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# GSTATISTIC procedure

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` Type of test required (`twosided`, `positive`, `negative`); default `twos`

### Parameters

`DATA` = tables Tables of data each classified by the two variables (factors) of interest Save the value of gamma for each data table 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 ith level of variable `A` occurs with the jth 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.

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
```
Updated on March 7, 2019