Presenting Statistics

This Web page offers format guidelines for some tables and graphs commonly used in sociology.

Many (but not all) sociology papers include statistical analyses, tables, and graphs. Your instructor will expect your paper to conform to the American Sociological Association's conventions for presenting statistical information. These conventions are described in the ASA's Style Guide (available in 217 Tisch Learning Center). For examples, see recent issues of the American Sociological Review and other major sociology journals. (Other disciplines such as psychology prefer slightly different formats, but you should stick to the ASA style in your sociology papers.)

While style must never be confused with substance, you owe both to your readers. Statistical tables and graphs should be "presentation-quality." How do you know if your statistical table or graph looks good? A reasonably intelligent person should be able to read the statistics with minimal effort and no ambiguity. So ask yourself when preparing tables: "Could my roommate read this table easily and accurately?" (Caution: Apply this test only if your roommate is reasonably intelligent.)

Univariate Tables (for single variables)

Here are some guidelines for presentation-quality tables describing the percentage distributions of individual variables:

• Number your tables with Arabic numerals.
  
  
• Use a straightforward title that clearly but succinctly identifies the variable described in the table.
  
  
• In parentheses after the title, report the data source or the set of cases used for the table unless you report that information in the text of your paper.
  
  
• Label left-hand column with the variable name (e.g., Civil Disobedience; Education). Use clear, descriptive names rather than the abridged, sometimes cryptic variable names often used in data files.
  
  
• Label the right-hand column Percent (or Frequency or Cumulative Percent, as appropriate).
  
  
• Be sure that value categories are mutually exclusive and collectively exhaustive. Every score should be included in one and only one value category.
  
  
• Include a Total row that adds up the percentages as a guide to the table's readers.
  
  
• Include an (N) row presenting the number of cases on which percentages are based. Sometimes this row is labeled "Number of Cases." (Presenting N allows a reader to assess the stability of percentages and to calculate the individual frequencies on which percentages are based.)
  
  
• Retain only significant digits in percentages. Usually you should round percentages to either whole numbers or one decimal place. (This guideline has exceptions, but not many when working with social scientific data.}
  
  
• Be consistent with decimal places. (For example, don't round some percentages to whole numbers and others to one decimal place.)
  
  
• Unless there is good reason to draw attention to frequencies, don't put individual frequencies in the table--just percentages. An interested table reader can recompute any frequency by multiplying N by the percentage and then dividing by 100.
  
  
• Keep percentages lined up and right-adjusted. (Your word processor allows you to align decimal points with a "decimal tab," which is even neater.)
  
  
• Don't put % signs after cell entries. They are not needed, they clutter a table, and they are just plain tacky.
  
  
• Do not draw vertical lines in a table. They also clutter. To guide a reader's eye and provide definition for the table, draw only a horizontal double-line between the title and the column headings and single horizontal lines below the column headings and at the bottom of the table, just as shown in the examples below.
  
  
• Be very neat. Keep cell entries lined up, align decimal points, keep horizontal lines the same length, etc.

Some variables are best described by means and standard deviations rather than percentages.

Bivariate Tables (for relationships between two variables)

Bivariate tables describe the relationship between two variables. Here are suggestions for preparing presentation-quality bivariate tables in sociology:

• Number your tables with Arabic numerals.
  
  
• Use a clear, straightforward title that describes the contents of the table in this form: Dependent Variable by Independent Variable (e.g., Civil Disobedience by Education).
  
  
• In parentheses after the title, report the data source or the set of cases used for the table unless you report that information in the text of your paper.
  
  
• Label the leftmost column with the name or description of the dependent variable (e.g., Civil Disobedience) and the other columns with the values of the independent variable (e.g., values of Education). Above the independent variable's values, enter the name of the independent variable, with a horizontal line below extending over the variable's values.
  
  
• Include a Total row that adds column percentages up as a guide to anyone reading the table. [Sometimes percentages do not total exactly 100 percent because of rounding errors. In such cases either enter the exact total (e.g., 99.9 or 100.1) or else enter 100.0 percent with a footnote below the table indicating that percentages may not sum to exactly 100 percent due to rounding.]
  
  
• Include an (N) row presenting the number of cases on which column percentages are based. (This N allows the table's reader to calculate cell frequencies and then combine categories in a different way if he/she wishes.) Report these totals in parentheses at the bottom of the independent variable columns. It is not conventional to report marginal totals for the dependent variable, so you should leave them off your table unless there is some good reason to present them.
  
  
• Retain only significant digits in percentages. Usually you should round percentages to either whole numbers or one decimal place. This guideline has exceptions, but not many when working with social scientific data.
  
  
• Use the same number of decimal places in all percentages.
  
  
• Do not put individual cell frequencies in the table--just percentages. (An interested table reader can recover any frequency by multiplying the total N by the percentage, and then dividing by 100.)
  
  
• Keep columns of percentages equal distances apart and right-adjust column percentages. (Better yet, align decimal points with your word processor's "decimal tab.")
  
  
• Do not put % signs after cell entries. As with univariate tables, % signs in bivariate tables are unnecessary, cluttery, and tacky, so leave them out.
  
  
• Do not draw vertical lines in a table. They too clutter. Guide the reader's eye and provide definition for the table simply by drawing a horizontal double-line between title and column headings and single horizontal lines below column headings and at the bottom of the table. Examples of these lines are shown in the tables below.
  
  
• As always when you present statistical analyses to others, be neat. Very neat. Keep cell entries lined up, horizontal lines the same length, etc. As I suggested earlier, you owe both style and substance to readers of your tables.
  

Graphs

Here are guidelines for simple bar graphs (and many other kinds of graphs, too):

• Number each graph as a "Figure" followed by an Arabic numeral.
  
  
• Give the graph a clear but concise title identifying the variable depicted. The graph's number and name go below the graph.
  
  
• The vertical axis should usually be approximately 60 to 75 percent the length of the horizontal axis. This ratio gives a uniform appearance to graphs and thus facilitates comparisons. You may need to stretch (quite literally) this guideline for variables like age in years that have many values.
  
  
• Keep the scales of graphs constant if you are creating two or more graphs with similar variables (e.g., respondent's education and spouse's education). Using the same scale makes comparisons easier.
  
  
• For ordinal or interval/ratio variables, list values from lowest to highest as you go from left to right on the horizontal axis.
  
  
• Bars should be of equal width so that areas of bars are proportional to their frequencies or percentages.
  
  
• There should be spaces between the bars of variables whose values are discrete categories (like broad educational categories—less than high school, high school, college, etc.). However, leave no space between the bars for a continuous variable (like education if it were measured in actual years completed).
  
  
• Label the vertical axis with "Frequency" or "Percent" so that a reader knows which it displays.
  
  
• The vertical axis usually should begin at zero to avoid distorting perceptions of the areas of the bars. Otherwise taller bars will seem unduly tall relative to shorter bars and differences between the heights of bars will appear magnified. (You often see this guideline violated in the mass media, and there are times when you will need to make exceptions yourself. Watch out for violations in the media, however, and be very careful with your own exceptions to this rule.)

These guidelines hit only some of the high points of well-designed tables and graphs. Frankly, however, you will be better off closely following examples in professional journals than you will be following guidelines.

For a classic work on presenting statistical information, see Edward Tufte's wonderful Visual Display of Quantitative Information (Cheshire, CT: Graphics Press, 1983).

Precision and Rounding

Be sure in your percentage tables (and, indeed, in any analysis) to claim no more precision than your data warrant. Retain only significant digits--that is, digits that are reliable and in which you have confidence. In practice this usually means you should round percentages off to either whole numbers or one decimal place. This guideline has exceptions, but not many when working with social scientific data. Percentages with more than one decimal place usually make false claims to precision. Calculators and computers usually give many decimal places (often as many as eight), but most of those digits are not significant.

As a general rule in statistics, keep as many digits as you can while applying formulas and calculating in order to minimize rounding errors during computation. Then round off your final number to no more than one more decimal place than you started with. If you begin with whole numbers (as in tallies of cases), round your final numbers (e.g., percentages) to one decimal place or perhaps even whole numbers. Since this is only a general rule, it has exceptions. As always, therefore, think about what you are doing and decide how many digits you have confidence in.

Ridiculous extra digits (generally those beyond one decimal place) normally should be rounded to the nearest number. Some examples: Round 21.32 to 21.3 and round 15.66 to 15.7. What about rounding a number ending in 5 like 48.65 or 17.35? A common practice is to round 5s off to the nearest even number. Thus, for example, 48.65 is rounded to 48.6, while 17.35 is rounded to 17.4. This "even rule" for rounding insures that in the long run about half of numbers ending in 5 are rounded up and about half are rounded down.