Appendix A: Data Presentation

  • Number figures, tables, schemes, and equations consecutively in order of appearance in the text.
  • Equations should be presented on their own line and centered with an equation number to the right in parentheses. See Equations sub-section for more detail.
  • Placement of figures, tables, and schemes.
    • In general chemistry (CHE 13X) labs and papers in my liberal studies courses, place figures, tables, and schemes after the paragraph in which they are first mentioned.
    • In my CHE 2XX and 3XX labs, you may simply present your figures, tables, and schemes together at the start of the Results and Discussion section. When you submit a manuscript to a journal, you are responsible for the content only, professional layout designers will integrate your text and graphics appropriately to make sure that each graphic is placed where it fits on the page after its first mention in your text. Lab reports in these courses have so many figures and tables that they often break up the text too often. We do not want you spending any time on layout design to deal with this issue. If you prefer to incorporate your figures, tables, and schemes into the report text you will not be penalized.
  • Make sure that each image and its associated text is visually separate. It is good practice to separate each item with horizontal lines.
    • Tip: In Microsoft Word, type three hyphens (---) then press Enter to create a horizontal line.
    • Tip: In Google Docs, from the menu select Insert → Horizontal line.
Uncertainty
  • All measured values in Results and Discussion must include an estimated uncertainty and units.
  • Exact values do not require uncertainty, unless of course the quantity was measured by some estimating method.
    • Example: "The gel had 12 lanes." The number 12 has no associated uncertainty.
  • The standard deviation of replicate measurements will express the uncertainty for most values in this class.
    • Tip: Use the =STDEV or STDEV.S function in Excel.
  • When you have no replicate measurements, use your judgement to estimate the uncertainty based on the limits of your measuring method.
    • Example: You measure the diameter of a quarter dollar coin with a millimeter ruler. You can see that the quarter is more than 24.0 and less than 25.0 mm, so you could estimate it as 24.5 ± 0.5 mm.
  • If you have no basis for estimating uncertainty the convention in science is to assume that the uncertainty is ± 1 in the position of the last digit. Often in the literature authors omit uncertainty in their text when it is stated elsewhere. However, in this course you should demonstrate your understanding by always reporting the uncertainty in the Results and Discussion section.
    • Example: You have no other information about the uncertainty of 2.50 g. Report it as 2.50 ± 0.01 g.
  • For values derived from multiplication or division of two measurements, the percent uncertainty is the square root of the sum of the squares of the percent uncertainty of the measurements.
    • Example: (862 ± 3 g)/(1.51 ± 0.02 mol) = 571 g/mol. The uncertainty is
      eq
      The reported value is 571 ± 8 g/mol.
  • Round your uncertainty to one significant digit.
    • Your value may not have precision beyond your uncertainty.
      • Example: Report 8.7 ± 0.5 μM, not 8.73 ± 0.48 μM.
Significant digits
  • For measurments with uncertainty, your uncertainty should have one significant digit (see above) and this will typically limit the significant digits of your value.
    • Example: Report 8.7 ± 0.5 μM, not 8.73 ± 0.48 μM.
  • Guard digits are numbers reported beyond the significant digits that are sometimes provided to reduce rounding errors in numerical analysis. To be safe, we suggest that you avoid them when reporting your values. Nonetheless, since they are accepted by professional journals, we will also accept guard digits. If you report guard digits you must clearly indicate your significant digits using one of the conventions below.
    • Older conventions:  Traditionally, guard digits have been distinguished by either underlining or subscripting all of them.
      • Examples: 8.736 ± 0.487 μM and 8.736 ± 0.487 μM. By older conventions, the tenths place is understood to be the last significant digit.
    • Latest conventions: Recently, many textbooks and style guides recommend using either an overline or underline to represent the last significant digit. These styles look neater on the page. I recommend underlining since it is a familiar and universal word processor feature (see MSWord tips for instructions on overlining).
      • Examples: 8.736 ± 0.487 μM, and 8.736 ± 0.487 μM. By the latest conventions, the tenths place is understood to be the last significant digit.
  • It is common in publishing to report trendline equations with one or two guard digits because they are meant to be used for numerical analysis. For this reason, you may report up to five significant digits for trendline equations.
    • Example: It is acceptable to report y = 23.495 x + 1.2948 as a trendline equation.
Units
  • All values must include units unless the quantity is unitless by definition.
  • Use a space between the numeral and the unit, except %, $, and ° (angular degrees).
    • Examples: 150 ml, 17%, 180°, 76 °C.
  • Absorbance is the common log of the intensity ratio and thus has no units for the same reasons that pH has no units. Some scientists erroneously report absorbance units as "a.u." (arbitrary units). This is not correct.1
  • First-order and second-order rate constants (including steady-state values of kcat and kcat/KM for enzymes) should be reported in units of s-1 and M-1 s-1, respectively.
  • Equilibrium binding constants should be reported as dissociation constants (Kd) with units of concentration (M, mM, μM, etc.).
  • Steady-state enzyme activity (specific activity) should be optimally reported as kcat or, if there is uncertainty in the molar concentration of the catalyst, as a Vmax in amount of product formed per amount of protein per unit time (e.g μmol·min-1).
  • You must include units in the coefficients of trendline equations. (Note: At the start of Autumn Quarter 2019 CHE 341, units for coefficients were not required when the equation is presented in a figure caption. This rule will remain in place for the remainder of this quarter and this class specifically).
Figure format
  • Information conveyed in Figures and Schemes should be understandable without reference to the text.
  • Below every figure you should include a figure number (number consecutively) in bold text, a descriptive title (the image itself should not have a title), and a detailed caption.
    • Tip: An easy way to add a caption to a table or figure in Word is to right click it and select the "Add caption" action. This will add a caption to your figure that will stay grouped with it throughout the document and will prevent it from ending up on a separate page.
  • Either the figure or the caption should explain what is being plotted including the essential experimental conditions. See Methods Details Section for what details to include.
  • The only text on a graph should be the axes and data labels. Legends are discouraged, but permitted if they are clear and concise.
  • Important derived values and trend line equations should be presented in the caption, not on the graph itself.
  • Explain all symbols and abbreviations used in the illustrations. Simple symbols such as O, Δ, and ◊. The use of error bars on the data points is recommended.

Example of a good figure: 


imaginase activity

Figure 2. The initial rate of product formation as a function of imaginase concentration. Product formation was monitored by absorbance at 400 nm at 23 °C in 50 mM pH = 7.0 phosphate buffer. The trendline relationship is y = 5.03 (M·sec-1·mM-1imag) x + 0.0210 (M·sec-1) (R2 = 0.992).


Table format
  • Use tables only when the data cannot be presented clearly otherwise.
  • By convention, the table number and title are above the table.
  • Tables are meant to organize information from your text. Do not repeat table data as lists in your text.
  • Tables should not have a caption. If you want to include explanatory material, create footnotes to the title or headings designated by a lowercase letter.
  • Every table column should have a heading.
  • Clearly indicate the units of measure in the heading.
  • Data should be rounded to the nearest significant figure.
  • Give uncertainty estimates to all values, if appropriate.
  • If you choose not to use lines for table cells, the layout should be clear and easy to read.
  • It is good practice to separate your tables from the text with horizontal lines.
    • Tip: In Microsoft Word, type three hyphens (---) then press Enter to create a horizontal line. In Google Docs, from the menu select Insert → Horizontal line.

Below is an example of a perfectly reported table taken from a random article in Biochemistry. Note that one guard digit is included on both the measurement and uncertainty. See above section on Uncertainty for more details.


Table 2. Binding and Antiviral Activities of DV1 and DV1 Dimer a

Analogue

CXCR4 binding (nM) b

antiviral activity using infectious virus assays (μM)

antiviral activity using single-cycle focal infectivity assays (μM)

DV1

43.0  ± 5.0

12.1  ± 3.2

24.03  ± 0.10

DV1 dimer

3.02  ± 0.52

4.4  ± 3.1

10.12  ± 0.49


a. The binding and antiviral activities of DV1 and DV1 dimer are shown by their IC50 values. All data are shown as means ± the standard deviation from at least three independent experiments.
b. 12G5 antibody competition binding assays were used to determine CXCR4 IC50 values. Stably transfected 293 cells were used in the binding experiments. The binding data were analyzed using PRISM (GraphPad Inc., San Diego, CA).


 References

  1. Croarkin C, Tobias P, editors (2012) Engineering Statistics Handbook. National Institute of Standards and Technology, U.S. Department of Commerce: Washington DC, Section 4.1.4. https://www.itl.nist.gov/div898/handbook/pmd/section1/pmd14.htm (accessed Aug 18, 2018).