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Dataplot Vol 1 Auxiliary Chapter

PORPORTION CONFIDENCE LIMITS

Name:
    PROPORTION CONFIDENCE LIMITS
Type:
    Analysis Command
Purpose:
    Generates a confidence interval for proportions.
Description:
    Given a set of N observations in a variable X, we can compute the proportion of successes. In addition, the PROPORTION CONFIDENCE LIMITS command computes a confidence interval for the proportion of successes.

    In Dataplot, you define a success by entering the command

      ANOP LIMITS <lower limit> <upper limit>

    before entering the PROPORTION CONFIDENCE LIMITS command. That is, you specify the lower and upper values that define a success. Then the estimate for the proportion of successes is simply the number of points in the success region divided by the total number of points. Note that in many programs you would simply enter your data as a series of 0's and 1's where one of these defines a success and the other defines a failure. If your data is already in this format, simply define appropiate limits (e.g., ANOP LIMITS 0.5 1.5).

    If there are P successes in N observations and the significance level is alpha (e.g., 0.05), then the 2-sided confidence interval for the proportion of successes is:

      (BINPPF(ALPHA/2,P,N)/N, BINPPF(1-ALPHA/2,P,N)/N)

    Dataplot computes this inverval for a number of different probability levels.

Syntax:
    PROPORTION CONFIDENCE LIMITS <y>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y> is the response variable;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    ANOP LIMITS 0.80 1.0
    PROPORTION CONFIDENCE LIMITS Y

    ANOP LIMITS 0.80 1.0
    PROPORTION CONFIDENCE LIMITS Y SUBSET TAG = 1 TO 3

Note:
    A table of confidence intervals is printed for alpha levels of 50.0, 75.0, 90.0, 95.0, 99.0, 99.9, 99.99, and 99.999. The sample size, sample number of successes, and sample proportion of successes are also printed.
Default:
    None
Synonyms:
    None
Related Commands:
    ANOP LIMITS = Specify success region for proportions.
    DIFFERENCE OF PROPORTION CONFIDENCE LIMITS = Compute the confidence interval for the difference of proportions.
    ANOP PLOT = Generate an analysis of proportions plot.
    CONFIDENCE LIMITS = Generate the confidence limits for the mean.
Reference:
    "Statistical Methods", Eigth Edition, Snedecor and Cochran, 1989, Iowa State University Press, pp. 121-124.
Applications:
    Confirmatory Data Analysis
Implementation Date:
    1999/5
Program:
    SKIP 25
    SERIAL READ CLEAR.DAT Y
    ANOP LIMITS 1.5 2.0
    PROPORTION CONFIDENCE LIMITS Y

    This command generated the following output: 

          ******************************************
      **      PROPORTION CONFIDENCE LIMITS Y  **
      ******************************************
 
 
                   CONFIDENCE LIMITS FOR A PROPORTION
                           (2-SIDED)
 
          NUMBER OF OBSERVATIONS     =      325
          NUMBER OF SUCCESSES        =       87
          PORPORTION OF SUCCESS      =    .2676923
 
   CONFIDENCE   LOWER         UPPER
   VALUE (%)    LIMIT         LIMIT
------------------------------------
     50.000   .252308       .283077
     75.000   .240000       .295385
     90.000   .227692       .307692
     95.000   .221538       .316923
     99.000   .206154       .332308
     99.900   .190769       .350769
     99.990   .175385       .366154
     99.999   .163077       .378462

    Date created: 6/5/2001
    Last updated: 4/4/2003
    Please email comments on this WWW page to alan.heckert@nist.gov.