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