Dataplot Vol 1 Vol 2

# 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)

with BINPPF denoting the binomial percent point function. 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. ANOP PLOT = Generate an analysis of proportions plot. CONFIDENCE LIMITS = Generate the confidence limits for the mean.
Reference:
Snedecor and Cochran, 1989, "Statistical Methods," Eigth Edition, Iowa State University Press, pp. 121-124.
Applications:
Confirmatory Data Analysis
Implementation Date:
1999/5
Program:
SKIP 25
SET WRITE DECIMALS 4
ANOP LIMITS 1.5 2.0
PROPORTION CONFIDENCE LIMITS Y

This command generated the following output:
             Two-Sided Confidence Limits for a Proportion

Response Variable: Y

Sample 1:
Number of Observations:                  325
Number of Successes:                     87
Proportion of Successes:                 0.2677

------------------------------------------
Confidence          Lower          Upper
Value (%)          Limit          Limit
------------------------------------------
50.000         0.2523         0.2831
75.000         0.2400         0.2954
90.000         0.2277         0.3077
95.000         0.2215         0.3169
99.000         0.2062         0.3323
99.900         0.1908         0.3508
99.990         0.1754         0.3662
99.999         0.1631         0.3785


NIST is an agency of the U.S. Commerce Department.

Date created: 06/05/2001
Last updated: 11/04/2015