Performs a one or two sample sign test (E. Stephens & P.W. Goedhart).

### Options

`PRINT` = string token |
Whether to print the test statistic with the associated probability and sample size (`test` ); default `test` |
---|---|

`METHOD` = string token |
Type of test (`twosided` , `greaterthan` , `lessthan` ); default `twos` |

`GROUPS` = factor |
Defines the groups for a two-sample test if only the `Y1` parameter is specified |

`NULL` = scalar |
Median value or difference in medians under the null hypothesis; default 0 |

### Parameters

`Y1` = variates |
Data values for a one-sample sign test (neither `Y2` nor `GROUPS` specified), or for the first sample of a two-sample test (`Y2` also specified) or the values in both samples of a two-sample test (`GROUPS` specified but not `Y2` ) |
---|---|

`Y2` = variates |
Data values for the second sample of a two-sample test |

`STATISTIC` = scalars |
To save the sign test statistic |

`NBINOMIAL` = scalars |
To save the effective sample size |

`PROBABILITY` = scalars |
To save the probability level of the test |

### Description

The sign test is a nonparametric test for difference in location between two related samples, or for testing the location of a single sample. The data values are specified by the parameters `Y1`

and `Y2`

and the option `GROUPS`

. For a one-sample test, the `Y1`

parameter should be set to a variates containing the data. The data for a two-sample test can either be specified in two separate variates using the parameters `Y1`

and `Y2`

. Alternatively, they can be given in a single variate, with the `GROUPS`

option set to a factor to identify the two samples; the units are then assumed to be specified in the same order within each group. The `GROUPS`

option is ignored when the `Y2`

parameter is set. The `NULL`

option defines the size of the median under the null hypothesis for a one-sample test, or the difference between the two medians in a two-sample test. By default `NULL=0`

.

The test is assumed to be two-sided unless otherwise requested by the `METHOD`

option. Settings `greaterthan`

or `lessthan`

will give one-sided tests for the median or the difference between medians greater than, or less than, the null hypothesis value respectively.

In a one-sample test, units that are equal to the null hypothesis median are excluded and the effective sample-size is reduced. Similarly, in a two-sample test, units are excluded where the differences between the pairs of values are equal to that required by the null hypothesis. Units with missing values are also excluded.

By default, `SIGNTEST`

prints the test statistic, the effective sample size and the (exact) probability level. This information can also be saved in named scalars using the `STATISTIC`

, `NBINOMIAL`

and `PROBABILITY`

parameters repectively, and printing can be suppressed by setting option `PRINT=*`

.

Options: `PRINT`

, `METHOD`

, `GROUPS`

, `NULL`

.

Parameters: `Y1`

, `Y2`

, `STATISTIC`

, `NBINOMIAL`

, `PROBABILITY`

.

### Method

The procedure uses standard Genstat directives for calculation and manipulation.

### Action with `RESTRICT`

If the variates or the factor are restricted, the test is calculated using only the units not excluded by the restriction. In a two-sample test, the two variates or the variate and factor should be restricted in the same way. `RESTRICT`

can be used for example to limit the data to only one or two groups when the `GROUPS`

factor has more than two levels.

### Reference

Siegel, S. (1956). *Nonparametric Statistics for the Behavioural Sciences*. McGraw-Hill, New York.

### See also

Procedure: `SSIGNTEST`

, `MANNWHITNEY`

, `TTEST`

, `WILCOXON`

.

Commands for: Basic and nonparametric statistics.

### Example

CAPTION 'SIGNTEST example',\ 'Data from Siegel (1956), Nonparametric Statistics, p. 70.',\ !t('1. Carry out a two-sample, two-sided test, saving the sign test',\ 'statistic, effective sample size and binomial probability in',\ 'scalars Stat, Nbin and Prob respectively.');\ STYLE=meta,plain,plain VARIATE [VALUES=4,4,5,5,3,2,5,3,1,5,5,5,4,5,5,5,5] F & [VALUES=2,3,3,3,3,3,3,3,2,3,2,2,5,2,5,3,1] M SIGNTEST Y1=F; Y2=M; STATISTIC=Stat; NBINOMIAL=Nbin; PROBABILITY=Prob PRINT Stat,Nbin,Prob CAPTION !t('2. Repeat example 1 for a one-sided alternative hypothesis',\ 'that variate F has a greater median than M.') SIGNTEST [METHOD=greaterthan] F ; M CAPTION !t('3. Repeat example 2 using a single variate with the GROUPS',\ 'option set.') VARIATE [VALUES=#F, #M] Single FACTOR [LABELS=!t(F,M); VALUES=17(1,2)] Group SIGNTEST [METHOD=greaterthan; GROUPS=Group] Single CAPTION !t('4. Carry out a one-sample, two-sided sign test with the null',\ 'hypothesis that the median of variate F is 3.') SIGNTEST [NULL=3] F