Calculates the gamma statistic of agreement for ordinal data (A.W. Gordon).

### Options

`PRINT` = string token |
Whether to print the statistic with its associated information and the resulting test (`test` ); default `test` |
---|---|

`METHOD` = string token |
Type of test required (`twosided` , `positive` , `negative` ); default `twos` |

### Parameters

`DATA` = tables |
Tables of data each classified by the two variables (factors) of interest |
---|---|

`STATISTIC` = scalars |
Save the value of gamma for each data table |

`VARIANCE` = scalars |
Save the corresponding variances |

### Description

The gamma statistic (Siegel & Castellan 1988, pages 291-298) provides a way of assessing the agreement between two variables measured using ordinal scales. In Genstat these would each be represented as factors whose levels represent a ranking of the individuals according to some measurement.

For example, suppose we have a factor `A`

with *r* levels and a factor `B`

with *k* levels. The data for `GSTATISTIC`

, specified by the `DATA`

parameter, consists of an *r* by *k* table classified by `A`

and `B`

, whose entries indicate the number of times that the *i*th level of variable `A`

occurs with the *j*th level of variable `B`

. The table must not contain any missing values. The statistic has the value 1 when there is no disagreement in the ordering of the variables, -1 if the ordering defined by `A`

has no disagreement with the reverse of the ordering defined by `B`

, and zero if the variables are independent.

The printing of the test statistic and its associated information is controlled by the `PRINT`

option. With the default, `test`

, the procedure prints the number of times that the variables agree and disagree, the resulting value of gamma and its variance. When the number of observations *N* is large, the sampling distribution of gamma is approximately Normal. The procedure thus also prints the value of gamma divided by the variance, and its probability assuming a Normal distribution. A warning is printed if *N* is less than 20.

The test is assumed to be two-sided (i.e. no prior knowledge is assumed about the type of association) unless otherwise requested by the `METHOD`

option. Setting `METHOD=positive`

will give a one-sided test of the null hypothesis that there is a positive association. Similarly, `METHOD=negative`

will produce a one-sided test that there is a negative association.

The `STATISTIC`

and `VARIANCE`

parameters allow gamma and its variance to be saved, in scalars.

Option: `PRINT`

, `METHOD`

.

Parameters: `DATA`

, `STATISTIC`

, `VARIANCE`

.

### Method

The method used is as described in Siegel & Castellan (1988, pages 291-298).

### Reference

Siegel, S. & Castellan, N.J. (1988). *Nonparametric Statistics for the behavioural sciences (second edition)*. McGraw-Hill, New York.

### See also

Procedure: `KAPPA`

.

Commands for Basic and nonparametric statistics.

### Example

CAPTION 'GSTATISTIC example',\ 'Data from Siegel & Castellan (1988) p. 296'; STYLE=meta,plain FACTOR [LABELS=!t('Successful quitter','In-process quitter',\ 'Unsuccessful quitter')] Ability & [LABELS=!t('1','2-4','5-9','10-14','15-19','20-25','>25')] Time TABLE [CLASSIFICATION=Ability,Time; VALUES=13,29,26, 22,9,8, 8,5,2,\ 6,2,1, 3,0,1, 9,16,14, 21,16,29] Nurses PRINT Nurses; FIELD=6; DECIMALS=0 GSTATISTIC Nurses