\title{\LaTeX{} and tables}
\author[R. Allan Reese]{R. Allan Reese\\ Computer Centre\\Hull
  University\\
\texttt{r.a.reese@ucc.hull.ac.uk}}

\begin{Article}

\section{Tables}

Kroonenberg's article on tables (\cite{Kroo}) made some useful
suggestions on \LaTeX{} coding but the examples left much to be
desired as patterns to follow. I fully agree that the \LaTeX{} User
Guide (\cite{lamport}), \cite{kopka} and virtually every book
on word processing place far too much stress on rules as boxes.
\cite{chapman} gives better guidance on the presentation of
tables; I particularly enjoy commending this book, as it challenges one
of the Great Lies of Life.\footnote{I'm from the Government and I'm here
to help you.} Ehrenberg's short article (\cite{ehrena}) should be studied
by anyone putting figures into a table. \cite{reynolds} is a
more general book and discusses presentations of all types.

Chapman gives clear, straightforward guidance with many examples of
good and bad practice. Here, for example, is a point almost
always overlooked by people who believe `a picture is worth a thousand
words':
\begin{quote}
``Since neither charts nor tables ever `speak for
themselves', in order to communicate a message effectively either must
be accompanied by a verbal summary.''
\end{quote}

Tabular material tends to be complex. For a recent workshop on table
construction in \LaTeX{}, I selected what seemed to me the simplest
tables from journals to hand. The criteria for simplicity were small
size and not appearing to need a wide variety of \LaTeX{} commands. In
serious use, you would expect to use more commands than when teaching,
so this restriction would be relaxed. More complex tables were often
`tables within tables', for which \LaTeX's analytical approach of
defining logical units is well suited. However, another of Chapman's
truths that is easily swept aside by an author's enthusiasm is:
\begin{quote} ``Tables should be
small. It is better to include three or four compact tables, each
illustrating one or two points succinctly, rather than construct a
single large table which is then referred to in text covering a large
number of paragraphs or pages.''
\end{quote}

Her next sentence will strike a chord with any \LaTeX{} user:
\begin{quote}
``Small tables are easier to position close to their verbal summary, and
are easier to include in the main report.''
\end{quote}

Several problems arose in recreating the examples using \LaTeX. Some
were due to the desire to reproduce the table exactly as seen, rather
than re-present the information in a natural way. On the other hand,
the exercise did bring out the flexibility of \LaTeX's standard
tabulation tools.

The short workshop was successful, in that most of my (Computer Centre)
colleagues were able to add further lines into a part-built table
despite having no previous experience of \LaTeX. They followed the
layout by copying the commands that they saw; this contrasts greatly
with WYSIWYG word processors where you may see a table but have no
idea of how it was constructed.

\LaTeX{} is an excellent program for formatting tables. It is not,
however, realistic to expect tables to be laid out optimally first
time and automatically. This is one area where the author must be
prepared to make judgements and manual adjustments.

\section{Rules of thumb}

Rules for constructing tables can be divided into those dealing with the
content and those dealing with the layout. The typesetter will generally
have little say in the content or ordering of the information, but an
editor might (should) make suggestions. The evidence of most journals
suggests their editors are not as critical of tables or graphics as of
text.

Chapman distinguishes between demonstration tables and reference
tables. The reader uses the former to perceive a pattern and the
latter to look up a value. Tables that try to do both are rarely
successful. Ehrenberg's examples would come under the demonstration
category, for which he suggests:
\begin{enumerate}
\item give marginal averages to provide a visual focus
\item order the rows or columns by the marginal averages or some
relevant measure of size
\item put figures to be compared in columns rather than in
rows (i.e., to aid mental arithmetic)
\item round all numbers to two effective digits, unless the exact
value is for reference
\end{enumerate}
See \cite{ehrena} and 1978 for further explanation and discussion.

Layout can make a table easier to read\Dash or can destroy its
meaning.

Sweep away the black boxes and apply two principles. A table is a
discontinuity in reading. The reader is not to scan it linearly, as if
reading text. You must therefore guide their eyes:
\begin{enumerate}
\item use white space to separate objects
\item use lines (rules) to join or point connections.
\end{enumerate}

As when setting text, beginners tend to add too much space, though
Chapman complains that even professional compositors like to widen
tables to fill the text width. Physically compact tables are easier
to scan. \cite{visdis} makes this point about graphics; make them
smaller so the reader can see the pattern not the dots. This applies
also to tables. White space is used to set off the table from the body
text, usually by centering. Spaces within the table are used to indent
hierarchical headings and to break the table into sections. In another
article (\cite{reesettn}) I discuss \LaTeX{} constructs for interposing
space after a set number of lines or when the initial letter changes.

Horizontal rules are standard at top and bottom to further demarcate
the table. There is usually a thick rule under the table heading, a
thin rule under the banner (column) headings and a thin rule between
the table body and any explanatory notes.  Incidentally, one of
Chapman's warning examples shows how disastrous it is to rely on the reader
reading the footnotes to understand the table. They must be strictly
to expand or qualify a detail.

Kroonenberg mentions the problem of text coming too close to rules.
This can be adjusted with struts or non-aligned \verb|\vspace|; I like to
insert a small extra space above the first row and after the last, to
unify the body of the table and distinguish it from the headings.
Vertical rules are used sparingly, if at all. It is better to put
a little space between stubs (row labels) and the `data' columns, and
between the columns and the marginal `averages', than to add rules
crossing the direction of scanning. You can help the reader scan
across gaps by adding leaders, or by centering rather than justifying
short items.

Use a smaller font inside tables. Kroonenberg implies this by
discussing sans serif fonts ``to set off the table.'' It is another
way to make the table more compact and visually distinguished.

Telephone directories are large reference tables which demonstrate
these principles. They are set in the smallest readable font size,
have leaders to bridge the gap between name and number, and are
usually multi-column with white space separators.

\section{Implementation}

The layout principles are easily implemented in standard \LaTeX. The
table itself uses the \verb|tabular| environment. The number of
columns will often be greater than at first apparent, with many
multicolumn items. For example, this is a natural way to handle
hierarchical stubs, where the primary labels span two columns and the
secondary labels start in column two (indented). \LaTeX{} will
calculate column widths but it is often desirable to force several
columns to have the same width. Headings will often require either
\verb|\multicolumn| or \verb|\noalign| to position them aesthetically.

\LaTeX{} 2.09 had only \verb|\hline| and \verb|\cline|.  The
\verb|hhline| package is worth fetching from CTAN\@. Line spacing for
the whole table can be adjusted with \verb|\arraystretch| and made
different from \verb|\baselinestretch|. Bear in mind that the table
can be compressed as well as extended, and \verb|\arraystretch|$=0.9$
may make the pattern more obvious and the table \emph{more} readable.

The table is then embedded in an environment to set it off from the
text. You can choose from \verb|quote|, \verb|center|, display maths or
\verb|table|. Set the font size smaller within that environment, sans
serif for the table and body text style for the captions. (The examples
in this article follow their originals as closely as possible and don't
do this. I think they would be improved if they did.) The table
environment makes the object into a float, hence not to be broken
between pages and with a cross-referencing label. The \verb|longtable|
package caters for tables that are too large for a single page.

Some mechanism should be used to create a left and right indent, the
most obvious being to define the table width explicitly and center it.
\verb|minipage| puts the footnotes to the table at the bottom of the table,
using different marks from those in the body text. Putting the
\verb|minipage| round the \verb|table| rather than just the
\verb|tabular| also makes the caption narrower. I prefer the table
reference to stand out, and often use the \verb|hangcapt| package.

When there are several tables or a house style, it is better to
define a new environment to ensure consistency in their presentation.
I also commonly define new length constants for use in tables rather
than copy the values.

\section{A \LaTeX{} gap}

One common format for tables has rows of short data values but a final
column containing texts. The description parameter may therefore tell
\LaTeX{} to calculate the widths of data columns from the values, but
the final column will be a \verb|parbox| and should sensibly use the
remainder of the \verb|linewidth|. This is one need that \LaTeX{} (2.09)
blatantly fails to meet. You have to set the width of a \verb|parbox| or
\texttt{p}(aragraph) column. Kroonenberg implies this problem when discussing
\verb|\raggedright|; as she points out, to choose unjustified text you
have to enclose each text in a \verb|parbox|. This is less work if the width
is set as a name (to be calculated) and not the numeric length. My
pragmatic solution is to set the value for the final column initially
to the \verb|\linewidth|, run \LaTeX{}, note (from the log) the
overfill, and subtract that from \verb|\linewidth|.

\section{Kroonenberg's `after' table}

The `after' table of Economic Forecasts is still poor. This is partly
due to the content. It lacks a text explanation (possibly the primary
source had one), but I \emph{guess} that the intention is to compare
forecasts from two sources. Numbers going \emph{down} the columns are
not related (in this sense), so flipping (transposing) the table would
make logical sense. This might be the best solution on a wider page,
as having the table span two columns is yet another way of
distinguishing it from the body. If we insist on keeping it within one
(text) column, there is room for another column of values as a
`margin'.

Without a rubric, I cannot decide if the table is trying to show
disagreement between the two sets of forecasts, or similarity.
Dependent on the message, the best margin might be the difference
between each pair of forecasts, a $+$/$-$ sign for higher or lower,
the ratio, or the average. The forecasts themselves should all be
rounded to two significant digits.

We seem to have lost between the `before' and `after' the detail that
the figures are percentages; and \emph{was} government income really a
`percentage change of a percentage'? The labels that include ($\times$
1000 persons) are misleading; I take that notation to mean that the
numbers shown \emph{have been} multiplied by 1000 (like \TeX{}
magnifications). The correct notation would be (000s of persons).

Making the rules extend to the linewidth was presumably not thought
out. They unbalance the design, and all the white space implies an
omission. The spaces between the columns are too wide. If ``mutations
w.r.t.~1991'' and ``absolute quantities'' are to be used as primary
divisions, then the secondary stubs (``real consumption'' etc) should
be indented. If you think too deeply about the title, are these
forecast changes or changes to (earlier) forecasts? Follow Chapman's
advice and split the table into two, with headings of the form
``Forecast percentage changes 1991/92 in National Economy'' and
``Forecast quantities\ldots''. I leave
this redrafting as an exercise for the reader.

A parenthetic remark for those preparing tables of accounts comes from
\cite{townsend}. He suggests that ``statements comparing budgets
to actual should be written not in the usual terms of higher (lower)
but in plain English of better (or worse) than predicted by the
budget. This eliminates the mental gear changes between income items
(where parentheses are bad) and expense items (where parentheses are good).''
Typography helping the reader.


\section{New examples}

The following examples are shown as output, in the expectation that
the interested reader will obtain the `input'  from the 
the author or the editor. If there is sufficient interest, the \LaTeX\
source for the tables can be placed on the CTAN archives.

\subsection{Example 1\Dash Cohabitation}

This is taken from \textit{Key Data 88} (\cite{key}) which had itself
extracted it from \textit{Social Trends}. \textit{Key Data} is a sample of
UK government statistics published annually as an educational resource
and a guide to the more extensive sources. The table as printed had
inconsistencies in the use of italic and upright fonts, and in its
indentation.
\begin{table*}
\begin{center}
\caption{Cohabitation}
\label{cohab} 
% The table in the book is sans-serif with the heading bold.
{\sffamily
\setlength{\doublerulesep}{0pt}
\begin{tabular}{llrrrrr}
\multicolumn{7}{p{.5\textwidth}}%
{\begin{tabbing}
\bf 2.12\quad  \= Percentage of women aged 18--49 cohabiting:\\
               \> by age
\end{tabbing}}\\
\multicolumn{2}{c}\textit{Great Britain}&
                          \multicolumn{5}{r}{Percentage and numbers}\\
\hline
\hline
     &         &   1979 & 1981 & 1983 & 1984 & 1985 \\
\hline
\multicolumn{2}{l}{Age group \textit{(percentages)}} \\
\hspace*{1em} & \textit{18--24} &  4.5 & 5.6 & 5.2 & 7.3 & 9.1 \\
              & \textit{25--49} &  2.2 & 2.6 & 3.2 & 3.3 & 3.9 \\
\multicolumn{2}{c}\textit{All aged 18--49}
                             &   2.7 & 3.3 & 3.6 & 4.2 & 5.0 \\
\\
\multicolumn{2}{l}{Women in sample \textit{(numbers)}} \\
      & (=100\% above)\\
                    & 18--24 & 1,353 & 1,517 & 1,191 & 1,174 & 1,182 \\
                    & 25--49 & 4,651 & 5,007 & 4,094 & 4,070 & 4,182 \\
      \cline{3-7}
\multicolumn{2}{c}\textit{All aged 18--49}
                             & 6,004 & 6,524 & 5,285 & 5,244 & 5,364\\
\hline
\hline
\end{tabular}
}
\end{center}
\end{table*}

Table~\ref{cohab} could be further improved by a distinct split and
putting the two halves the other way round: ``Numbers of women surveyed
in each year, in two age groups'' and ``Of the samples, percentage
cohabiting''. Note that the first half is essentially for reference and
the second half for demonstration.

\subsection{Example 2\Dash Vulture meat}

Table~\ref{meat} is taken from Ibis (\cite{thibault}), journal of the British
Ornithologists' Union. It is a simple table, but appears in a two-column
layout and has footnotes. The original used numbers as the footnote
markers. I found this disconcerting, as \textit{G${}^\mathrm{2}$} looks
like a numeric power; so I'll use the \LaTeX{} default in a minipage,
which also sets the table to the width of an Ibis column.

This table is adequate for reference, and is discussed in an adjacent
text. ``Comparison of food availability among territories showed
significant differences.\ \ldots'' The rows are not in an obvious order,
and if the primary aim is to compare the number of, say, sheep in each
territory, it might have been better flipped. A marginal total of the
number of prey animals, or their biomass, in each territory would have
been helpful. It is debatable whether the figures should be rounded,
since they are taken from previous studies which are themselves recorded
or reported with different precisions.
\begin{table}[H]
\begin{center}
\begin{minipage}{81mm}
\caption{\em Numbers of ungulates in Lammergeier territories
(except for wild boar, differences among territories are statistically
significant, $\chi^2_{16}=16.825, \mbox{P} < 0.001$).}\label{meat}
\vspace{1ex}\ \\
\renewcommand{\footnoterule}{\rule{0pt}{0pt}}
\begin{tabular*}{81mm}{l@{\quad\extracolsep{\fill}}rrrrr}
\hline\vspace{.4ex}\\
& \multicolumn{5}{c}{Territory}\vspace{.2ex}\\
\cline{2-6}\vspace{.2ex}\\
Species & \textit{B}\footnote{Dubray \& Roux(1990)}
& \textit{G}\footnote{Anonymous (1989).}
& \textit{R}\footnote{Direction \dots}
& \textit{T}${}^\alph{mpfootnote}$ % Gash way of repeating superscript.
& \textit{V}${}^\alph{mpfootnote}$
\\
\hline\vspace{.2ex}\\
Sheep   & 2000   & 1400 & 5240 & 3165   & 3480 \\
Mouflon & $<200$ & $-$  & $-$  & $<400$ & $<5$ \\
Goat    & 570    & 4142 & 1880 & 1510   & 820  \\
Cattle  & 2300   & 6402 & 7204 & 6774   & 965  \\
Pig     & 3400   & 7188 & 1900 & 400    & 522 \\
Boar    & $+$\footnote{$+ =$ present. $- =$ absent.}
                 & $+$ & $+$ & $+$ & $+$\\[.5ex]
\vspace{.2ex}\\
\hline
\end{tabular*}
\end{minipage}
\end{center}
\end{table}


\subsection{Example 3\Dash YOPs}

The problem with this table from \cite[p11 and, slightly changed,
p35]{chapman} is that one column has an entry spreading over several
lines (the brace linking them). The hint for doing this is in
\cite[p79]{kopka}, but they show only one optional argument to
\verb|\raisebox|. Using both optional arguments (setting height and
depth to zero) and putting the `brace array' on the line opposite its
middle, is the easiest way to centralize it vertically. A convenient
feature is that you can reset the \verb|\arraystretch| and the brace is
still the right size to cover three rows. This example is also set in
a minipage but the footnote markers have been reset as numeric. Follow
DEK's advice: \emph{don't use footnotes in text.}

% The table in the book is column-width, sans-serif with the heading bold.
\begin{center}
\begin{minipage}{85mm}
\small
\sffamily % choose font
\renewcommand{\footnoterule}{\rule{0pt}{0pt} \vspace{0pt}}
\renewcommand{\thempfootnote}{\arabic{mpfootnote}}
\renewcommand{\arraystretch}{1.1}
\begin{tabular*}{85mm}{@{}l@{\extracolsep{\fill}}r@{\extracolsep{2em}}r@{}}
\noalign{\bf % bold font for whole heading
\begin{tabbing}
Table 3\quad  \= Entrants to Youth Opportunities\\
                \> Programme in Wales: by type of\\
                \> scheme
\end{tabbing}}\\
\multicolumn{3}{l}\textit{Wales 1978 to 1980\hfill Percentages}\\
\hline
                             & 1978/79 & 1979/80\\
\cline{2-2} \cline{3-3}
\noalign{\vspace{3pt}}
WEEP\footnote{Work Experience on Employers' Premises}
                              & 89    & 73\\
Short Training Course         & 10    & 10\\
Community Service             &       & 9\\
Project based work experience &       & 7\\
Training Workshops            &\raisebox{0pt}[0pt][0pt]{% Centre brace
\(\begin{array}{lr}
\left.                         % null delimiter to match brace
\begin{array}{@{\extracolsep{0pt}}l}\strut \\ \strut \\ \strut \end{array}
\right\}     % the big brace
\end{array}\)}                  1    & 1\\
Induction and other\footnote{Employment induction courses and
other remedial and preparatory courses}
                             &         & 1\\
\noalign{\vspace{3pt}}
\hline
\noalign{\vspace{3pt}}
Total (100\%)                 & 15,000 & 22,000\\
\noalign{\vspace{3pt}}
\hline
\end{tabular*}
\end{minipage}%end of \sf default
\end{center}

The table has a large gap between columns 1 and 2, making it difficult
to see at a glance whether the brace includes `Community Service'. The
original rubric (\cite{msc}) was:
\begin{quote}
``One of the major aims in 1979/80 was to increase the range of provision
available to meet the varying needs of unemployed young people. In the
early days of the Programme, there was heavy reliance on the Work
Experience on Employers' Premises (WEEP) element, but the table reflects
the increasing provision that has now been made in the other elements of
YOP.''
\end{quote}
As presented, the first impression is that the number of schemes
apparently grew, but each scheme attracted only a small percentage. `1'
as a rounded value is very uninformative, especially as the compared
figures are about 10 and 80\%. There is also a wide gap between the
caption `(100\%)' and the figures it refers to. A quick sum shows that
the numbers entering WEEP went \textit{up} by 20\% between the two periods.
It's a classic political table; you can fiddle it to either praise or
condemn.


\begin{thebibliography}{99}
\frenchspacing
\bibitem[Chapman 1986]{chapman}{Chapman M. \& B. Mahon (1986)\textit{Plain Figures}.
HMSO}
\bibitem[Ehrenberg 1981]{ehrena}{Ehrenberg A.S.C. (1981) \textit{The Problem of Numeracy}.
The American Statistician, Vol 35, No 2}
\bibitem[Ehrenberg 1978]{ehrenb}{Ehrenberg A.S.C. (1978) \textit{Data Reduction: Analysing
and Interpreting Statistical Data}. John Wiley}
\bibitem[CSO 1988]{key}{Central Statistical Office (1988) \textit{Key Data 88}. HMSO London}
\bibitem[Kopka \& Daly 1993]{kopka}{Kopka H. \& P.W. Daly (1993) \textit{A Guide to \LaTeX}.
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\bibitem[Kroonenberg 1994]{Kroo}{Kroonenberg S. (1994) \textit{Table Design}. Baskerville
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\bibitem[Lamport 1986]{lamport}{Lamport L. (1986,1994) \textit{\LaTeX: User's Guide}.
Addison-Wesley}
\bibitem[MSC 1979/80]{msc}{Manpower Services Commission \textit{Annual Report 1979/80},
para~8.34 and Table~35. HMSO}
\bibitem[Reese forthcoming]{reesettn}{Reese R.A. \textit{Dividing a Table Alphabetically},
submitted to TTN}
\bibitem[Reynolds 1983]{reynolds}{Reynolds, L. (1983) \textit{Presentation of Data in
Science}. Nijhoff, The Hague}
\bibitem[Thibault et al. 1993]{thibault}{Thibault J.-C., Vigne J.-D. \& J. Torre (1993) {\it
The Diet of young Lammergeiers in Corsica}. Ibis Vol.~135 No.~1}
\bibitem[Townsend 1970]{townsend}{Townsend R. (1970) \textit{Up the Organization}.
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\bibitem[Tufte 1983]{visdis}{Tufte, E. (1983) \textit{The Visual Display of
Quantitative Information}. Graphic Press, Conn}

\end{thebibliography}

\end{Article}