Title stata.com
tabulate twoway — Two-way table of frequencies
Syntax Menu Description Options
Remarks and examples Stored results Methods and formulas References
Also see
Syntax
Two-way table
tabulate varname
1
varname
2
if
in
weight
, options
Two-way table for all possible combinations—a convenience tool
tab2 varlist
if
in
weight
, options
Immediate form of two-way tabulations
tabi #
11
#
12
. . .
\ #
21
#
22
. . .
\ . . .
, options
options Description
Main
chi2 report Pearson’s χ
2
exact
(#)
report Fisher’s exact test
gamma report Goodman and Kruskal’s gamma
lrchi2 report likelihood-ratio χ
2
taub report Kendall’s τ
b
V report Cram
´
er’s V
cchi2 report Pearson’s χ
2
in each cell
column report relative frequency within its column of each cell
row report relative frequency within its row of each cell
clrchi2 report likelihood-ratio χ
2
in each cell
cell report the relative frequency of each cell
expected report expected frequency in each cell
nofreq do not display frequencies
missing treat missing values like other values
wrap do not wrap wide tables
no
key report/suppress cell contents key
nolabel display numeric codes rather than value labels
nolog do not display enumeration log for Fisher’s exact test
∗
firstonly show only tables that include the first variable in varlist
1
2 tabulate twoway — Two-way table of frequencies
Advanced
matcell(matname) save frequencies in matname; programmer’s option
matrow(matname) save unique values of varname
1
in matname; programmer’s option
matcol(matname) save unique values of varname
2
in matname; programmer’s option
‡
replace replace current data with given cell frequencies
all equivalent to specifying chi2 lrchi2 V gamma taub
∗
firstonly is available only for tab2.
‡
replace is available only for tabi.
by is allowed with tabulate and tab2; see [D] by.
fweights, aweights, and iweights are allowed by tabulate. fweights are allowed by tab2. See [U] 11.1.6 weight.
all does not appear in the dialog box.
Menu
tabulate
Statistics > Summaries, tables, and tests > Frequency tables > Two-way table with measures of association
tab2
Statistics > Summaries, tables, and tests > Frequency tables > All possible two-way tables
tabi
Statistics > Summaries, tables, and tests > Frequency tables > Table calculator
Description
tabulate produces a two-way table of frequency counts, along with various measures of association,
including the common Pearson’s χ
2
, the likelihood-ratio χ
2
, Cram
´
er’s V , Fisher’s exact test, Goodman
and Kruskal’s gamma, and Kendall’s τ
b
.
Line size is respected. That is, if you resize the Results window before running tabulate,
the resulting two-way tabulation will take advantage of the available horizontal space. Stata for
Unix(console) users can instead use the set linesize command to take advantage of this feature.
tab2 produces all possible two-way tabulations of the variables specified in varlist.
tabi displays the r × c table, using the values specified; rows are separated by ‘\’. If no options
are specified, it is as if exact were specified for a 2 × 2 table and chi2 were specified otherwise.
See [U] 19 Immediate commands for a general description of immediate commands. See Tables with
immediate data below for examples using tabi.
See [R] tabulate oneway if you want a one-way table of frequencies. See [R] table and [R] tabstat
if you want one-, two-, or n-way table of frequencies and a wide variety of summary statistics. See
[R] tabulate, summarize() for a description of tabulate with the summarize() option; it produces a
table (breakdowns) of means and standard deviations. table is better than tabulate, summarize(),
but tabulate, summarize() is faster. See [ST] epitab for a 2 × 2 table with statistics of interest
to epidemiologists.
tabulate twoway — Two-way table of frequencies 3
Options
Main
chi2 calculates and displays Pearson’s χ
2
for the hypothesis that the rows and columns in a two-way
table are independent. chi2 may not be specified if aweights or iweights are specified.
exact
(#)
displays the significance calculated by Fisher’s exact test and may be applied to r × c as
well as to 2 × 2 tables. For 2 × 2 tables, both one- and two-sided probabilities are displayed. For
r ×c tables, one-sided probabilities are displayed. The optional positive integer # is a multiplier on
the amount of memory that the command is permitted to consume. The default is 1. This option
should not be necessary for reasonable r × c tables. If the command terminates with error 910,
try exact(2). The maximum row or column dimension allowed when computing Fisher’s exact
test is the maximum row or column dimension for tabulate (see [R] limits).
gamma displays Goodman and Kruskal’s gamma along with its asymptotic standard error. gamma is
appropriate only when both variables are ordinal. gamma may not be specified if aweights or
iweights are specified.
lrchi2 displays the likelihood-ratio χ
2
statistic. lrchi2 may not be specified if aweights or
iweights are specified.
taub displays Kendall’s τ
b
along with its asymptotic standard error. taub is appropriate only when
both variables are ordinal. taub may not be specified if aweights or iweights are specified.
V (note capitalization) displays Cram
´
er’s V . V may not be specified if aweights or iweights are
specified.
cchi2 displays each cell’s contribution to Pearson’s chi-squared in a two-way table.
column displays the relative frequency of each cell within its column in a two-way table.
row displays the relative frequency of each cell within its row in a two-way table.
clrchi2 displays each cell’s contribution to the likelihood-ratio chi-squared in a two-way table.
cell displays the relative frequency of each cell in a two-way table.
expected displays the expected frequency of each cell in a two-way table.
nofreq suppresses the printing of the frequencies.
missing requests that missing values be treated like other values in calculations of counts, percentages,
and other statistics.
wrap requests that Stata take no action on wide, two-way tables to make them readable. Unless wrap
is specified, wide tables are broken into pieces to enhance readability.
no
key suppresses or forces the display of a key above two-way tables. The default is to display the
key if more than one cell statistic is requested, and otherwise to omit it. key forces the display
of the key. nokey suppresses its display.
nolabel causes the numeric codes to be displayed rather than the value labels.
nolog suppresses the display of the log for Fisher’s exact test. Using Fisher’s exact test requires
counting all tables that have a probability exceeding that of the observed table given the observed
row and column totals. The log counts down each stage of the network computations, starting from
the number of columns and counting down to 1, displaying the number of nodes in the network
at each stage. A log is not displayed for 2 × 2 tables.
firstonly, available only with tab2, restricts the output to only those tables that include the first
variable in varlist. Use this option to interact one variable with a set of others.
4 tabulate twoway — Two-way table of frequencies
Advanced
matcell(matname) saves the reported frequencies in matname. This option is for use by programmers.
matrow(matname) saves the numeric values of the r × 1 row stub in matname. This option is for
use by programmers. matrow() may not be specified if the row variable is a string.
matcol(matname) saves the numeric values of the 1 × c column stub in matname. This option is
for use by programmers. matcol() may not be specified if the column variable is a string.
replace indicates that the immediate data specified as arguments to the tabi command be left as
the current data in place of whatever data were there.
The following option is available with tabulate but is not shown in the dialog box:
all is equivalent to specifying chi2 lrchi2 V gamma taub. Note the omission of exact. When
all is specified, no may be placed in front of the other options. all noV requests all association
measures except Cram
´
er’s V (and Fisher’s exact). all exact requests all association measures,
including Fisher’s exact test. all may not be specified if aweights or iweights are specified.
Limits
Two-way tables may have a maximum of 1,200 rows and 80 columns (Stata/MP and Stata/SE),
300 rows and 20 columns (Stata/IC), or 160 rows and 20 columns (Small Stata). If larger tables are
needed, see [R] table.
Remarks and examples stata.com
Remarks are presented under the following headings:
tabulate
Measures of association
N-way tables
Weighted data
Tables with immediate data
tab2
Video examples
For each value of a specified variable (or a set of values for a pair of variables), tabulate
reports the number of observations with that value. The number of times a value occurs is called its
frequency.
tabulate
Example 1
tabulate will make two-way tables if we specify two variables following the word tabulate.
In our highway dataset, we have a variable called rate that divides the accident rate into three
categories: below 4, 4 – 7, and above 7 per million vehicle miles. Let’s make a table of the speed
limit category and the accident-rate category:
tabulate twoway — Two-way table of frequencies 5
. use http://www.stata-press.com/data/r13/hiway2
(Minnesota Highway Data, 1973)
. tabulate spdcat rate
Speed Accident rate per million
Limit vehicle miles
Category Below 4 4-7 Above 7 Total
40 to 50 3 5 3 11
55 to 50 19 6 1 26
Above 60 2 0 0 2
Total 24 11 4 39
The table indicates that three stretches of highway have an accident rate below 4 and a speed limit of
40 to 50 miles per hour. The table also shows the row and column sums (called the marginals). The
number of highways with a speed limit of 40 to 50 miles per hour is 11, which is the same result
we obtained in our previous one-way tabulations.
Stata can present this basic table in several ways—16, to be precise—and we will show just a
few below. It might be easier to read the table if we included the row percentages. For instance, of
11 highways in the lowest speed limit category, three are also in the lowest accident-rate category.
Three-elevenths amounts to some 27.3%. We can ask Stata to fill in this information for us by using
the row option:
. tabulate spdcat rate, row
Key
frequency
row percentage
Speed Accident rate per million
Limit vehicle miles
Category Below 4 4-7 Above 7 Total
40 to 50 3 5 3 11
27.27 45.45 27.27 100.00
55 to 50 19 6 1 26
73.08 23.08 3.85 100.00
Above 60 2 0 0 2
100.00 0.00 0.00 100.00
Total 24 11 4 39
61.54 28.21 10.26 100.00
The number listed below each frequency is the percentage of cases that each cell represents out of
its row. That is easy to remember because we see 100% listed in the “Total” column. The bottom
row is also informative. We see that 61.54% of all the highways in our dataset fall into the lowest
accident-rate category, that 28.21% are in the middle category, and that 10.26% are in the highest.
tabulate can calculate column percentages and cell percentages, as well. It does so when we
specify the column or cell options, respectively. We can even specify them together. Below is a
table that includes everything:
6 tabulate twoway — Two-way table of frequencies
. tabulate spdcat rate, row column cell
Key
frequency
row percentage
column percentage
cell percentage
Speed Accident rate per million
Limit vehicle miles
Category Below 4 4-7 Above 7 Total
40 to 50 3 5 3 11
27.27 45.45 27.27 100.00
12.50 45.45 75.00 28.21
7.69 12.82 7.69 28.21
55 to 50 19 6 1 26
73.08 23.08 3.85 100.00
79.17 54.55 25.00 66.67
48.72 15.38 2.56 66.67
Above 60 2 0 0 2
100.00 0.00 0.00 100.00
8.33 0.00 0.00 5.13
5.13 0.00 0.00 5.13
Total 24 11 4 39
61.54 28.21 10.26 100.00
100.00 100.00 100.00 100.00
61.54 28.21 10.26 100.00
The number at the top of each cell is the frequency count. The second number is the
row percentage — they sum to 100% going across the table. The third number is the column
percentage—they sum to 100% going down the table. The bottom number is the cell percentage— they
sum to 100% going down all the columns and across all the rows. For instance, highways with a
speed limit above 60 miles per hour and in the lowest accident rate category account for 100% of
highways with a speed limit above 60 miles per hour; 8.33% of highways in the lowest accident-rate
category; and 5.13% of all our data.
A fourth option, nofreq, tells Stata not to print the frequency counts. To construct a table consisting
of only row percentages, we type
. tabulate spdcat rate, row nofreq
Speed Accident rate per million
Limit vehicle miles
Category Below 4 4-7 Above 7 Total
40 to 50 27.27 45.45 27.27 100.00
55 to 50 73.08 23.08 3.85 100.00
Above 60 100.00 0.00 0.00 100.00
Total 61.54 28.21 10.26 100.00
tabulate twoway — Two-way table of frequencies 7
Measures of association
Example 2
tabulate will calculate the Pearson χ
2
test for the independence of the rows and columns if we
specify the chi2 option. Suppose that we have 1980 census data on 956 cities in the United States
and wish to compare the age distribution across regions of the country. Assume that agecat is the
median age in each city and that region denotes the region of the country in which the city is
located.
. use http://www.stata-press.com/data/r13/citytemp2
(City Temperature Data)
. tabulate region agecat, chi2
Census agecat
Region 19-29 30-34 35+ Total
NE 46 83 37 166
N Cntrl 162 92 30 284
South 139 68 43 250
West 160 73 23 256
Total 507 316 133 956
Pearson chi2(6) = 61.2877 Pr = 0.000
We obtain the standard two-way table and, at the bottom, a summary of the χ
2
test. Stata informs us
that the χ
2
associated with this table has 6 degrees of freedom and is 61.29. The observed differences
are significant.
The table is, perhaps, easier to understand if we suppress the frequencies and print just the row
percentages:
. tabulate region agecat, row nofreq chi2
Census agecat
Region 19-29 30-34 35+ Total
NE 27.71 50.00 22.29 100.00
N Cntrl 57.04 32.39 10.56 100.00
South 55.60 27.20 17.20 100.00
West 62.50 28.52 8.98 100.00
Total 53.03 33.05 13.91 100.00
Pearson chi2(6) = 61.2877 Pr = 0.000
Example 3
We have data on dose level and outcome for a set of patients and wish to evaluate the association
between the two variables. We can obtain all the association measures by specifying the all and
exact options:
8 tabulate twoway — Two-way table of frequencies
. use http://www.stata-press.com/data/r13/dose
. tabulate dose function, all exact
Enumerating sample-space combinations:
stage 3: enumerations = 1
stage 2: enumerations = 9
stage 1: enumerations = 0
Function
Dosage < 1 hr 1 to 4 4+ Total
1/day 20 10 2 32
2/day 16 12 4 32
3/day 10 16 6 32
Total 46 38 12 96
Pearson chi2(4) = 6.7780 Pr = 0.148
likelihood-ratio chi2(4) = 6.9844 Pr = 0.137
Cramr’s V = 0.1879
gamma = 0.3689 ASE = 0.129
Kendall’s tau-b = 0.2378 ASE = 0.086
Fisher’s exact = 0.145
We find evidence of association but not enough to be truly convincing.
If we had not also specified the exact option, we would not have obtained Fisher’s exact test.
Stata can calculate this statistic both for 2 × 2 tables and for r × c. For 2 × 2 tables, the calculation
is almost instant. On more general tables, however, the calculation can take longer.
We carefully constructed our example so that all would be meaningful. Kendall’s τ
b
and Goodman
and Kruskal’s gamma are relevant only when both dimensions of the table can be ordered, say, from
low to high or from worst to best. The other statistics, however, are always applicable.
Technical note
Be careful when attempting to compute the p-value for Fisher’s exact test because the number of
tables that contribute to the p-value can be extremely large and a solution may not be feasible. The
errors that are indicative of this situation are errors 910, exceeded memory limitations, and 1401,
integer overflow due to large row-margin frequencies. If execution terminates because of memory
limitations, use exact(2) to permit the algorithm to consume twice the memory, exact(3) for three
times the memory, etc. The default memory usage should be sufficient for reasonable tables.
N-way tables
If you need more than two-way tables, your best alternative to is use table, not tabulate; see
[R] table.
The technical note below shows you how to use tabulate to create a sequence of two-way tables
that together form, in effect, a three-way table, but using table is easy and produces prettier results:
tabulate twoway — Two-way table of frequencies 9
. use http://www.stata-press.com/data/r13/birthcat
(City data)
. table birthcat region agecat, c(freq)
agecat and Census Region
birthcat 19-29 30-34
NE N Cntrl South West NE N Cntrl South West
29-136 11 23 11 11 34 27 10 8
137-195 31 97 65 46 48 58 45 42
196-529 4 38 59 91 1 3 12 21
agecat and Census Region
birthcat 35+
NE N Cntrl South West
29-136 34 26 27 18
137-195 3 4 7 4
196-529 4
Technical note
We can make n-way tables by combining the by varlist: prefix with tabulate. Continuing with
the dataset of 956 cities, say that we want to make a table of age category by birth-rate category by
region of the country. The birth-rate category variable is named birthcat in our dataset. To make
separate tables for each age category, we would type
. by agecat, sort: tabulate birthcat region
-> agecat = 19-29
Census Region
birthcat NE N Cntrl South West Total
29-136 11 23 11 11 56
137-195 31 97 65 46 239
196-529 4 38 59 91 192
Total 46 158 135 148 487
-> agecat = 30-34
Census Region
birthcat NE N Cntrl South West Total
29-136 34 27 10 8 79
137-195
48 58 45 42 193
196-529 1 3 12 21 37
Total 83 88 67 71 309
10 tabulate twoway — Two-way table of frequencies
-> agecat = 35+
Census Region
birthcat NE N Cntrl South West Total
29-136 34 26 27 18 105
137-195 3 4 7 4 18
196-529 0 0 4 0 4
Total 37 30 38 22 127
Weighted data
Example 4
tabulate can process weighted as well as unweighted data. As with all Stata commands, we
indicate the weight by specifying the [weight] modifier; see [U] 11.1.6 weight.
Continuing with our dataset of 956 cities, we also have a variable called pop, the population of
each city. We can make a table of region by age category, weighted by population, by typing
. tabulate region agecat [freq=pop]
Census agecat
Region 19-29 30-34 35+ Total
NE 4,721,387 10,421,387 5,323,610 20,466,384
N Cntrl 16,901,550 8,964,756 4,015,593 29,881,899
South 13,894,254 7,686,531 4,141,863 25,722,648
West 16,698,276 7,755,255 2,375,118 26,828,649
Total 52,215,467 34,827,929 15,856,184 102899580
If we specify the cell, column, or row options, they will also be appropriately weighted. Below we
repeat the table, suppressing the counts and substituting row percentages:
. tabulate region agecat [freq=pop], nofreq row
Census agecat
Region 19-29 30-34 35+ Total
NE 23.07 50.92 26.01 100.00
N Cntrl 56.56 30.00 13.44 100.00
South 54.02 29.88 16.10 100.00
West 62.24 28.91 8.85 100.00
Total 50.74 33.85 15.41 100.00
tabulate twoway — Two-way table of frequencies 11
Tables with immediate data
Example 5
tabi ignores the dataset in memory and uses as the table the values that we specify on the
command line:
. tabi 30 18 \ 38 14
col
row 1 2 Total
1 30 18 48
2 38 14 52
Total 68 32 100
Fisher’s exact = 0.289
1-sided Fisher’s exact = 0.179
We may specify any of the options of tabulate and are not limited to 2 × 2 tables:
. tabi 30 18 38 \ 13 7 22, chi2 exact
Enumerating sample-space combinations:
stage 3: enumerations = 1
stage 2: enumerations = 3
stage 1: enumerations = 0
col
row 1 2 3 Total
1 30 18 38 86
2 13 7 22 42
Total 43 25 60 128
Pearson chi2(2) = 0.7967 Pr = 0.671
Fisher’s exact = 0.707
. tabi 30 13 \ 18 7 \ 38 22, all exact col
Key
frequency
column percentage
Enumerating sample-space combinations:
stage 3: enumerations = 1
stage 2: enumerations = 3
stage 1: enumerations = 0
col
row 1 2 Total
1 30 13 43
34.88 30.95 33.59
2 18 7 25
20.93 16.67 19.53
3 38 22 60
44.19 52.38 46.88
Total 86 42 128
100.00 100.00 100.00
12 tabulate twoway — Two-way table of frequencies
Pearson chi2(2) = 0.7967 Pr = 0.671
likelihood-ratio chi2(2) = 0.7985 Pr = 0.671
Cramr’s V = 0.0789
gamma = 0.1204 ASE = 0.160
Kendall’s tau-b = 0.0630 ASE = 0.084
Fisher’s exact = 0.707
For 2 × 2 tables, both one- and two-sided Fisher’s exact probabilities are displayed; this is true of
both tabulate and tabi. See Cumulative incidence data and Case–control data in [ST] epitab for
more discussion on the relationship between one- and two-sided probabilities.
Technical note
tabi, as with all immediate commands, leaves any data in memory undisturbed. With the replace
option, however, the data in memory are replaced by the data from the table:
. tabi 30 18 \ 38 14, replace
col
row 1 2 Total
1 30 18 48
2 38 14 52
Total 68 32 100
Fisher’s exact = 0.289
1-sided Fisher’s exact = 0.179
. list
row col pop
1. 1 1 30
2. 1 2 18
3. 2 1 38
4. 2 2 14
With this dataset, you could re-create the above table by typing
. tabulate row col [freq=pop], exact
col
row 1 2 Total
1 30 18 48
2 38 14 52
Total 68 32 100
Fisher’s exact = 0.289
1-sided Fisher’s exact = 0.179
tabulate twoway — Two-way table of frequencies 13
tab2
tab2 is a convenience tool. Typing
. tab2 myvar thisvar thatvar, chi2
is equivalent to typing
. tabulate myvar thisvar, chi2
. tabulate myvar thatvar, chi2
. tabulate thisvar thatvar, chi2
Video examples
Pearson’s chi2 and Fisher’s exact test in Stata
Tables and cross-tabulations in Stata
Immediate commands in Stata: Cross-tabulations and chi-squared tests from summary data
Stored results
tabulate, tab2, and tabi store the following in r():
Scalars
r(N) number of observations r(p exact) Fisher’s exact p
r(r) number of rows r(chi2 lr) likelihood-ratio χ
2
r(c) number of columns r(p lr) significance of likelihood-ratio χ
2
r(chi2) Pearson’s χ
2
r(CramersV) Cram
´
er’s V
r(p) significance of Pearson’s χ
2
r(ase gam) ASE of gamma
r(gamma) gamma r(ase taub) ASE of τ
b
r(p1 exact) one-sided Fisher’s exact p r(taub) τ
b
r(p1 exact) is defined only for 2×2 tables. Also, the matrow(), matcol(), and matcell() options allow you to
obtain the row values, column values, and frequencies, respectively.
Methods and formulas
Let n
ij
, i = 1, . . . , I and j = 1, . . . , J, be the number of observations in the ith row and jth
column. If the data are not weighted, n
ij
is just a count. If the data are weighted, n
ij
is the sum of
the weights of all data corresponding to the (i, j) cell.
Define the row and column marginals as
n
i·
=
J
X
j=1
n
ij
n
·j
=
I
X
i=1
n
ij
and let n =
P
i
P
j
n
ij
be the overall sum. Also, define the concordance and discordance as
A
ij
=
X
k>i
X
l>j
n
kl
+
X
k<i
X
l<j
n
kl
D
ij
=
X
k>i
X
l<j
n
kl
+
X
k<i
X
l>j
n
kl
along with twice the number of concordances P =
P
i
P
j
n
ij
A
ij
and twice the number of discordances
Q =
P
i
P
j
n
ij
D
ij
.
14 tabulate twoway — Two-way table of frequencies
The Pearson χ
2
statistic with (I − 1)(J − 1) degrees of freedom (so called because it is based
on Pearson (1900); see Conover [1999, 240] and Fienberg [1980, 9]) is defined as
X
2
=
X
i
X
j
(n
ij
− m
ij
)
2
m
ij
where m
ij
= n
i·
n
·j
/n.
The likelihood-ratio χ
2
statistic with (I − 1)(J − 1) degrees of freedom (Fienberg 1980, 40) is
defined as
G
2
= 2
X
i
X
j
n
ij
ln(n
ij
/m
ij
)
Cram
´
er’s V (Cram
´
er 1946) is a measure of association designed so that the attainable upper bound
is 1. For 2 × 2 tables, −1 ≤ V ≤ 1, and otherwise, 0 ≤ V ≤ 1.
V =
(
(n
11
n
22
− n
12
n
21
)/(n
1·
n
2·
n
·1
n
·2
)
1/2
for 2 × 2
(X
2
/n)/min(I − 1, J − 1)
1/2
otherwise
Gamma (Goodman and Kruskal 1954, 1959, 1963, 1972; also see Agresti [2010,186–188])
ignores tied pairs and is based only on the number of concordant and discordant pairs of observations,
−1 ≤ γ ≤ 1,
γ = (P − Q)/(P + Q)
with asymptotic variance
16
X
i
X
j
n
ij
(QA
ij
− P D
ij
)
2
/(P + Q)
4
Kendall’s τ
b
(Kendall 1945; also see Agresti 2010, 188–189), −1 ≤ τ
b
≤ 1, is similar to gamma,
except that it uses a correction for ties,
τ
b
= (P − Q)/(w
r
w
c
)
1/2
with asymptotic variance
P
i
P
j
n
ij
(2w
r
w
c
d
ij
+ τ
b
v
ij
)
2
− n
3
τ
2
b
(w
r
+ w
c
)
2
(w
r
w
c
)
4
tabulate twoway — Two-way table of frequencies 15
where
w
r
=n
2
−
X
i
n
2
i·
w
c
=n
2
−
X
j
n
2
·j
d
ij
=A
ij
− D
ij
v
ij
=n
i·
w
c
+ n
·j
w
r
Fisher’s exact test (Fisher 1935; Finney 1948; see Zelterman and Louis [1992, 293–301] for
the 2 × 2 case) yields the probability of observing a table that gives at least as much evidence of
association as the one actually observed under the assumption of no association. Holding row and
column marginals fixed, the hypergeometric probability P of every possible table A is computed,
and the
P =
X
T ∈A
Pr(T )
where A is the set of all tables with the same marginals as the observed table, T
∗
, such that
Pr(T ) ≤ Pr(T
∗
). For 2 × 2 tables, the one-sided probability is calculated by further restricting A to
tables in the same tail as T
∗
. The first algorithm extending this calculation to r × c tables was Pagano
and Halvorsen (1981); the one implemented here is the FEXACT algorithm by Mehta and Patel (1986).
This is a search-tree clipping method originally published by Mehta and Patel (1983) with further
refinements by Joe (1988) and Clarkson, Fan, and Joe (1993). Fisher’s exact test is a permutation
test. For more information on permutation tests, see Good (2005 and 2006) and Pesarin (2001).
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tabulate twoway — Two-way table of frequencies 17
Also see
[R] table — Flexible table of summary statistics
[R] tabstat — Compact table of summary statistics
[R] tabulate oneway — One-way table of frequencies
[R] tabulate, summarize() — One- and two-way tables of summary statistics
[D] collapse — Make dataset of summary statistics
[ST] epitab — Tables for epidemiologists
[SVY] svy: tabulate oneway — One-way tables for survey data
[SVY] svy: tabulate twoway — Two-way tables for survey data
[XT] xttab — Tabulate xt data
[U] 12.6.3 Value labels
[U] 25 Working with categorical data and factor variables
