
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:
\( p_{\mbox{se}} = \sqrt{\frac{p_1(1  p_1)} {n_1} + \frac{p_2(1  p_2)}{n_2}} \)
\( p_{\mbox{diff}} \pm p_{se} \Phi^{1}(1  \alpha/2) \)
with \( \Phi^{1} \) denoting the percent point function of the standard normal distribution. 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
ANOP LIMITS 0.80 1.0
SKIP 25 READ NATR332.DAT Y1 Y2 ANOP LIMITS 138 142 SET WRITE DECIMALS 5 DIFFERENCE OF PROPORTION CONFIDENCE LIMITS Y1 Y2This command generates the following output. TwoSided Confidence Limits for the Difference of Proportions First Response Variable: Y1 Second Response Variable: Y2 Sample 1: Number of Observations: 10 Number of Successes: 5 Proportion of Successes: 0.50000 Sample 2: Number of Observations: 10 Number of Successes: 9 Proportion of Successes: 0.90000 Difference Between Proportions: 0.40000 Warning: if either sample size is less than 20, the normal approximation may not be accurate.  Confidence Lower Upper Value (%) Limit Limit  50.000 0.52437 0.27563 75.000 0.61211 0.18789 90.000 0.70330 0.09670 95.000 0.76140 0.03860 99.000 0.87496 0.07496 99.900 1.00674 0.20674 99.990 1.11739 0.31739 99.999 1.21449 0.41449  
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Date created: 6/5/2001 