
DIFFERENCE OF PORPORTION CONFIDENCE LIMITSName:
In Dataplot, you define a success by entering the command
before entering the DIFFERENCE OF 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 in each sample is simply the number of points in the success region divided by the total number of points. The difference of proportions is then the difference between these two sample proportions. 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 P1 successes in N1 observations for sample 1 and P2 successes in N2 observations for sample 2, and the significance level is alpha (e.g., 0.05), then the 2sided confidence interval for the difference of proportions of successes is computed as:
PSE = SQRT(P1*(1.0P1)/N + P2*(1.0P2)/N2) (PDIFF  PSE*NORPPF(ALPHA/2), PDIFF + PSE*NORPPF(1ALPHA/2)) where NORCDF is the normal cumulative distribution function. Dataplot computes this inverval for a number of different probability levels.
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
DIFFERENCE OF PROPORTION CONFIDENCE LIMITS Y1 Y2
DIFFERENCE OF PROPORTION CONFIDENCE LIMITS Y1 Y2 SUBSET TAG > 2
READ NATR332.DAT Y1 Y2 ANOP LIMITS 138 142 DIFFERENCE OF PROPORTION CONFIDENCE LIMITS Y1 Y2 This command generates the following output. CONFIDENCE LIMITS FOR DIFFERENCE OF PROPORTIONS (2SIDED) NUMBER OF OBSERVATIONS FOR SAMPLE 1 = 10 NUMBER OF SUCCESSES FOR SAMPLE 1 = 5 PORPORTION OF SUCCESS FOR SAMPLE 1 = .5000000 NUMBER OF OBSERVATIONS FOR SAMPLE 2 = 10 NUMBER OF SUCCESSES FOR SAMPLE 2 = 9 PORPORTION OF SUCCESS FOR SAMPLE 2 = .9000000 DIFFERENCE BETWEEN PROPORTIONS = .4000000 WARNING: IF EITHER OF THE SAMPLE SIZES IS LESS THAN 30, THE NORMAL APPROXIMATION MAY NOT BE ACCURATE. CONFIDENCE LOWER UPPER VALUE (%) LIMIT LIMIT  50.000 .524370 .275630 75.000 .612114 .187886 90.000 .703296 .967040E01 95.000 .761400 .386004E01 99.000 .874960 .749596E01 99.900 1.00675 .206747 99.990 1.11738 .317382 99.999 1.21443 .414432
Date created: 6/5/2001 