyond the needs of the freshman laboratory.

In the first year physics laboratory one seldom takes sufficient data to mathematically justify the use of the standard deviation. The student who takes upper level physics courses will encounter laboratory work that requires careful statistical treatment of errors; the freshman does not.

The first year physics course has a very full academic menu, so we must use care and good judgment in deciding what essential material to include and what material to omit.

To totally omit a concern for errors does a disservice to the student and leaves the false (and harmful) notion that "getting the right answer" represents the major objective of laboratory work. If students measure the "goodness" of the experiment by how close they come to the "textbook value," then we have perpetuated an attitude that runs counter to good scientific method.

I propose a shift of emphasis. To talk about sophisticated statistical measures of error has little value when one hasn't taken enough data to even know what kind of error distribution the measurements have. One might as well use the crude "maximum error" measure, even with its limitations.

We can, and should, emphasize propagation of errors, and the error propagation equation. No matter what the error distribution, or what fancy, or crude, error measures one uses, error propagation equations describe the effect that errors have on results. The error equations have a far greater importance than merely calculating the error in a result. When a student uses the error equation to optimize the experimental procedure and thereby minimize errors in results, this improves the experiment and its results no matter what error measure one happens to use.

This approach has value even if the student has never heard of "standard deviation" or "kurtosis." As engineer Hilbert Schenck, Jr. has said, "The problem is not...that a model or method may be used clumsily or in the wrong place. Far more serious in the present state of engineering experimentation is that the statistical model will not be used at all." [1]

The error propagation equation serves to guide the experimental strategy, identifying those variables that most affect the error, and it shows what must be done to attain a desired precision in the result. The error equation may sometimes guide the experimenter in the choice of the sizes of variables to produce the best results.

Once the student learns the technique of error propagation analysis, and its use becomes habitual, a solid foundation has been built for later work, and for conceptually understanding the more sophisticated mathematical analyses of error.

Attention to error propagation encourages the student to think, in a critical manner, about the entire experiment, from overall strategy to the minutest detail. This may represent the most valuable benefit from concern for error analysis in the elementary laboratory.

Donald E. Simanek, September 2, 1988

1. Schenck, Hilbert, Jr. Theories of Engineering Experimentation, 2nd Ed. 1968. McGraw-Hill.

Preface to the 1996 revision:

This printing results from a thorough reworking of the text from start to finish, with particular emphasis on tightening the prose, eliminating flabby passages, improving clarity and consistency, and improving readability. Hardly a page escaped numerous changes. Certain parts, particularly the introduction and chapter 9, now conform to the standards of E-prime, by avoiding all forms of the verb "be." Such strict adherence to E-prime does not seem to me appropriate for material which must include physical and mathematical definitions. However, attention has been paid throughout the text to avoid misleading and ambiguous statements resulting from "be", "is", etc.

Preface to the 2004 revision:

This online version is a project that will extend through late 2004 and into 2005. Some additional material and edits have been made, but the material is substantially unchanged.

© 1996, 2004 by Donald E. Simanek.