Lab Report Format Handouts - Occidental College

Occidental College
Physics Department
Advanced Lab I/II
Lab Report Format
Format. This is the format for this semester’s laboratory reports. Note that this is not
the same format that was used for labs in introductory physics. Some parts may have to be
modified in content to conform to the special requirements of a particular experiment. The
guiding rule for any report is that the report must be intelligible, without reference to other
material, to a person familiar with basic physics (i.e. the content of Physics 106, 110, 120,
240, and 250).
• Start the report with the experiment’s title, your name and that of your partner (if
any), and the date of the report.
• Objective. This part should be only a few words in length, describing the objective of
the experiment. Care must be taken in defining the scope of the experiment.
• Introduction. A full discussion of the relevant background, keeping in mind the guiding
rule given above. Discuss the importance of the experiment (why you are doing it) and
develop any theoretical results used in the remainder of the report.
• Methods and Apparatus. Describe in detail what was measured and how it was measured.
Do not simply refer to the lab manual or other reference. This part should include
block diagrams, circuit diagrams, and/or descriptions or pertinent experimental
apparatus. Where appropriate, specifications (meter range, etc.) and type (manufacturer
and model number etc.) of apparatus should be included.
• Analysis of Data. This part generally includes data reduction which may be included in
tabular form with the raw experimental data, and the compilation of the experimental
results pertinent to the experiment objective. A discussion of experimental error is an
important part of the analysis of most experiments and should include a determination
of the largest source of error. Answers to assigned questions should also be included
in this part of the report.
• Conclusion. This part includes a statement concerning the attainment of the objective
of the experiment. This statement should include a summary of numerical results
of the experiment. In addition, this part may include the experimenter’s comments
concerning the adequacy of the apparatus, alternative approaches to the objective, etc.

Some Common Problems/Mistakes in Advanced Lab Reports
• Plagiarism. It is not OK to copy parts of another document into your report. Figures
and quotes taken from the literature must be referenced appropriately. See the student
handbook under ”Academic Policies” for more detail. It is also not OK to quote or
paraphrase large portions of other documents (e.g. the lab manual) even if properly
referenced. Referenced quotes should support your writing, not substitute for it.
• Poor writing. It is important that you be able to communicate your knowledge to
others in written form. Correct spelling and sentence structure are important in any
scientific report. The report should flow like a story, with details included as they are
relevant. The conclusion is a brief summary of results, not a collection of last minute
thoughts or details you forgot to put in earlier. Proofread your report before handing
it in. Obvious mistakes and omissions reflect badly on the author.
• Significant figures and error analysis. Take care to present the correct number of significant
figures in your answer. Do a complete job with the error analysis. Simplifications
(e.g. ignoring some of the uncertainties) are OK if you carefully justify them. “It
makes my life easier” is not an appropriate justification.
• Examine the entire lab description for items to be included in your report. They are
not all listed in the “Procedure” portion of the lab manual.
• The basic rule is that the report must be intelligible, without reference to other material,
to a person familiar with basic physics. You must include enough background
material to inform such a person of the necessary details.
• Include your raw experimental data in your report. Give a sample calculation showing
how you analyzed the raw data as well as how you obtained your uncertainty.
• When comparing your experimental result to a known value, do not discuss the discrepany
in terms of percentage error. Rather, discuss any discrepancy in comparison
to the relevant uncertainties.

Occidental College
Physics Department
Some Rules for Lab Reporting
1. Numbers less than one should include leading zeros (e.g., 0.235, not .235)
2. When an end result is an experimentally obtained value, the value should always be given
along with its uncertainty. For example, h/e = (4.212 ± 0.071) × 10 −15 J · s/C.
3. When using scientific notation to state a result and its uncertainty, use the same factor of ten
for both. For example, (1.50 ± 0.02) × 10 −3 rather than 1.50 × 10 −3 ± 2 × 10 −5 .
4. The final reported uncertainty should never have more than two significant figures
5. The experimentally obtained value and the uncertainty should have consistent number of
digits. When using a common scientific notation to state a result and its uncertainty, this
means that the number of digits to the right of the decimal point will be the same. See the
above examples.
6. If you find an experimental value for a quantity that has a well-known value, you should always
compare your result with the well-known value. Further, this comparison should always be
in terms of your uncertainty value(s) and be followed by a simple statement about the level
of agreement. For example, “The absolute difference between our experimental value and the
accepted value is less than the experimental uncertainty. The agreement is therefore good”
rather than “The experimental value and the accepted value differ by three percent, which is
close.”
7. In most cases, the scales on a graph should be adjusted so that the data fills the graph. There
is no rule that the origin must always be displayed.
8. The axis labels should include the quantity being plotted and its units. Be specific on the
names. For example, use “Stopping Potential, V s (V)”, not “voltage”.
9. The numerical labels for the tic marks on the graph axes should have no more significant
figures than is necessary to properly distinguish the labels. Also, the labels should all have
the same number of significant figures. For example, use 0.5, 1.0, 1.5, 2.0 rather than 0.5, 1,
1.50, 2.
10. Common multiplicative factors should be removed from the tic mark labels and included in
the units for that axis. For example, use tic mark labels 1,2,3 and make the units 10 14 Hz or
use tic mark labels 100,200,300 and make the units THz rather than use use tic mark labels
1 E14, 2 E14, 3 E14.
11. Each column of a table should have a unique label and, when appropriate, the units for
the quantity should be given. If you use a symbol for a column label, make sure that it is
explained somewhere in the report and that the symbol is consistent with usage in the rest
of the report. For example, if you used f for frequency in a displayed equation, then your
column heading for frequency should be f(Hz), not F or ν. Numerical data and column labels
should be aligned vertically. The same sig fig rules given above apply to tables.
Rev. 1/2013 DLE

Occidental College
Advanced Lab
Physics Department
Lab
Forms for References
The following are standard forms for references in the journals of the American Institute of Physics,
followed by examples of proper usage. Standard abbreviations for journal names and additional
details and examples may be found in the AIP Style Manual, (American Institute of Physics,
Melville, N.Y, 1990) which is also available at http://www.aip.org/pubservs/style/4thed/toc.html.
Where there is variation amongst the journals we have followed the format of the American Journal
of Physics. Note the need for page numbers in book references.
Book: author(s), title, (publisher, place, date), page(s) referenced.
John David Jackson, Classical Electrodynamics, 2nd Edition, (Wiley, New York, 1975), pp. 582-584.
David J. Griffiths, Introduction to Electrodynamics, 3rd Edition, (Prentice Hall, New Jersey, 1999),
pp. 369-370.
Journal article: author(s), title, journal, volume, pages, (year).
J. H. Malmberg and C. F. Driscoll, “Long-Time Containment of a Pure Electron Plasma,” Phys.
Rev. Lett. 44, 654-657 (1980).
J. Notte and J. Fajans, “The effect of asymmetries on non-neutral plasma confinement time,” Phys.
Plasmas 1, 1123 (1994).
Paper in edited volume: author(s), paper title, volume title, editor(s), (publisher, place, date),
page(s) referenced.
Roy W. Gould, “Wave Angular Momentum in Nonneutral Plasmas,” in Non-Neutral Plasmas III,
edited by John J. Bollinger, Ross L. Spencer, and Ronald C. Davidson, (American Institute of
Physics, Melville, N.Y, 1999), p. 170.
Websites (MLA format): Author’s Last Name, First Name (if available). “Title of Page/Document”.
Title of the Web Site. Sponsoring Organization, Publication/Updated Date. Medium of Publication.
Date of Access. < URL >.
Bromwich, Michael R. “Criminal Calls: A Review of the Bureau of Prisons’ Management of Inmate
Telephone Privileges.” United States Department of Justice, Aug. 1999. Web. 10 Jan. 2004.
< http : //www.usdoj.gov/oig/special/9908/exec.htm >.
“Argonne Researchers Create Powerful Stem Cells From Blood.” Argonne National Laboratory, 24
Feb. 2003. Web. 10 Jan. 2004. < http : //www.anl.gov/Media Center/News/2003/news030224.htm >.
Rev. 1/2013 DLE

Occidental College
Advanced Lab
Physics Department
Lab
Weighted Least Squares Linear Fit
From the introductory physics labs you are familiar with the process of obtaining a least squares
linear fit to a set of data. In this process you find, for a set of data pairs (x i , y i ), the best fit straight
line y = mx+b. The procedure gives the slope of the line m and the y-intercept b. It also gives the
uncertainty in these quantities: σ m and σ b . This can be done by using the standard equations for
least squares linear fit 1 or, in Excel, by using the Regression tool under the Tools/Data Analysis
tab or by using the function LINEST.
The basic least squares fit procedure, however, assumes that the uncertainty in your data is
the same for each data point. In experiments it is not unusual for the uncertainty to vary from
point to point, so we need a method to include this variation in our analysis. The basic idea is
that data points with small uncertainties should be weighted more heavily than those with large
uncertainties when determining the linear fit. The results below show how this is done.
We assume N data pairs (x i , y i ) with i running from 1 to N. Let each y i have an associated
uncertainty σ i . We define a weight for the i th data point as W i = 1/σi 2 . This makes sense because
a small uncertainty should have a heavier weight. Given this setup and using the same technique
in Ref. 1 of maximizing the probability, we obtain
b = (∑ W i x 2 i )(∑ W i y i ) − ( ∑ W i x i )( ∑ W i x i y i )
( ∑ W i )( ∑ W i x 2 i ) − (∑ W i x i ) 2 (1)
m = (∑ W i )( ∑ W i x i y i ) − ( ∑ W i x i )( ∑ W i y i )
( ∑ W i )( ∑ W i x 2 i ) − (∑ W i x i ) 2 (2)
σ 2 b =
∑ Wi x 2 i
( ∑ W i )( ∑ W i x 2 i ) − (∑ W i x i ) 2 (3)
σ 2 m =
where the sum in these expressions runs from i = 1 to N.
∑ Wi
( ∑ W i )( ∑ W i x 2 i ) − (∑ W i x i ) 2 (4)
Rev. 1/2013 DLE
1 John R. Taylor, An Introduction to Error Analysis, 2nd ed. (University Science Books, CA, 1997), pp. 182–190.