Statistics in Crosstabulations
Crosstabulations generally allow us to identify relationships between
the crosstabulated variables. The following table illustrates an example
of a very strong relationship between two variables: variable Age
(Adult vs. Child)
and variable Cookie preference
(A vs. B).

COOKIE:
A 
COOKIE:
B 

AGE:
ADULT 
50 
0 
50 
AGE:
CHILD 
0 
50 
50 

50 
50 
100 
All adults chose cookie A,
while all children chose cookie B.
In this case there is little doubt about the reliability of the finding,
because it is hardly conceivable that one would obtain such a pattern
of frequencies by chance alone; that is, without the existence of a "true"
difference between the cookie preferences of adults and children. However,
in reallife, relations between variables are typically much weaker, and
thus the question arises as to how to measure those relationships, and
how to evaluate their reliability (statistical
significance). The following review includes the most common measures
of relationships between two categorical variables; that is, measures
for twoway tables. The techniques used to analyze simultaneous relations
between more than two variables in higher order crosstabulations are discussed
in the context of the LogLinear
Analysis module and the Correspondence
Analysis module.
Crosstabulation tables with up to 6 variables (6way tables) can be
generated automatically. Higherway tables of practically unlimited order
can be produced using the case
selection conditions option. All measures of relations between crosstabulated
variables are reported for twoway tables, even if they represent only
"slices" of a larger multiway table (see the description of
the Crosstabulation Tables Results
dialog).
See also:
Pearson
Chisquare
Maximumlikelihood
Chisquare
Yates
correction
Fisher
exact test
McNemar
Chisquare
Coefficient
Phi
Tetrachoric
correlation
Coefficient
of contingency
Interpretation
of contingency measures
Statistics
based on ranks
Cramer's
V
Generalized Linear/Nonlinear Models (GLZ).
An alternative way to analyze crosstabulation tables is also provided
in the Generalized
Linear/Nonlinear Models (GLZ) module. This module is an implementation
of the generalized
linear model and allows you to compute a standard, stepwise,
or best
subset multiple regression analysis with categorical (as well as continuous)
predictors, and for binomial
or multinomial
dependent
(response) variables (see Link
function).