Vanderbilt University Assessment Website

Reporting Quantitative Results

General Practices in Reporting Quantitative Data

  • Data can be presented in text, table, or chart form. When presenting data in all three forms, care should be taken to include only information and/or images that help to clarify points being made.
  • For reference purposes, tables are usually the sensible option. Extensive tables should usually appear as appendices at the end of a report.
  • In general, tables are better than graphs for giving structured numeric information. Graphs are better for demonstrating trends, making comparisons or showing relationships.
  • Text alone should not be used to convey more than three or four numbers. Sets of numerical results should usually be presented as tables or pictures, rather than included in the text.
  • When whole numbers are given in text, numbers less than, or equal to, nine should be written as words, while numbers from 10 upwards should be written in digits.
  • When decimal numbers are quoted, the number of significant digits should be consistent. Generally, one point past the decimal point is sufficient.
  • Tables and graphs should be self-explanatory. The reader should be able to understand them without detailed reference to the text. The title should be informative and rows and columns of tables or axes of graphs should be clearly labeled. On the other hand, the text should always include mention of the key points in a table or figure. If a table does not warrant discussion, it should not be there.
  • Statistical information beyond means and frequencies (e.g., standard deviations, p-values, t-values), is usually required in formal scientific papers, but may not be necessary for a more general readership. When presented, care should be taken to do so in a way that does not obscure the main message of the table or graph.

Back to Top

Presenting Data in Charts and Graphs

Charts and graphs are often the best way to demonstrate trends in data and make comparisons between different groups. Different types of graphs are required to most efficiently and effectively present different types of findings. The following sections detail the most common types of charts and graphs and the important rules governing their use.

Pie Charts

  • Pie charts have limited utility. They can only be used to show parts of a whole (if all parts total 100%).
  • Pie charts emphasize general findings, but do not make small differences apparent.
  • Pie charts should only be used to represent categorical data with a relatively small number of values and should not consist of more than five or six slices.
  • When presenting a pie chart, it is better not to use 3-D features, or break out the pieces, as this often makes it more difficult to compare the relative size of the slices.

    3d
    2d
  • It is always necessary to include category labels or a legend that describes which slice corresponds with which category. If labels are brief enough, it is better to place category labels directly next to the pie slices to which they correspond.
  • It is good practice to include value labels (indicating the percentage of the pie represented by a given slice).
  • It is also good to pre-sort data so that, clockwise or counter-clockwise, the relative size of pie slices is most apparent.

    Unsorted
    Sorted
  • The purpose of color in pie charts is to differentiate between pie slices to further facilitate comparison. When using color, it should be used thematically. The best use of color in a size-ordered pie chart is a progression of dark to light hues from the largest slice to smallest slice (see 2-D pie chart above).
  • A bar graph, rather than multiple pie graphs, is the better option if data need to be compared by more than one value. Pie graphs should not be used to represent more than one categorization of data.

    Multiple Pie Graphs

    Pie1
    Pie2

    A Single Bar Graph

    Singlebar

Back to Top

Bar Graphs

  • Bar graphs are used for direct comparison of data (e.g., student GPA’s by class year).
  • Bar graphs can also be used to show time series data when the number of time intervals is small.
  • If all values are positive integers, the scale should generally use 0 as a baseline. In the event that values include both positive and negative integers (e.g., in graphing differences in means), 0 should be the midpoint of the scale.
  • Scale ranges should be standardized and not vary between graphs, when possible.
  • Always try to avoid using 3-D features in a bar graph. The complexity of 3-D graphs makes them ineffective in conveying results to most audiences and there is usually a greater amount of data distortion that occurs.
  • Bar graphs may be vertical or horizontal. The only difference between horizontal and vertical bars is that horizontal bar charts are seldom used to portray time series.
  • To facilitate comparison and analysis, it is desirable that columns be sorted in some systematic order. The most common and visually effective schema is according to size of value.

    UnsortedBar
    SortedBar
  • It may also be desirable to order findings by a particular category such as class year (see Clustered Bar Graph below), where it is best to order sequentially from freshman to senior year or visa versa, or by grade achieved, where it is best to order by the standardized grade scale.
  • Stacked bar graphs, which consist of one or more segmented bars where each segment represents the relative share of a total category, are generally not preferred because it is difficult to make comparisons among the second, third, or subsequent segments without a standard baseline.
  • When graphing data from two or more different series, or different classes within the same series, it is preferable to create a bar graph that groups these values together, side by side (see below).

    Stacked
    Clustered

Back to Top

Line Graphs

  • Line graphs are most often used to display time series data (e.g., the average GPA of students in a starting cohort over their first eight semesters, or program enrollment over the past 10 years). See graph below.

    Line
  • Compared with bar graphs, line graphs are more effective in presenting five or more data points, but less effective in providing emphasis on differences over relatively few periods of time.
  • When plotting time series data in a line graph, it is convention that the x-axis (horizontal) contains the categories of time (e.g., days of the week, months, years – depending on the data), and the y-axis (vertical) has frequencies of what is being measured (see graphs below).
  • Graphs with more than four or five lines tend to become confusing unless the lines are well separated.

    Multiple
    4Lines
  • In a line graph with more than one line, different line styles (e.g., solid line, dashed line, etc.), colors and/or plotting symbols (e.g., asterisks, circles, etc.) should be used to distinguish the lines.

Back to Top

Presenting Data in Tables

  • Tables are the most effective way to present data for reference purposes.
  • A table should always be given a meaningful, self-explanatory title.
  • Each part of a table should be labeled clearly and abbreviations should be avoided.
  • The number of digits and decimal places presented should be consistent and should be the minimum number that is compatible with the purpose of the table.
  • It is usually better to convert counts into percentages, unless providing a simple frequencies table. More readers will care that 78% of students agreed with a statement rather than 325 students agreed.
  • It is always important to include information in a table about the size of the sample from which a percentage is derived.
  • A table should be constructed so that it is easy for readers to see differences and trends. If a table is presenting results from two or more different groups, years or survey cycles, it is good to include a column that indicates either the percentage change or the significance of differences observed.

    Table 1

    Comparision of Course Satisfaction Measures for Course X
    2008 vs 2009
    Satisfaction Measure 2009 2008
    Applicability of Material Covered 88% 86%
    Access to Professor 79% 68%
    Course Content 72% 67%
    Course Organization 56% 53%
    Class Size 43% 44%

    Improved Version of Table 1

    Comparision of Course Satisfaction Measures for Course X
    2008 vs 2009
    (% "Satisfied" or "Very Satisfied")
    Satisfaction Measure 2009
    (N = 134 )
    2008
    (N = 123 )
    Difference
    Applicability of Material Covered 88% 86% 2
    Access to Professor 79% 68% 11
    Course Content 72% 67% 5
    Course Organization 56% 53% 3
    Class Size 43% 44% -1
    Note: Data taken from 2008 and 2009 end of term course evaluations for Course X

  • It is best to present information in an order that makes sense to the reader by sorting from most frequently chosen response or highest score to lowest (see tables above).
  • A table should draw attention to the most salient points. Use boldface, italics, borders, and/or colors to draw attention to the most important figures, and put totals in boldface (see tables above).
  • Always note the source of data presented in a table (see tables above).
  • More complex tables that organize information by more than one level should be constructed to best reflect how data are grouped. It is best to merge cells that apply to more than one column in a table, rather than repeating the grouping information in more than one column. Shading can also provide greater organization and distinction between groups of data (see tables below).

    Table 2

    2008 vs 2009 Divisional Enrollments by Gender
    Academic Division 2009 2009 2008 2008
    Males Females Males Females
    Physical Sciences 368 182 355 173
    Natural Sciences 658 495 642 505
    Humanities 352 435 375 415
    Social Sciences 786 962 801 1002
    Total 2164 2074 2173 2095

    Improved Version of Table 2

    2008 vs 2009 Divisional Enrollments by Gender
      2009 2008
    Males Females Males Females
    Physical Sciences 368 182 355 173
    Natural Sciences 658 495 642 505
    Humanities 352 435 375 415
    Social Sciences 786 962 801 1002
    Total 2164 2074 2173 2095

Back to Top