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PNTEST procedure

Calculates one- and two-sample Poisson 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); default norm
S1 = scalar Sample size for sample 1; default 1
S2 = scalar Sample size for sample 2; default 1
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


MU1 = scalars or variates Numbers recorded in the first sample
MU2 = scalars or variates Numbers recorded in the second sample
NORMAL = scalars Saves the Normal approximation
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


PNTEST calculates one- and two-sample Poisson tests. The value for the mean under the null hypothesis for a one-sample test is specified by the option NULL. You can supply the sample mean m1 as a scalar using the MU1 parameter. The sample size is then specified by the S1 option (with default 1). Alternatively, you can set MU1 to a variate containing the counts in the individual samples (and the sample size is then the number of non-missing values that it contains). With a two-sample test, parameters MU1 and MU2 similarly provide the means (m1 and m2) for samples 1 and 2 respectively, and the sample sizes can be specified using the S1 and S2 options.

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 will give a one-sided test of the null hypothesis that m1 > m2 or NULL (for a two-sample or one-sample test, respectively). Similarly, METHOD=lessthan will produce a test of the null hypothesis m1 < m2 or NULL. A small “p-value” indicates that the data are inconsistent with the null hypothesis. The TEST option specifies the form of test used for the one-sample test; either an exact test or a Normal approximation can be selected.

Printed output is controlled by the PRINT option with settings:

    summary mean, sample size, standard error (for Normal approximation);
    test Normal approximation and probability level, or just probability level for the exact test;
    confidence confidence interval for the difference between the mean and NULL for a one-sample test, or the two means for a two-sample test.

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 NORMAL, PROBABILITY, LOWER and UPPER parameters. NORMAL saves the Normal approximation for the one- and two-sample tests, PROBABILITY saves the probability level. LOWER and UPPER save the lower and upper limits, respectively, of the confidence interval.




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 141) of Arimitage & Berry (1994).


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

See also


Commands for: Basic and nonparametric statistics, Regression analysis.


CAPTION 'PNTEST example',\
        !t('Data from Armitage & Berry (1994), Statistical Methods in',\
        'Medical Research, pages 142 and 145.');\
PNTEST  [NULL=20] MU1=33
CAPTION 'One-sample test, using exact test and confidence intervals.'
PNTEST  [NULL=20; TEST=exact] MU1=33
CAPTION 'One-sample test, one-sided.'
PNTEST  [NULL=20; METHOD=greater] MU1=33
CAPTION !t('Two-sample test, saving Normal approximation,',\
        'probability and confidence interval.')
PNTEST  MU1=13;MU2=31; NORMAL=norm; PROBABILITY=prob; LOWER=lower; UPPER=upper
PRINT   norm,prob,lower,upper
Updated on March 6, 2019

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