
BINOMIAL PROPORTIONName:
In this context, we define success as "1" and failure as "0". Dataplot actually allows any two distinct values to be used. However, the larger value will always be considered "success" and the smaller value will always be considered "failure". If the variable contains more than two distinct values, an error is reported. The case where the data consists of a sequence of 0's and 1's is referred to as the raw data case. There may be times where we only have summary data. This case is referred to as the summary data case. The two response variables are the number of successes and the number of trials and we use the BINOMIAL RATIO command instead of the BINOMIAL PROPORTION command. We may also sometimes be interested in the difference of two binomial proportions. The DIFFERENCE OF BINOMIAL PROPORTIONS command can be used for this case.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <par> is a parameter where the computed binomial proportion is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This is for raw data case and <y> should contain a sequence of 0's and 1's.
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; <par> is a parameter where the computed difference of binomial proportions is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax computes the binomial proportions of <y1> and <y2> and then computes their difference. The <y1> and <y2> variables do not need to be the same length. This is for raw data case and <y1> and <y2> should both contain a sequence of 0's and 1's.
<SUBSET/EXCEPT/FOR qualification> where <ysucc> is a variable that contains the number of successes; <ytrial> is a variable that contains the number of trials; <par> is a parameter where the computed binomial proportion is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
This is for summary data case. The The elements in <ysucc> and <ytrial> are summed if they have length greater than one and a single binomial proportion is returned. If they have only a single element, they must still be defined as variables rather than parameters. For example,
LET YTRIAL = DATA 20 defines YSUCC and YTRIAL as variables with a single row. However
LET YTRIAL = 20 defines them as parameters and they cannot be used with this command.
LET A = BINOMIAL PROPORTION Y1 SUBSET TAG > 2 LET A = DIFFERENCE OF BINOMIAL PROPORTION Y1 Y2
These various commands are actually where the BINOMIAL PROPORTION and BINOMIAL RATIO statistics are most commonly used. For the BINOMIAL PROPORTION and BINOMIAL RATIO statistics, the TABULATE/CROSS TABULATE commands will return the number of trials and the AgrestiCoull lower and upper confidence limits in addition to the binomial proportion. For the BINOMIAL PROPORTION and BINOMIAL RATIO statistics, the FLUCTUATION PLOT command supports an uncertainty option based on the AgrestiCoull interval. Enter HELP FLUCTUATION PLOT for details.
Thomas Ryan (2008), "Modern Engineering Statistics," Wiley, pp. 124126.
2008/9: DIFFERENCE OF BINOMIAL PROPORTIONS added 2010/1: BINOMIAL RATIO added LET N = 1 LET P = 0.8 LET Y = BINOMIAL RANDOM NUMBERS FOR I = 1 1 50 LET A = BINOMIAL PROPORTION YA result of 0.78 is returned (this may vary if you have modified the seed, specified a difference random number generator or have generated random numbers earlier in your Dataplot session.  
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Date created: 10/05/2010 