
DIFFERENCE OF PORPORTION CONFIDENCE LIMITSName:
For most applications, you typically define success as a "1" and failure as a "0". However, in Dataplot you can also specify the range of values that constitute success (all other values denote failure) by entering the command
The default limits are 0.5 and 1.5 so that if your data contains 0's and 1's this command can be omitted. Several methods have been proposed for the confidence limits for the difference between binomial proportions. The following methods are currently supported in Dataplot (other methods are available)
To specify the method to use, enter the command
The default is the adjusted Wald (AgrestiCaffo) interval. 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
SET DIFFERENCE OF BINOMIAL METHOD ADJUSTED WALD
DIFFERENCE OF PROPORTION CONFIDENCE LIMITS Y1 Y2 ...
LET A = DIFF OF BINOMIAL PROPORTIONS LOWER CONFIDENCE ... LIMIT Y1 Y2 LET A = DIFF OF BINOMIAL PROPORTIONS UPPER CONFIDENCE ... LIMIT Y1 Y2 In addition to the above LET commands, builtin statistics are supported for about 20+ different commands (enter HELP STATISTICS for details).
Agresti and Caffo (2000), "Simple and Effective Confidence Intervals for Proportions and Differences of Proportions Result From Adding Two Successes and Two Failures", The American Statistician, Vol. 54, No. 4, pp. 280288. Carlin and Louis (1996), "Bayes and Empirical Bayes Methods for Data Analysis", Chapman and Hall.
2017/11: Added the adjusted Wald (AgrestiCaffo) and Bayesian intervals 2017/11: Made the adjusted Wald (AgrestiCaffo) interval the default let n1 = 40 let nsuc1 = 8 let y1 = 0 for i = 1 1 n1 let y1 = 1 for i = 1 1 nsuc1 . let n2 = 30 let nsuc2 = 11 let y2 = 0 for i = 1 1 n2 let y2 = 1 for i = 1 1 nsuc2 . . Now do proportions confidence interval . set write decimals 5 let alpha = 0.95 . set difference of binomial method wald difference of proportion confidence interval y1 y2 set difference of binomial method adjusted wald difference of proportion confidence interval y1 y2 set difference of binomial method bayesian difference of proportion confidence interval y1 y2This command generates the following output. Difference of Proportions TwoSided Confidence Limits (Wald Method) First Response Variable: Y1 Second Response Variable: Y2 Sample 1: Number of Observations: 40 Number of Successes: 8 Proportion of Successes: 0.20000 Sample 2: Number of Observations: 30 Number of Successes: 11 Proportion of Successes: 0.36667 Difference Between Proportions: 0.16667  Confidence Lower Upper Value (%) Limit Limit  50.000 0.23975 0.09358 75.000 0.29131 0.04202 90.000 0.34489 0.01156 95.000 0.37904 0.04570 99.000 0.44577 0.11244 99.900 0.52321 0.18988 99.990 0.58823 0.25490 99.999 0.64529 0.31195 Difference of Proportions TwoSided Confidence Limits (AgrestiCaffo (Adjusted Wald) Method) First Response Variable: Y1 Second Response Variable: Y2 Sample 1: Number of Observations: 40 Number of Successes: 8 Proportion of Successes: 0.20000 Sample 2: Number of Observations: 30 Number of Successes: 11 Proportion of Successes: 0.36667 Difference Between Proportions: 0.16667  Confidence Lower Upper Value (%) Limit Limit  50.000 0.23252 0.08891 75.000 0.28318 0.03825 90.000 0.33582 0.01439 95.000 0.36936 0.04794 99.000 0.43493 0.11350 99.900 0.51101 0.18958 99.990 0.57489 0.25346 99.999 0.63095 0.30952 Difference of Proportions TwoSided Confidence Limits (Carlin and Louis Bayesian Method) First Response Variable: Y1 Second Response Variable: Y2 Sample 1: Number of Observations: 40 Number of Successes: 8 Proportion of Successes: 0.20000 Sample 2: Number of Observations: 30 Number of Successes: 11 Proportion of Successes: 0.36667 Difference Between Proportions: 0.16667  Confidence Lower Upper Value (%) Limit Limit  50.000 0.23151 0.08992 75.000 0.28146 0.03997 90.000 0.33337 0.01194 95.000 0.36644 0.04501 99.000 0.43109 0.10966 99.900 0.50611 0.18468 99.990 0.56909 0.24766 99.999 0.62437 0.30294  
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Date created: 06/05/2001 