Calculates chi-square statistics for one- and two-way tables (A.D. Todd & P.K. Leech).

### Options

`PRINT` = string tokens |
Output required (`test` , `probability` , `fittedvalues` , `tchisquare` ); default `test` , `prob` |
---|---|

`METHOD` = string token |
Method for calculating chi-square (`pearson` , `maximumlikelihood` ); default `pear` |

`GOODNESSOFFIT` = string token |
Whether to carry out a goodness-of-fit test for the `DATA` values against a supplied set of `FITTEDVALUES` (`yes` , `no` ); default `no` |

### Parameters

`DATA` = tables |
Table containing observed data |
---|---|

`CHISQUARE` = scalars |
Scalar to save the chi-square value |

`DF` = scalars |
Scalar to supply or save the degrees of freedom |

`PROBABILITY` = scalars |
Scalar to save the probability value |

`FITTEDVALUES` = tables |
Table of expected values |

`RESIDUALS` = tables |
Table of standardized residuals |

`TCHISQUARE` = tables |
Table whose cells show the individual contributions to the chi-square value |

### Description

The `CHISQUARE`

procedure calculates chi-square statistics. The `DATA`

parameter supplies the data values. If these are in a two-way table, `CHISQUARE`

produces the usual test of association between the row and column factor of the table; if a one-way table is supplied, the statistic assesses whether the different cells of the table contain different proportions of the data. Alternatively, you can set option `GOODNESSOFFIT=yes`

to request a goodness-of-fit test between the data values and the set of expected values supplied by the `FITTEDVALUES`

parameter; if you provide the degrees of freedom, using the `DF`

parameter, the procedure can also calculate the probability value.

The `PRINT`

option controls the printed output, with the settings: `test`

to print the chi-square value and degrees of freedom; `probability`

for the probability value; `fittedvalues`

data, fitted (expected) values and standardized residuals; and `tchisquare`

to show the contribution of each cell of the table to the chi-square value. By default, the statistic is calculated by the usual Pearson approximation (see the *Method* section), but you can set option `METHOD=likelihood`

to calculate the chi-square by maximum likelihood (using the Genstat facilities for generalized linear models).

Parameters `CHISQUARE`

, `DF`

, `PROBABILITY`

, `FITTEDVALUES`

, `RESIDUALS`

and `TCHISQUARE`

allow the results to be saved in appropriate Genstat data structures.

Options: `PRINT`

, `METHOD`

, `GOODNESSOFFIT`

.

Parameters: `DATA`

, `CHISQUARE`

, `DF`

, `PROBABILITY`

, `FITTEDVALUES`

, `RESIDUALS`

, `TCHISQUARE`

.

### Method

With option `METHOD=pearson`

, the statistic is calculated by the usual Pearson formula:

chi-square = sum( (*o*–*e*) × (*o*–*e*) / *e* ),

where *o* = observed, and *e* = expected.

If `GOODNESSOFFIT=yes`

, the table *e* is supplied by the `FITTEDVALUES`

parameter. Otherwise, for a one-way table *e* is the mean of the `DATA`

values, while for a two-way table

*e* = (row total) × (column total) / (total in table).

For `METHOD=maximumlikelihood`

, `CHISQUARE`

takes the deviance from fitting a generalized linear model with a log link and a Poisson distribution.

### See also

Procedures: `CHIPERMTEST`

, `CATRENDTEST`

, `CMHTEST`

.

Commands for: Basic and nonparametric statistics, Regression analysis.

### Example

CAPTION 'CHISQUARE example',!t('1) Data from Snedecor & Cochran (1980)',\ 'Statistical Methods (7th edition), p. 210.'); STYLE=meta,plain FACTOR [LABELS=!T(Ulcer,Cancer,Control); VALUES=3(1...3)] Disease FACTOR [LABELS=!T(O,A,B); VALUES=(1...3)3] BloodTp TABLE [CLASSIFICATION=Disease,BloodTp; VALUES=983,679,134,\ 383,416,84, 2892,2625,570] Cases CHISQUARE Cases CAPTION !t('2) Goodness of fit test: Mead, Curnow & Hasted (1993),',\ 'Statistical Methods in Agriculture & Experimental Biology,',\ 'Chapman & Hall, Example 14.1, p. 306-7. Test that that 3 types',\ 'of cell AA, AS, SS occur in ratio 3:7:3 for total over 5 plants.',\ 'There are 2 df as 1 parameter (total) has been calculated from',\ '3 data values i.e. df=3-1.') FACTOR [LABELS=!t(AA,AS,SS)] Assoc TABLE [CLASSIFICATION=Assoc] Observed,Expratio;\ VALUES=!(152,340,175),!(3,7,3) CALCULATE Expected = SUM(Observed)*Expratio/SUM(Expratio) CHISQUARE [PRINT=test,probability,fitted; GOODNESSOFFIT=yes]\ Observed; DF=2; FITTED=Expected