PNTEST procedure

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

Options

PRINT = strings

Controls printed output (test, summary, confidence); default test, summ, conf

METHOD = string

Type of test required (twosided, greaterthan, lessthan); default twos

TEST = string

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

Parameters

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

Description

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.

Options: PRINT, METHOD, TEST, S1, S2, CIPROBABILITY, NULL.

Parameters: MU1, MU2, NORMAL, PROBABILITY, LOWER, UPPER.

Method

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).

Reference

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