NASA TM-105419

Chapter 4—Experiment and Analysis Descriptions

Most NASA reports include one or more sections immediately following the Introduction, or the Symbols section if there is one, that describe how the research or analysis was performed and what types of equipment and materials were used. A precise record of the procedures used is vital in establishing the validity of the results.

This chapter gives the format of the experiment and analysis descriptions as well as information on symbols, units, and errors and precision.

Format of Experiment Descriptions

The format of experiment descriptions varies greatly with the type of work being reported. For example, a report on an experimental program may have separate sections entitled "Apparatus," "Test Procedure," and "Test Specimens," or it may have one combined section entitled "Apparatus and Procedure" with appropriate subsections.

The extent to which the descriptive material is divided by subheadings depends on its complexity or length. Unless the description is brief, the use of subheadings will be extremely helpful to your readers. New and different equipment or procedures require more detailed description than if they are standard. When possible, construct subheadings that relate to those used in the Results section.

It is usually best to describe first the whole and then the parts. Organize descriptions so that statements need not be repeated to bring out associated material. Give enough information directly, or indirectly by reference, so that your readers could reproduce the experiments. Refer where necessary to previous reports, but do not reference another report for one sentence of additional description.

Apparatus Sections

Test facilities section

Generally a new test facility should be described in sufficient detail that its essential workings could be reproduced. A good initial description that can be referenced may greatly simplify future reports. Be sure to note special mechanical devices used. Use photographs and diagrammatic sketches with adequate notation. Try to use standard, accepted terms for equipment, but avoid trade names.

If the basic facility has been adequately described in a previous report, do not repeat the detailed description but reference that report. In your report give the reader just enough information to visualize the equipment. Sometimes reproducing a figure that shows the equipment layout is desirable. Describe any important modifications to the original facility.

Instrumentation section

The discussion of instrumentation may be organized according to normal flow paths through the test facility or according to particular types of instrumentation. Photographs or drawings of the test facility may show the position of instruments, such as thermocouples, pressure tubes, cameras, photoelectric cells, and sampling tubes. A specialized instrument may require more detailed description and additional drawings. The design of instruments may be illustrated with a sketch or referenced to previous work. Commercial instruments are usually described only to the extent necessary to duplicate the results (e.g., "self-balancing potentiometer," "calibrated rotameter," or "flat-plate orifice installed according to ASME specifications").

Materials Section

In reports describing the testing or evaluation of materials, the test materials should be characterized in detail, including the purity of the material, its grain size and density, the method used to produce it, and its thermal history prior to testing. These characteristics are needed to compare the test results with other data on similar materials.

Test Procedure Section

In describing the procedures used in a test program, it is helpful to begin with an introductory paragraph that describes the kind of data obtained in the program. If the procedures used were numerous and complex, summarize them in the introductory paragraph.

The conditions studied can usually be described clearly in a few sentences but may be sufficiently numerous or complex to warrant listing them in a table. State your reasons for selecting these particular conditions.

Describe the test procedures in enough detail that your readers can judge the value of the results and could repeat the experiment. If the procedures are detailed in other publications, reference them and only briefly describe the major steps. Always include enough description to give an overall picture of the operation. A unique operation will require more detail.

Where the calculations performed in analyzing the test data are conventional, it is usually sufficient to reference the type of analysis made and merely include the final equation (or equations) used. Describe nonconventional or little-known analytical methods in more detail. When these methods are lengthy or complex, a sample calculation would be helpful to most readers. It is best included as an appendix.

Format of Analysis Descriptions

If a report presents the results of a theoretical analysis, the experiment description section is replaced by a section that might be entitled "Analysis." If the analysis is lengthy, the details may be included as an appendix. The Analysis section in the main text then includes (1) a statement of the problem, (2) the assumptions and limitations of the analysis, and (3) a brief description of the general analytical method. (Refer your readers to the appendix for details.)

In preparing an Analysis section note the following items:

  1. All numbered and most unnumbered equations are centered between margins and set off from the text by spacing.
  2. An equation and the introductory material that directly precedes it should be presented in correct grammatical form. The introductory material may be followed by a colon, a comma, or no mark of punctuation.
  3. Equations needed for later reference are numbered (1), (2), (3), etc. Identification such as (1a) and (1b) may be used for equivalent or derivative equations. A brace may be used to connect a group of equations with the same number. Equations in appendixes are usually numbered according to the appendix in which they appear ((Al), (A2), (Bl), (B2), etc).
  4. When a numbered equation is repeated, it retains its original number. An equation given more than once should be repeated in exactly the same form.

Symbols Section

Use consistent mathematical notation throughout a report. Because many symbols have different meanings in various fields of science, define all symbols used in a NASA report, including those in figures and tables. If only a few symbols are used, define each in the text as it first occurs. If many symbols are used, group their definitions in a separate section entitled "Symbols." This section directly follows the Introduction or is either the first or the last appendix. Make a symbols list an appendix when it contains more than 30 symbols, when the symbols are used mainly in the appendixes, or when some or all symbols have been used and defined only on the figures and tables.

List symbols in alphabetical order with English symbols preceding Greek symbols. These are followed by subscripts and then superscripts. Capital symbols precede corresponding lowercase ones. Do not define mathematical conventions such as d, exp, and - (bar). When subscripts or superscripts apply to several main-line symbols, do not define them with each symbol but list them separately. Explanatory information (such as formulas or units) follows the definition. No symbol may be used for more than one concept, and usage of symbols and units must be consistent throughout the text, appendixes, tables, and figures. Use symbols that are conventional in your particular field of work.

Define acronyms, initialisms, abbreviations, and the symbols for chemical elements and compounds at their first occurrence in the Summary and again in the main text (e.g., monolithic microwave integrated circuit (MMIC)). They are not defined in the Symbols section. Chemical names are preferably written out throughout the text except when formulas are used or the terms appear frequently.

Abbreviate units after numbers, but write them out otherwise.

Errors and Precision

In any report concerned with numerical values, the accuracy, precision, and reproducibility of the data presented must be clearly stated. Discrepancies within the data should be explained. This material fits best in the Results and Discussion section if based on a comparison of duplicate test results and in the Test Procedure section if based on instrument calibration data. The experimental work must obviously be planned so as to yield the necessary data on accuracy, precision, and reproducibility. Day-to-day check tests at identical test conditions and periodic calibrations of instruments are necessary parts of most experimental programs.

When the terms "accuracy," "precision," and "reproducibility" are used, their exact meanings should be clearly stated, for such terms have different connotations to different people. Accuracy usually denotes the absolute correctness of the determination; precision generally denotes the extent to which a result is free from random accidental errors. A result can be very precise (i.e., all measurements agree) but also inaccurate because of inherent errors in the measurements. Reproducibility denotes the agreement, or lack thereof, between values obtained in like determinations at different times during the test program. Poor reproducibility may be the result of either the precision or the accuracy.

A discussion of accuracy should contain an analysis of possible errors involved in individual measurements and how these errors are reflected in the final results. This is generally expressed as the "maximum probable error." A discussion of precision usually involves comparisons of duplicate results, and the precision is generally expressed in terms of a "deviation." Use standard methods of computing probable errors and deviations whenever possible, and indicate for your reader the methods used.

Questions on policies and procedures should be directed to Natalie Henrich, (216) 433-5301.

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