(sample multiple crosstabulation table)

SEX AND 1980 PRESIDENTIAL VOTE BY INCOME GROUPS

Presidential Vote                                                                                  $17,000 to                   $25,000
(major parties only)       Total Sample                Under $17,000             $24,999                       and over

Female Male                Female Male                Female Male                Female Male

Carter                          47%     40%                 57%     43%                 40%     36%                 36%     34%

Reagan                         53%     61%                 43%     57%                 60%     64%                 64%     65%

Total                            100%   101%               100%   100%               100%   100%               100%   99%

N of cases                    (482)    (395)                (108)    (86)                  (78)      (92)                  (102)    (140)

X²= 4.8                        X² = 3.96                     X² = .08                       X² = .01

p = .03                         p = .05                         p = .77                         p = .89

There is a statistically significant relationship between sex and presidential vote for the sample as a whole. 61% of the men voted for Reagan as compared to 53% of the women. When controlling for family income group, however, we found that the relationship between sex and the vote was significant only for the under $17,000 family income group. Among this group, 57% of the men voted for Reagan, as compared to 43% of the women. Among the higher income groups, there was no significant difference with 60% or more of both sexes voting for Reagan.

------------------------   The explanatory material below this line is not part of the sample, it is for your information -------------------

In this example, sex is the Independent variable, presidential vote is the dependent variable, and income is the test variable.

In analyzing a multivariate crosstabulation, we compare the total sample table with the "partial" sample tables, the tables using a sub-group.  In this case the partial sample tables are income groups.  Income is our "test" variable because we are using it to test the relationship between the independent and dependent variables.

Our first question is whether the test variable is "antecedent" or "intervening".  Does it occur BEFORE the independent variable is determined, or BETWEEN the independent or dependent variable.  This is a matter of the logic of causal sequence.  In this case we say that it is intervening because sex can determine income, but income does not determine sex.  Income is an intervening variable between sex and vote.

We may get different results when we compare the  partial tables to the total sample tables.

We may find that they are the same.  In this case, in the terminology of the Elaboration Paradigm, we would say that we have REPLICATED    our findings.

We may find that the relationship is much less or disappears altogether.  In this case, we must ask whether the test variable was antecedent or intervening.  If it is ANTECEDENT we say that we found a SPURIOUS relationship or that the relationship has been EXPLAINED.  If it is INTERVENING, we say that we have INTERPRETED the relationship, we have shown a causal link.

Or our results may be split, different for some variables than for others.  This particular example is a case of  specification.  The relationship is replicated for the low income group, but not for the upper income group.

Of course, real data may be more ambiguous.  Relationships often decline somewhat but not altogether.  Statistical significance is not always a useful test because sample sizes go down as we introduce test variables.  These ambiguous results should be described accurately in the accompanying text.