Crosstabs & Measures of Association
Most causal thinking in social sciences is probablistic, not
deterministic: as x increases, the probability of Y increase, not that X
invariably produces Y.
WE can observe only association per Hume
We must therefore infer causation
Not one, but many possible causes.
Inferring Causal Relations
1) There must be association
X Y; ~X ~Y
2) Time order must be considered
3) Must rule out possible rival explanations
4) Must be able to identify the process by which one factor brings about
change in another
• With nominal or ordinal data, relationship usually presented in tabular
or table form.
• Why? Hypotheses rest on core idea of comparison.
Ex: If we compare respondents on basis of their value on the IV
(independent variable), say party identification, they should also differ
along DV (dependent variable), say support for gay rights
• Crosstabs are a wonderful means of making comparisons • “God speaks to you through crosstabs!”
• Data arranged in side-by-side frequency distributions
• Independent Variable (X) presented across the top of the table – in
If ordinal, arrange from low scores (on left) to high scores (on right)
• Dependent Variable (Y) presented down the left hand side of the
table – in rows
Again, if ordinal, arrange from low (at bottom) to high (at bottom)
• Data presented so that categories of the IV ad to 100%
(precentagaing within categories of the IV down in a table))
• Comparisons are made across categories of the IV (from left to right.
To see the effect of the IV on the DV).
Rules of Crosstabs
1) Make the IV define the columns and the DV define the rows of the
2) Always percentage down within categories of the IV
3) Interpret the relationship by comparing columns across the rows.
Main diagonal: running to the right and down.
• When larger proportion of cases fall on main diagonal, relationship is
said to be direct or positive.
• Low values on X associated with low values on Y; high values on X
associated with high values on Y.
Off diagonal: running to the right and up • When larger proportion of cases fall on off diagonal, relationship is
said to be inverse or negative
• Low values on X associated with high values on Y
• Low values on Y associated with high values on X
Explaining Variation in Y
• There is likely to be more than one explanation or ‘cause’ in Y
• So we will generally be looking at:
o X1 Y
o X2 Y
• To compare, we want to know relative strength of each relationship
• A variety of summary terms called measures of association are used.
Measures of Association
• Compress information that appears in a crosstab into a single number
o Magnitude (strength) of the relationship
o Direction of the relationship
• Magnitude: ranges from 0 (completely unpredictable) to 1
Two Cautionary Notes
• Direction is not useful wi