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CONTAB(1) |STAT February 3, 1987
NAME
contab - contingency table and chi-square analysis
SYNOPSIS
contab [-bsy] [-i nfactors] [-c entries] [factor names]
OPTIONS
-b Use blank lines to make frequency tables more readable. This
option is recommended when the cells are filled with values from
the cell entry format option.
-c cell-entries
Choose table cell entries from expected values (e), differences
of obtained and expected frequencies (d), all percentages (p),
row percentages (r), column percentages (c), or cell percentages
of the total count (t).
-i nfactors
Maximum number of factors in interactions. By default, all
interactions are analyzed, however, it may be that only those
contingency tables involving one or two factors will be of
interest.
-s Do not print significance tests (only print tables).
-y Do not apply Yates' correction for continuity for chi-square
tests with one degree of freedom.
DESCRIPTION
Hays (1973) warns ``...there is probably no other statistical method
that has been so widely misapplied.'' (p. 735). Contingency tables
and chi-square are used to summarize and test for association between
frequencies of events.
Input Format
The input format is simple. Each cell frequency is preceded by codes
of the levels of factors under which it was obtained. For example, if
rats are categorized by age and are further categorized by the length
of their tails, the contingency data would look like:
young long 12
old long 10
young short 30
old short 2
young short 3
Note that the cell frequencies for young short-tailed rats add up to
33.
The most important assumption for the input data is that all
frequencies are independent. For example, each subject in an
experiment must contribute one and only one count to one cell. Also,
if more than a small percentage of expected cell frequencies are
small, then the chi-square statistic may be invalid. A text should be
consulted.
Output
_c_o_n_t_a_b prints a summary of the names and number of levels of factors.
For main effects, a frequency table and significance test of deviation
from equal cell frequencies is printed. For each two-way interaction,
a contingency table and test for independence is printed. Yates'
correction for continuity is applied whenever there is one degree of
freedom. For total cell frequencies in 2x2 tables up to 100, the
Fisher exact test is computed for both one and two tailed cases. A
text should be used to interpret the output statistics.
ALGORITHM
The calculation of chi-square is standard for designs with more than
one degree of freedom and adequate expected cell frequencies.
Different texts have different methods for corrections for small
designs. The methods used here reflect several sources.
When there is one degree of freedom, small cell frequencies can bias
the chi-square test. Yates' correction for continuity reduces the
absolute differences of obtained and expected frequencies by up to
0.5, following the discussion by Fisher (1970) in ``Statistical
Methods for Research Workers.'' The Fisher Exact test for 2x2 tables
is drawn from Bradley (1968) ``Distribution-Free Statistical Tests.''
The two-tailed calculation has only been tested against Bradley's one
example.
FILES
UNIX /tmp/contab.????
MSDOS contab.tmp
STATUS
This is the second version of the program. Later versions will have
tests of association for contingency tables with greater than 2
dimensions. The ability to supply expected frequencies may be added
if there is demand. Suggestions are welcome.
LIMITS
Use the -L option to determine the program limits.
These are the contents of the former NiCE NeXT User Group NeXTSTEP/OpenStep software archive, currently hosted by Netfuture.ch.