Calculates the sample size for a sign test (R.W. Payne).

### Options

`PRINT` = string token |
What to print (`replication` , `power` ); default `repl` , `powe` |
---|---|

`PROBABILITY` = scalar |
Significance level at which the response is to be tested; default 0.05 |

`POWER` = scalar |
The required power (i.e. probability of detection) of the test; default 0.9 |

`TMETHOD` = string token |
Whether to a one- or two-sided test is to be made (`onesided` , `twosided` ); default `twos` |

`REPLICATION` = variate |
Replication values for which to calculate and print or save the power; default `*` takes 11 replication values centred around the required number of replicates |

### Parameters

`RESPONSE` = scalars |
Probability of response (i.e. the probability that an observation in one sample will be greater than the equivalent observation in the other sample) that should be detectable |
---|---|

`NREPLICATES` = scalars |
Saves the required number of replicates |

`VREPLICATION` = variates |
Numbers of replicates for which powers have been calculated |

`VPOWER` = variates |
Power (i.e. probability of detection) for the various numbers of replicates |

### Description

`SSIGNTEST`

calculates the number of replicates (or sample size) required for a sign test (see procedure `SIGNTEST`

). By default the calculations are done for a one-sided test (testing for evidence that the location of one sample is greater than the other, but you can set option `TMETHOD=onesided`

for a two-sided test (testing that locations of the samples are different). The significance level for the test is specified by the `PROBABILITY`

option (default 0.05 i.e. 5%).

The probability of response (i.e. the probability that an observation in one sample will be greater than the equivalent observation in the other sample) that should be detectable is supplied by the `RESPONSE`

parameter. The required probability for detection of the response (that is, the *power* of the test) is specified by the `POWER`

option (default 0.9). The sample size can be saved using the `NREPLICATES`

parameter.

The `PRINT`

option controls printed output, with settings:

`replication` |
to print the required number of replicates in each sample (i.e. the size of each sample); |
---|---|

`power` |
to print a table giving the power (i.e. probability of detection) provided by a range of numbers of replicates. |

By default both are printed.

The replications and corresponding powers can also be saved, in variates, using the `VREPLICATION`

and `VPOWER`

parameters. The `REPLICATION`

option can specify the replication values for which to calculate and print or save the power; if this is not set, the default is to take 11 replication values centred around the required number of replicates.

Options: `PRINT`

, `PROBABILITY`

, `POWER`

, `TMETHOD`

, `REPLICATION`

.

Parameters: `RESPONSE`

, `NREPLICATES`

, `VREPLICATION`

, `VPOWER`

.

### Method

An approximate number of replicates is calculated initially assuming a Normal approximation. This is then refined by calculating powers for a range of replications centred around that approximation.

### See also

Procedure: `SIGNTEST`

.

Commands for: Design of experiments.

### Example

CAPTION 'SSIGNTEST example',\ !t('One-sided tests, anticipated probabilities of response',\ '0.6, 0.7, 0.8 and 0.9.'); STYLE=meta,plain SSIGNTEST [PRINT=replication,power] 0.6,0.7,0.8,0.9