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

### Options

`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 |

### 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 *m*_{1} 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 (*m*_{1} and *m*_{2}) 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 *m*_{1} > *m*_{2} or `NULL`

(for a two-sample or one-sample test, respectively). Similarly, `METHOD=lessthan`

will produce a test of the null hypothesis *m*_{1} < *m*_{2} 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.

### See also

Procedures: `BNTEST`

, `SPNTEST`

, `TTEST`

.

Commands for: Basic and nonparametric statistics, Regression analysis.

### Example

CAPTION 'PNTEST example',\ !t('Data from Armitage & Berry (1994), Statistical Methods in',\ 'Medical Research, pages 142 and 145.');\ STYLE=meta,plain 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