
BINOMIAL RATIO CONFIDENCE LIMITSName:
with ^{1} denoting the normal percent point function. If p_{1} and p_{2} are both 1, the resulting uncertainty is zero. If either p_{1} or p_{2} is zero, we have division by zero in the above formula. For that reason, we use the Bayes estimators of p_{1} and p_{2}:
with V and U denoting the number of successes in the binomial trials. We then use these updated estimates for p_{1} and p_{2} in the above formula.
<p1> <n1> <p2> <n2> <alpha> <SUBSET/EXCEPT/FOR qualification> where <p1> is constant, parameter, or variable that contains the proportion of successes for the first sample; <n1> is constant, parameter, or variable that contains the number of trials for the first sample; <p2> is constant, parameter, or variable that contains the proportion of successes for the second sample; <n2> is constant, parameter, or variable that contains the number of trials for the second sample; <alpha> is constant or parameter that contains the significance level; <ratio> is a variable that contains the computed ratio (p_{1}/p_{2}); <lowlim> is a variable that contains the computed lower confidence limit; <upplim> is a variable that contains the computed upper confidence limit; and where the <SUBSET/EXCEPT/FOR qualification> is optional. The <p1>, <n1>, <p2>, and <n2> arguments can be either parameters or variables. If they are 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 <p1> <n1> <p2> and <n2> are all parameters, then <ratio> <lowlim> and <upplim> will be parameters. Otherwise, they will be variables.
P1 N1 P2 N2 ALPHA
LET N1 = SIZE Y1 LET P1 = YSUM1/N1 LET YSUM2 = SUM Y2 LET N2 = SIZE Y2 LET P2 = YSUM2/N2 LET RATIO AL AU = BINOMIAL RATIO CONFIDENCE LIMITS ... P1 N1 P2 N2 ALPHA If you have groupid variables (X1 and X2), you would do something like
LET YSUM1 = CROSS TABULATE SUM Y1 X1 LET N1 = CROSS TABULATE SIZE Y1 X1 LET P1 = YSUM1/N1 LET YSUM2 = CROSS TABULATE SUM Y2 X2 LET N2 = CROSS TABULATE SIZE Y2 X2 LET P2 = YSUM2/N2 LET RATIO AL AU = BINOMIAL RATIO CONFIDENCE LIMITS ... P1 N1 P2 N2 ALPHA In this case, P1, N1, P2, and N2 are now variables rather than parameters.
LET P1 = 8/12 LET N1 = 12 LET P2 = 7/8 LET N2 = 8 LET ALPHA = 0.05 . LET ARATIO LOWLIM UPPLIM = BINOMIAL RATIO CONFIDENCE LIMIT ... P1 N1 P2 N2 ALPHAThe values of ARATIO, LOWLIM, and UPPLIM are 0.7846, 0.4687, and 1.3135, respectively.
Date created: 10/5/2010 