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BNTEST procedure

Calculates one- and two-sample binomial tests (D.A. Murray).


PRINT = string tokens Controls printed output (test, summary, confidence); default test, summ, conf
METHOD = string token Type of test required (twosided, greaterthan, lessthan); default twos
TEST = string token Form of the test for one-sample test (exact, normalapproximation) or for two-sample (normalapproximation, oddsratio); default norm
CIPROBABILITY = scalar The probability level for the confidence interval; default 0.95
NULL = scalar The value of the probability of success under the null hypothesis for the one-sample test; default 0.5


R1 = scalars or variates Number of successes (scalar) or results (variate) for the first sample
N1 = scalars Sample size of the first sample
R2 = scalars or variates Number of successes (scalar) or results (variate) for the second sample
N2 = scalars Sample size of the second sample
STATISTIC = scalars Saves the Normal approximation from the one-sample or two-sample tests, or the odds ratio
PROBABILITY = scalars Saves the probability value from the one-sample or two-sample tests
LOWER = scalars Saves the lower limit of the confidence interval
UPPER = scalars Saves the upper limit of the confidence interval


BNTEST calculates one- and two-sample binomial tests, and odds ratios. For a one-sample test, the number of successes r1 can be specified using the R1 parameter, and the sample size n1 using the N1 parameter (both as scalars). Alternatively you can supply the raw data, by setting R1 to a variate containing one in the units corresponding to successful trials and zero in those for unsuccessful trials. The test is for the probability of success under a binomial distribution. The value for the probability under the null hypothesis is 0.5 by default, but you can specify other probabilities using the NULL option. With a two-sample test, R1 and N1 similarly provide the number of successes and sample size for the first sample (r1 and n1), and R2 and N2 those for the second sample (r2 and n2).

For both one- and two-sample cases, the test is assumed to be two-sided unless otherwise requested by the METHOD option. Setting METHOD=greaterthan gives a one-sided test of the null hypothesis that r1/n1 > r2/n2 or NULL (for a two-sample or one-sample test, respectively). Similarly, METHOD=lessthan produces a test of the null hypothesis r1/n1 < r2/n2 or NULL. A small “p-value” indicates that the data are inconsistent with the null hypothesis.

The TEST option specifies the form of test to be used. For the one-sample test, an exact test or Normal approximation can be selected. For a two-sample test, a Normal approximation or odds ratio can be chosen.

Printed output is controlled by the PRINT option with settings:

    summary number of successes, sample size, proportion, standard error (for Normal approximation and odds ratio) and odds ratio (when TEST=ODDSRATIO is selected);
    test test and probability level;
    confidence confidence interval for the probabilities of success; for the odds ratio the confidence interval is displayed for the true log-odds ratio and odds ratio.

The default is to print everything.

By default a 95% confidence interval is calculated, but this can be changed by setting the CIPROBABILITY option to the required value (between 0 and 1).

Results can be saved using the STATISTIC, PROBABILITY, LOWER and UPPER parameters. STATISTIC saves the Normal approximation for the one- and two-sample tests or the odds ratio, PROBABILITY saves the probability level. LOWER and UPPER save the lower and upper limits, respectively, of the confidence interval; for the odds ratio the confidence interval is saved for the true odds ratio.




A standard Normal approximation is used for both the one- and two-sample tests. The exact test and confidence intervals are based on the methodology described in Chapter 4 (page 121) of Armitage & Berry (1994). The odds ratio is a relative measure of the odds of a success in one set of data relative to that in the other. The estimate of the ratio is defined as

p1 (1 – p1) / p2 (1 – p2)

where p1 and p2 are the success probabilities in two sets of data. The calculation of the approximate standard error of the estimated log-odds ratio and confidence intervals is described in Chapter 2 (page 36) of Collett (1991).


Armitage, P. & Berry, G. (1994). Statistical Methods in Medical Research. Blackwell Science, Oxford.

Collett, D. (1991). Modelling Binary Data. Chapman & Hall, London.

See also


Commands for: Basic and nonparametric statistics, Regression analysis.


CAPTION 'BNTEST example',\
        !t('Data from Statistical Methods in Medical Research',\
        '(Armitage & Berry 1994, page 119).'); STYLE=meta,plain
BNTEST  65; N1=100
CAPTION !t('One-sample, two-sided exact test, saving the 95% confidence',\
        'interval and the probability.')
BNTEST  [TEST=exact] R1=65; N1=100; PROBABILITY=prob; LOWER=lower; UPPER=upper
PRINT   prob,lower,upper
CAPTION 'One-sample, one-sided exact test on the same data.'
BNTEST  [METHOD=greater; TEST=exact] R1=65; N1=100
CAPTION 'Two-sample, two-sided test.'
BNTEST   R1=41; N1=257; R2=64; N2=244
CAPTION 'Odds ratio.'
BNTEST  [TEST=oddsratio] R1=148; N1=520; R2=75; N2=418
Updated on March 8, 2019

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