
EXACT BINOMIALName:
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 BINOMIAL PROPORTION command is used to compute a point estimate of the probability of success. Confidence intervals for the binomial proportion can be computed using one of the following methods:
If either the number of failures or the sample size is small, the commonly used symmetrical confidence limits based on the normal approximation may not be accurate enough. In that case, the following exact method can be used.
Note that these intervals are not symetric about p. Onesided intervals can be computed by replacing \( z_{\alpha/2} \) by \( z_{\alpha} \) in the above equations.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <par> is a parameter where the computed value 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. This returns the lower confidence limit for the twosided exact binomial interval.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <par> is a parameter where the computed value 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. This returns the upper confidence limit for the twosided exact binomial interval.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <par> is a parameter where the computed value is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
This is for raw data case and
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <par> is a parameter where the computed value 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. This returns the upper confidence limit for the onesided upper tailed exact binomial interval.
LET A = TWOSIDED UPPER EXACT BINOMIAL Y1 LET A = ONESIDED LOWER EXACT BINOMIAL Y1 LET A = ONESIDED UPPER EXACT BINOMIAL Y1 LET A = TWOSIDED LOWER EXACT BINOMIAL Y1 SUBSET TAG > 2
The default value of alpha is 0.95.
These various commands are actually where the EXACT BINOMIAL statistics are most commonly used.
LET AL = EXACT BINOMIAL LOWER LIMITS P N ALPHA LET AU = EXACT BINOMIAL UPPER LIMITS P N ALPHA This command is a Math Let Subcommand rather than a Statistics LET Subcommand. The distinctions are:
Which form of the command to use is determined by the context of what you are trying to do. For details on the "Math" version of the commands, enter
LET N = 1 LET P = 0.8 LET ALPHA = 0.95 LET Y = BINOMIAL RANDOM NUMBERS FOR I = 1 1 50 LET EL = ONE SIDED LOWER EXACT BINOMIAL Y LET EU = ONE SIDED LOWER EXACT BINOMIAL Y LET EL = TWO SIDED LOWER EXACT BINOMIAL Y LET EU = TWO SIDED LOWER EXACT BINOMIAL YThe following output is generated. AL  0.6622259E+00 AU  0.8714431E+00 BL  0.7718925E+00 BU  0.7844336E+00  
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Date created: 10/05/2010 