
EXACT BINOMIAL CONFIDENCE LIMITSName:
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 by in the above equations.
<p> <n> <alpha> <SUBSET/EXCEPT/FOR qualification> where <p> is constant, parameter, or variable that contains the proportion of successes; <n> is constant, parameter, or variable that contains the number of trials; <alpha> is constant or parameter that contains the significance level; <lowlim> is a variable that contains the computed lower exact binomial confidence limit; <upplim> is a variable that contains the computed upper exact binomial confidence limit; and where the <SUBSET/EXCEPT/FOR qualification> is optional. The <p> and <n> arguments can be either parameters or variables. If they are both variables, then the variables must have the same number of elements. The <alpha> argument is always assumed to be either a constant or a parameter. If <p> and <n> are both parameters, then <lowlim> and <upplim> will be parameters. Otherwise, they will be variables.
<SUBSET/EXCEPT/FOR qualification> where <p> is constant, parameter, or variable that contains the proportion of successes; <n> is constant, parameter, or variable that contains the number of trials; <lowlim> is a variable that contains the computed lower exact binomail confidence limit; and where the <SUBSET/EXCEPT/FOR qualification> is optional. The <p> and <n> arguments can be either parameters or variables. If they are both variables, then the variables must have the same number of elements. The <alpha> argument is always assumed to be either a constant or a parameter. If <p> and <n> are both parameters, then >lowlim> will be a parameter. Otherwise, it will be a variable.
<SUBSET/EXCEPT/FOR qualification> where <p> is constant, parameter, or variable that contains the proportion of successes; <n> is constant, parameter, or variable that contains the number of trials; <alpha> is constant or parameter that contains the significance level; <upplim> is a variable that contains the computed upper exact binomail confidence limit; and where the <SUBSET/EXCEPT/FOR qualification> is optional. The <p> and <n> arguments can be either parameters or variables. If they are both variables, then the variables must have the same number of elements. The <alpha> argument is always assumed to be either a constant or a parameter. If <p> and <n> are both parameters, then <upplim> will be a parameter. Otherwise, it will be a variable.
LET AL = EXACT BINOMIAL LOWER LIMITS P N ALPHA LET AU = EXACT BINOMIAL UPPER LIMITS P N ALPHA LET AL AU = EXACT BINOMIAL CONFIDENCE LIMITS P N ALPHA ... SUBSET TAG > 2
LET NTRIAL = SIZE Y LET P = YSUM/NTRIAL LET AL AU = EXACT BINOMIAL CONFIDENCE LIMITS P NTRIAL ALPHA If you have a groupid variable (X), you would do something like
LET YSUM = CROSS TABULATE SUM Y X LET NTRIAL = CROSS TABULATE SIZE Y X LET P = YSUM/NTRIAL LET AL AU = EXACT BINOMIAL CONFIDENCE LIMITS P NTRIAL ALPHA In this case, P and NTRIAL are now variables rather than parameters.
LET A = TWO SIDED UPPER EXACT BINOMIAL Y LET A = ONE SIDED LOWER EXACT BINOMIAL Y LET A = ONE SIDED UPPER EXACT BINOMIAL Y This command is a Statistics Let Subcommand rather than a Math 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 "Statistics" version of the command, enter
CONFIDENCE is a synonym for CONFIDENCE LIMITS CONFIDENCE INTERVAL is a synonym for CONFIDENCE LIMITS
2010/10: Twosided limits implemented LET N = 25 LET P = 0.8 LET ALPHA = 0.95 LET AL AU = EXACT BINOMIAL CONFIDENCE LIMITS P N ALPHAThe returned value of AL and AU are 0.592962 and 0.9316878.
Date created: 10/5/2010 