RUKHIN 2 TEST

RUKHIN 2 TEST (LET)

Let Subcommand

For two binomial proportions, compute the p-value and lower and upper confidence limits for
H₀: p₁ = 0.5*p₂

with p₁ and p₂ denoting the two binomial proportions.

For each of the binomial proportions, we actually use the correction terms
p_i = (x_i + 0.5)/(n_i + 1)

with p_i x_i, and n_i denoting the binomial proportion, the number of successes and the number of trials for the i-th binomial proportion.

The computed test statistic is

p₁ - 0.5*p₂

and the associated standard error is

The p-value for a lower tailed test is

The p-value for an upper tailed test is

The p-value for a two tailed test is

The confidence interval is

LET <pval> <lowlim> <upplim> = RUKHIN 2 TEST
                        <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;
            <pval> contains the returned p-value;
            <lowlim> contains the computed lower confidence limit;
            <upplim> contains the computed upper confidence limit;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax performs a two-tailed hypothesis test.

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 the arguments are all parameters, then <pval>, <lowlim>, and <upplim> will be parameters. Otherwise, they will be variables.

LET <pval> <lowlim> <upplim> = RUKHIN 2 LOWER TAILED TEST
                        <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;
            <pval> contains the returned p-value;
            <lowlim> contains the computed lower confidence limit;
            <upplim> contains the computed upper confidence limit;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax performs a lower-tailed hypothesis test. However, the confidence limits correspond to the two-tailed test.

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 the arguments are all parameters, then <pval>, <lowlim>, and <upplim> will be parameters. Otherwise, they will be variables.

LET <pval> <lowlim> <upplim> = RUKHIN 2 UPPER TAILED TEST
                        <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;
            <pval> contains the returned p-value;
            <lowlim> contains the computed lower confidence limit;
            <upplim> contains the computed upper confidence limit;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax performs an upper-tailed hypothesis test. However, the confidence limits correspond to the two-tailed test.

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 the arguments are all parameters, then <pval>, <lowlim>, and <upplim> will be parameters. Otherwise, they will be variables.

LET PVAL AL AU = RUKHIN 2 TEST P1 N1 P2 N2 ALPHA
LET PVAL AL AU = RUKHIN 2 LOWER TAILED TEST ...
            P1 N1 P2 N2 ALPHA
LET PVAL AL AU = RUKHIN 2 UPPER TAILED TEST ...
            P1 N1 P2 N2 ALPHA

None

RUKHIN TWO is a synonym for RUKHIN 2

RUKHIN 1 TEST	= Test binomial proportions p1 = p2*p3.
RUKHIN 3 TEST	= Test binomial proportions p1*p2 = p3*p4.
BINOMIAL PRODUCT CONF LIMITS	= Compute confidence limits for the product of two binomial proportions.
BINOMIAL RATIO CONF LIMITS	= Compute confidence limits for the ratio of two binomial proportions.
AGRESTI-COULL CONFIDENCE LIMITS	= Compute Agresti-Coull confidence limits for binomial proportions.
EXACT BINOMIAL CONFIDENCE LIMITS	= Compute exact binomial confidence limits for binomial proportions.
AGRESTI-COULL	= Compute Agresti-Coull confidence limits statistic for binomial proportions.
EXACT BINOMIAL	= Compute the "exact" confidence limits statistic for binomial proportions.
BINOMIAL PROPORTION	= Compute the binomial proportion statistic.
BINOMIAL PROPORTION TEST	= Perform a binomial proportions test.
CROSS TABULATE	= Perform a cross-tabulation for a specified statistic.

Private communication with Andrew Rukhin and Bill Strawderman.

Statistics

2008/09

 
LET P1 = 0.9
LET N2 = 40
LET P2 = 0.6
LET N2 = 40
LET ALPHA = 0.90
.
LET PVAL AL AU = RUKHIN 2 TEST P1 N1 P2 N2 ALPHA
    

The returned values for PVAL, AL, and AU are 0.0000, 0.4993, and 0.7007, respectively.