## Stata 15 help for ci_14_0

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Title

[R] ci -- Confidence intervals for means, proportions, and counts (syntax
prior to version 14.1)

[The syntax of ci and cii was changed as of version 14.1.
This help file documents ci's and cii's old syntax and as
such is probably of no interest to you.  If you have set
version to less than 14.1 in your old do-files, you do not
have to translate cis or ciis to modern syntax.  This help
file is provided for those wishing to debug or understand
old code.  Click here for the help file of the modern ci
and cii commands.]

Syntax

Syntax for ci

ci [varlist] [if] [in] [weight] [, options]

Immediate command for variable distributed as normal

cii #obs #mean #sd [, ciin_option]

Immediate command for variable distributed as binomial

cii #obs #succ [, ciib_options]

Immediate command for variable distributed as Poisson

cii #exposure #events , poisson [ciip_options]

#succ and #events must be an integer or between 0 and 1.  If the number
is between 0 and 1, Stata interprets it as the fraction of successes
or events and converts it to an integer number representing the
number of successes or events.  The computation then proceeds as if
two integers had been specified.

options                Description
-------------------------------------------------------------------------
Main
binomial             binomial 0/1 variables; compute exact confidence
intervals
poisson              Poisson variables; compute exact confidence
intervals
exposure(varname)    exposure variable; implies poisson
exact                calculate exact confidence intervals; the default
wald                 calculate Wald confidence intervals
wilson               calculate Wilson confidence intervals
agresti              calculate Agresti-Coull confidence intervals
jeffreys             calculate Jeffreys confidence intervals
total                add output for all groups combined (for use with
by only)
separator(#)         draw separator line after every # variables;
default is separator(5)
level(#)             set confidence level; default is level(95)
-------------------------------------------------------------------------
by and statsby are allowed with ci; see prefix.
aweights and fweights are allowed, but aweights may not be specified with
the binomial or poisson option, see weight.

ciin_option            Description
-------------------------------------------------------------------------
level(#)               set confidence level; default is level(95)
-------------------------------------------------------------------------

ciib_options           Description
-------------------------------------------------------------------------
level(#)               set confidence level; default is level(95)
exact                  calculate exact confidence intervals; the default
wald                   calculate Wald confidence intervals
wilson                 calculate Wilson confidence intervals
agresti                calculate Agresti-Coull confidence intervals
jeffreys               calculate Jeffreys confidence intervals
-------------------------------------------------------------------------

ciip_options           Description
-------------------------------------------------------------------------
* poisson              numbers are Poisson-distributed counts
level(#)             set confidence level; default is level(95)
-------------------------------------------------------------------------
* poisson is required.

ci

Statistics > Summaries, tables, and tests > Summary and descriptive
statistics > Confidence intervals

cii for variable distributed as normal

Statistics > Summaries, tables, and tests > Summary and descriptive
statistics > Normal CI calculator

cii for variable distributed as binomial

Statistics > Summaries, tables, and tests > Summary and descriptive
statistics > Binomial CI calculator

cii for variable distributed as Poisson

Statistics > Summaries, tables, and tests > Summary and descriptive
statistics > Poisson CI calculator

Description

ci computes standard errors and confidence intervals for each of the
variables in varlist.  Normal confidence intervals are produced by
default.  However, a variety of binomial confidence intervals or exact
Poisson confidence intervals can be requested.

cii is the immediate form of ci; see immed for a general discussion of
immediate commands.

Options

+------+
----+ Main +-------------------------------------------------------------

binomial tells ci that the variables are 0/1 variables and that binomial
confidence intervals will be calculated. (cii produces binomial
confidence intervals when only two numbers are specified.)

poisson specifies that the variables (or numbers for cii) are
Poisson-distributed counts; exact Poisson confidence intervals will
be calculated.

exposure(varname) is used only with poisson.  You do not need to specify
poisson if you specify exposure(); poisson is assumed. varname
contains the total exposure (typically a time or an area) during
which the number of events recorded in varlist were observed.

exact, wald, wilson, agresti, and jeffreys specify that variables are 0/1
and specify how binomial confidence intervals are to be calculated.

exact is the default and specifies exact (also known in the
literature as Clopper-Pearson ) binomial confidence intervals.

wald specifies calculation of Wald confidence intervals.

wilson specifies calculation of Wilson confidence intervals.

agresti specifies calculation of Agresti-Coull confidence intervals.

jeffreys specifies calculation of Jeffreys confidence intervals.

See Brown, Cai, and DasGupta (2001) for a discussion and comparison
of the different binomial confidence intervals.

total is for use with the by prefix. It requests that, in addition to
output for each by-group, output be added for all groups combined.

separator(#) specifies how often separation lines should be inserted into
the output.  The default is separator(5), meaning that a line is
drawn after every five variables.  separator(10) would draw the line
after every 10 variables. separator(0) suppresses the separation
line.

level(#) specifies the confidence level, as a percentage, for confidence
intervals.  The default is level(95) or as set by set level.

Examples

---------------------------------------------------------------------------
Setup
. sysuse auto

Obtain normal-approximation 90% confidence intervals for means of
normally distributed variables
. ci mpg price, level(90)

---------------------------------------------------------------------------
Setup
. webuse promonone

Obtain various binomial confidence intervals for proportions
. ci promoted, binomial
. ci promoted, binomial wilson
. ci promoted, binomial agresti
. ci promoted, binomial jeffreys

---------------------------------------------------------------------------
Setup
. webuse petri

Obtain exact Poisson confidence interval for a count variable
. ci count, poisson

---------------------------------------------------------------------------
Setup
. webuse rm

Obtain confidence intervals for total exposure variables
. ci deaths, exposure(pyears)

Obtain confidence intervals for mean for data with 166 observations,
mean=19509, and sd=4379
. cii 166 19509 4379

Same as above, but obtain 90% confidence intervals
. cii 166 19509 4379, level(90)

Obtain binomial confidence intervals for data with 10 binomial events and
1 observed success
. cii 10 1

Same as above, but obtain the Wilson confidence interval
. cii 10 1, wilson

Obtain Poisson confidence intervals for data with 1 exposure and 27
events
. cii 1 27, poisson
---------------------------------------------------------------------------

Video examples

Immediate commands in Stata: Confidence intervals for Poisson data

Immediate commands in Stata: Confidence intervals for binomial data

Immediate commands in Stata: Confidence intervals for normal data

Stored results

ci and cii store the following in r():

Scalars
r(N)           number of observations or exposure
r(mean)        mean
r(se)          estimate of standard error
r(lb)          lower bound of confidence interval
r(ub)          upper bound of confidence interval

References

Brown, L. D., T. T. Cai, and A. DasGupta. 2001.  Interval estimation for
a binomial proportion.  Statistical Science 16: 101-133.

Clopper, C. J., and E. S. Pearson. 1934.  The use of confidence or
fiducial limits illustrated in the case of the binomial.  Biometrika
26: 404-413.

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