# EAX - Error Analysis Exercise

**All pages in this lab**

I. Error Analysis Exercise

II. See Error Analysis Notes for Optical Pumping

## Contents |

# Note

All new students of Physics 111B Experimentation Lab are required to complete this assignment at the beginning of the semester. It will be graded on 50 points basis; a late turn-in is allowed only with the instructor's approval before the due date. Don't jeopardize your grade on your first experiment by being late with this assignment. You need to know how to handle errors before you start a laboratory experiment.

**Important**: View the** video introduction to error analysis **(you need to use your Berkeley email to access this)**.** The Error Analysis Exercise due date is ** Experimentation Lab Report Due Dates.**

# References

[Books available online with UC Berkeley authentication]

- P. Bevington, '"
**Data Reduction and Error Analysis for the Physical Sciences",**McGraw-Hill. [An old standard that is pretty dry but straightforward. Chapter 5 is particularly important.] - A. C. Melissinos and J. Napolitano, ["
**Experiments in Modern Physics, 2nd Edition"**], Academic Press (2003). - W. H. Press, et al., ["
**Numerical Recipes in C**:] The Art of Scientific Computing, 2nd Edition", Cambridge University Press (1992); refer to Ch. 14—"Modeling of Data". [The Numerical Recipes in Pascal or FORTRAN books contain identical information. This book is the standard reference for doing scientific work on computers. Chapter 14 has a good introduction to the method of maximum likelihood, chi–square fitting, modeling data in general, error estimates of fit parameters, and, important for later experiments, the Monte Carlo method of simulation.] - I. G. Hughes and T. P. A. Hase,
**Measurements and their Uncertainties**, Oxford University Press (2010). [This is a well-written thin book that covers many basic concepts of statistics, extremely useful for this course.] - Louis Lyons, "
**A Practical Guide to Data Analysis for Physical Science Students"**(1991) Cambridge Press; QC33.L9 1991 - Yardley Beers, "
**Introduction to the Theory of Error"**; ADDISON-WESLEY PUBLISHING (1957) QA275 B4 1957;

Reprints and other information can be found at Physics 111 Library Site.

# Introduction

In the 111B lab, the experiment does not end when you have finished collecting your data. In many labs, you will be required to perform a detailed analysis of the data you have acquired. The point of any scientific experiment is to make quantitative statements about the properties of the physical world. A common question is, are your measurements consistent with a particular theory or not? This question can only be answered by careful analysis, including both systematic uncertainties and statistical error.

The goals of this exercise are twofold. One is to familiarize students with the basics of error analysis. Ideally, this will serve as a guide during the acquisition and analysis of data throughout the experimentation lab. The second goal is to introduce students to the Python or Matlab computing environments, which you will be using throughout the semester.

Before starting on EAX, please look over either the Python Tutorials https://github.com/avirukt/intro_python or the Intro to Matlab section. Additional resources for using Python are http://pythontutor.com/ and https://datahub.berkeley.edu/