
DIFFERENCE OF PROPORTION HYPOTHESIS TESTName:
The hypothesis test that the two binomial proportions are equal is
For a lower tailed test, the pvalue is equal to \( \Phi(Z) \). For an upper tailed test, the pvalue is equal to 1  \( \Phi(Z) \). For a twotailed test, the pvalue is equal to 2*(1  \( \Phi(Z) \) ). Alternatively, you can request that the lower and upper confidence limits for p_{1}  p_{2} be returned instead of the pvalue for the hypothesis 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> is the returned pvalue; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for the twotailed case. 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 <pval> will be a parameter. Otherwise, it will be a variable.
HYPOTHESIS 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> is the returned pvalue; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for the lower tailed case. 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 <pval> will be a parameter. Otherwise, it will be a variable.
HYPOTHESIS 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> is the returned pvalue; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for the upper tailed case. 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 <pval> will be a parameter. Otherwise, it will be a variable.
<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> is the returned difference of binomial proportions; <al> is the returned lower confidence limit; <au> is the returned 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 <al> and <au> will be parameters. Otherwise, they will be variables.
P1 N1 P2 N2 ALPHA LET PDIFF AL AU = DIFFERENCE OF PROPORTION CONFIDENCE LIMTIS ... P1 N1 P2 N2 ALPHA
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
In addition, the command
performs a difference of binomial proportions test. This command generates a more detailed output for the test. The LET version of the test is most useful when computing many values of the test statistic.
Ryan (2008), "Modern Engineering Statistics", Wiley, pp. 124126.
LET X1 = 32 LET N1 = 38 LET P1 = X1/N1 LET X2 = 39 LET N2 = 44 LET P2 = X2/N2 LET ALPHA = 0.05 LET PVAL = DIFFERENCE OF PROPORTION HYPOTHESIS TEST P1 N1 P2 N2 ALPHA LET PDIFF AL AU = DIFFERENCE OF PROPORTION CONFIDENCE LIMITS P1 N1 P2 N2 ALPHAThe resulting values for PDIFF, PVAL, AL, and AU are 0.044, 0.5576, 0.1974, and 0.1805, respectively.  
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Date created: 10/05/2010 