Writing up your results – something you will do a lot of in PHYS 211 – is meant to give practice in processing and presenting data to clearly show experimental results. This style guide is meant to help students learn how to appropriately and clearly communicate scientific results to their audience and will highlight both broad structure and fine details in crafting experiment reports.

In PHYS 211, we will not usually ask you to write a full report. Instead, we will ask you to complete smaller assignments which represent “parts” of a report (e.g. just the “Results of X” or just the “Conclusions”).

When writing up an analysis, you should present all the material asked for, but it need not appear in the same order as is listed there. You will need to use your judgement to determine an appropriate order and grouping for what you want to say. In general, discussion of any testing or calibration is done towards the beginning of an analysis, while interpreting the results of fitted quantities tends towards the end of the report.

Here are some general suggestions.

• Provide data tables and/or plots, but avoid “fact-dumps”.
  • Figures are usually better than lists of numbers.
  • If there is a lot of data, consider providing only representative data or plots in the main text, with the remaining placed in an appendix.
• Provide fits where appropriate, motive the fit models, and include relevant fit information and best-fit parameters.
• Provide representative examples of calculations when illustrative (especially for error propagation).
• Discuss error estimates (both systematic and statistical) and detail uncertainty propagation.

• Place your results in context. Compare with expectations and/or literature.
• Discuss the quality of the analysis and reliability of your interpretations.
• Include discussion of issues that arose or remain, and include some thoughts on improvement to the experiment if possible.
• Summarize the take-away points for the reader.

Science communication hinges on clear language. Avoid wishy-washy statements (i.e. statements that are ambiguous or which do not make a strong statement or argument), and be precise and quantitative whenever possible.

• Use terms correctly and define them carefully for the reader when necessary.
  • Any new or unfamiliar physics terms should be spelled out on first use.
  • Always explicitly define variables used in equations. 

• When discussing results, be quantitative and make direct comparisons (with error bars) whenever possible.
  • Talk about consistency and/or discuss probability based on standard deviations.
  • Avoid qualitative descriptions like “pretty close” or “good”.

BAD EXAMPLES:

• “I feel like our results match expectations…” or “I like this value …”
• “The results are pretty good.” or “The value is close to the literature value.”
• “Our value of 7 +/-2  T is not too far from the expected value of 15 T given how hard the experiment is.”
• “We are happy with the results.”

GOOD EXAMPLES:

• “Our value of 3.5 +/- 0.4 ns is consistent (within one standard deviation) with the literature value of 3.848 ns.”

For more information, see all the page Drawing Conclusions.

The discussion section is very important! It should not be an afterthought when writing the report. The discussion section is where you place your results in context.

• Discuss agreement with literature or expectations.
• Call out and discuss discrepancies. Give plausible and concrete suggestions for how these discrepancies can be explained or reconciled.
• Discuss the quality of the data and fits and comment on the uncertainties.
• Call out and discuss any points of concern.
• Discuss any attempts you made to improve the data collection or analysis, even if they did not lead to better results.
• Give further suggestions for improving the apparatus or measurement technique if possible.
• When possible, give broader context (other experiments or other related theory or phenomena) to help explain and interpret the results.

Conclusions need to be quantitative whenever possible.

• Use statistics - propagate errors (include details) and show error bars on plots.
• Include (and discuss) goodness-of-fit parameters (e.g. reduced chi-squared) when appropriate.

Avoid speculation, and instead make statements that you can justify or support.

• If a result does not match expectations, do not just list every possible problem.
• Come up with concrete ideas for what may explain the result and follow-up when possible.

BAD:

• “Human error”
• “Bad data”
• “Could have taken more/better data”
• “Could have done more/better analysis”

GOOD:

• “We thought that placing the scatterer too close to the detector may have led to an increase in the count rate, since photons which normally would have scattered out may have instead been scattered in. Retaking data with the scatterer further away led to count rates more consistent with our expectations.“

• If you cannot test a hypothesis, at least discuss what impact (magnitude, direction) it would have on the final result.

GOOD:

• “If the magnetic field reading were systematically low, that would lead to a final value for the magnetic moment that was higher than the real value, consistent with what we find.”
• “We found a large uncertainty in the timing, because there is ambiguity in when the process actually begins and stops. Modifying the apparatus so that [blah, blah] would make the transition cleaner and would bring that uncertainty down.

As this is an introductory course in experimental methods, a big part of the aim is to teach good uncertainty analysis. For that reason, the graders will be especially keen to see how you estimated uncertainties, quantified statistical and systematic effects, and propagated uncertainties. You must discuss your error analysis in every report, regardless of whether it is specifically mentioned in a rubric item.

A longer discussion of uncertainty analysis can be found on the page Uncertainty Analysis and Significant Digits.

All plots included in the report should be done with python (or an equivalent high-level scripting language or software package); Excel is not a suitable program because the fitting and plotting commands are limited and do not allow users to produce professional-looking plots.

General points to keep in mind when making plots include the following:

• Axes should be labeled with the quantity (and/or variable) being plotted and the unit.
• If multiple sets of data are plotted on the same figure, a legend (or clear description in the caption) should make clear how to identify each set.
• When plotting raw data, individual points should be shown rather than points connected by a line.
  • If error bars can be added without distracting from the readability, they should be explicitly shown.
  • If such error bars will obscure other data or make the plot look cluttered, an appropriate description of the uncertainties can be included in the caption instead.
• When plotting fit functions, a continuous line may be used, but it should not extend beyond the range over which fit data was used. If you wish to extend a fit function beyond the data range, use a dashed line and indicate in the caption.
• Titles are optional, but should be descriptive rather than a simple rehash of what appears on the axes. Avoid titles like “Magnetic Field versus Frequency” in favor of titles which provide new information like “Spectrum of Cs-137”.
• If including annotations on the plot (e.g. to report fit parameters or to indicate values or points of interest), make sure that the normal rules regarding significant figures, units, and overall formatting are followed.
  • If the annotations are so numerous as to be distracting, consider removing them to the caption or to a separate table.
• Avoid excess whitespace.
• Make sure that all points and lines are visible. Do not obscure data with annotations or legends. Extend the plot range if necessary if the first and/or last data point is cut off. Consider using a logarithmic scale if significant portions of the data are crunched into a small area.

Example plots are shown in Figs. 1 and 2.

Figure 1: A good example of a simple data set and fit. Note the error bars, fit (and annotations), clear legend, properly labeled axes, and descriptive title.

Figure 2: A good example of spectrum plot. Note that this time, error bars have been omitted (they would clutter the figure) and that a sub-set of data (that used in the fit) is highlighted.

Figures and tables should be numbered and each figure or table should have a caption which concisely describes what is shown. The caption and plot should be “stand-alone”, i.e. they should make sense when read in isolation without requiring reference to the surrounding text. (That is not to say the caption needs to be 100% complete… just that a person who flipped ahead or back in the report to a figure could reasonably understand what it shows.)

Figures and tables should be referenced in the text in the form Fig. n or Table n. When beginning the sentence with a reference to a figure, spell out the word “Figure” completely.

All numbers and uncertainty reported must include the appropriate number of significant figures. 

Variables should be italicized, but numbers and mathematical symbols should not (non-italicized characters are often referred to as Roman). Descriptive subscript or superscript labels should not be italicized, unless the label includes a variable. Vectors should be bolded or marked with an overarrow. Unit vectors should be indicated by a “hat”.

Units should not be italicized and should be separated from the number by a space. They may be abbreviated or spelled out completely. Use appropriate SI abbreviations for units. For example, Hz, not hz for hertz, and keV, not Kev or KeV for kilo-electron volts.

Reported numbers should include uncertainties and units whenever appropriate. It is always preferable to indicate the number and uncertainty together, before giving the unit, rather than list the two values separately. The preferred format is $n$ +/- $\Delta n$ or $n \pm \Delta n$

In the case of scientific notation, this same philosophy applies to grouping the prefactors together before giving the common exponent.

Short equations and equations which will not be used later can be written inline. Longer equations and equations which will be referenced later should be placed on their own line and numbered. Equations (and single variables) should be treated just like any other word when placed within a sentence. This means that equations (and variables) should include proper punctuation before or after (if applicable) and can be placed anywhere within a sentence. 

When referencing an equation in the text, use the format Eq. (n). When beginning the sentence with a reference to an equation, spell out the word “Equation” completely.

Include appropriate references (including to the lab manual or pages from the wiki) for both text and figures.

• If using an idea or fact which is not your own, or if reproducing a figure, a citation is necessary. Place the citation in the text or caption at the proper location.
• A general reference list at the end is not sufficient; you must additionally cite each use of a resource in the text.
• When using direct text, reproduce the text exactly and use quotation marks or block quote formatting. Again, include a citation in the text at the appropriate location.
• Include a reference list at the end of the report and format it appropriately.
• We do not ask for any particular style, but be consistent throughout the report.

REVIEW THE UNIVERSITY PLAGIARISM GUIDELINES. We have ZERO TOLERANCE for students who plagiarize and cases WILL be referred to the Dean of Students.

Use appendices (in the same PDF document as the rest of the report) to include additional information (e.g. data or additional plots, tedious calculations, sidebar theory, etc.) without breaking the flow of the main report. 

• If there is a single appendix, you may title it Appendix. If there are multiple appendices, you should number or letter them.
• All appendices should include at least some text for context. Don’t just plop down figures or math or tables, but instead give the reader enough information so that they can make sense of what they are looking at without returning to the main text.
• Reference all appendices at the appropriate place in the main text. An appendix should not just be a tack-on, but should be thought of more like “a really long footnote” for some topic in the report.

Avoid attachments and data dumps.

• We DO NOT want to see your code.
• We DO NOT want to see large amounts of raw data.
• It is fine to include tables of data when it is relevant, but it is not appropriate to include, for example, the straight output of from a detector or an attached Excel spreadsheet of collected values or intermediate calculations.
• Use your judgement to decide what is appropriate. Make plots and graphics when possible to handle large data sets.

Provide context.

• We DO want to see context for all plots and calculations. Integrate this information into the main text or relegate to an appendix with appropriate accompanying text.
• All plots and calculations should be discussed in words and referenced appropriately.
• Good example: “We find that the temperature increases linearly with increasing voltage, and a fit of the data yields a slope of $5.04 \pm 0.08$ K/V. (See Fig. 4.).
• Bad example: “Plots and fits are shown below.”

Limit how much you direct the reader to the manual for more information. If the material is key, it should be included, even if you choose to quote directly.

• On the other hand, remember that the report is not intended to be used to recreate the exact experiment, so there’s no need to give every detail; keep it focused.

Abstract are short, but very important. Look over our dedicated page, Writing an Abstract, for more information.