
BINOMIAL PROPORTION TESTName:
The hypothesis test that the two binomial proportions are equal is
Dataplot computes this test for a number of different significance levels.
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for the case where you have raw data and want to perform a twotailed test.
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for the case where you have raw data and want to perform a lower tailed test.
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for the case where you have raw data and want to perform a upper tailed test.
where <p1> is a parameter that specifies the proportion of successes for sample 1; <n1> is a parameter that specifies the sample size for sample 1; <p2> is a parameter that specifies the proportion of successes for sample 2; and <n2> is a parameter that specifies the sample size for sample 2. This syntax is used for the case where you have summary data and want to perform a twotailed test.
where <p1> is a parameter that specifies the proportion of successes for sample 1; <n1> is a parameter that specifies the sample size for sample 1; <p2> is a parameter that specifies the proportion of successes for sample 2; and <n2> is a parameter that specifies the sample size for sample 2. This syntax is used for the case where you have summary data and want to perform a lower tailed test.
where <p1> is a parameter that specifies the proportion of successes for sample 1; <n1> is a parameter that specifies the sample size for sample 1; <p2> is a parameter that specifies the proportion of successes for sample 2; and <n2> is a parameter that specifies the sample size for sample 2. This syntax is used for the case where you have summary data and want to perform an upper tailed test.
BINOMIAL PROPORTION TEST P1 N1 P2 N2
For a lower tailed test, the pvalue is equal to STATCDF. For an upper tailed test, the pvalue is equal to 1  STATCDF. For a twotailed test, the pvalue is equal to 2*(1  STATCDF).
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 SET WRITE DECIMALS 5 BINOMIAL PROPORTION TEST P1 N1 P2 N2The following output is generated. Binomial Test for Equal Proportions (Large Sample Case) H0: P1 = P2 Ha: P1 <> P2 Sample 1: Number of Observations: 38 Probability of Successes: 0.84210 Sample 2: Number of Observations: 44 Probability of Successes: 0.88636 Pooled Probability of Success: 0.86585 Pooled Standard Deviation: 0.07547 Test Statistic: 0.58640 PValue: 0.55760 CDF of Test Statistic: 0.27880  Null Hypothesis Null Null Confidence Critical Acceptance Hypothesis Hypothesis Level Value (+/) Interval Conclusion  P1 = P2 50.0% 0.67 (0.250,0.750) ACCEPT P1 = P2 80.0% 1.28 (0.100,0.900) ACCEPT P1 = P2 90.0% 1.64 (0.050,0.950) ACCEPT P1 = P2 95.0% 1.95 (0.025,0.975) ACCEPT P1 = P2 97.5% 2.24 (0.0125,0.9875) ACCEPT P1 = P2 99.0% 2.57 (0.005,0.995) ACCEPT  
Date created: 01/23/2009 Last updated: 12/11/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 