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| Univariate Tables | Bivariate
Tables | Graphs | Rounding
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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.
Here
is a percentage table that conforms to ASA guidelines:
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Example
to Be Added Soon
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Some
variables are best described by means and standard deviations
rather than percentages. Here is a table presenting means
and standard deviations for several variables:
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Example
to Be Added Soon
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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.
Here
is a percentage table for a bivariate table:
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Example
to Be Added Soon
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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.)
This
graph conforms to ASA guidelines:
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Example
to Be Added Soon
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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.