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POL242Y1 (17)


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University of Toronto St. George
Political Science
Joseph Fletcher

Crosstabs & Measures of Association Oct/9/12 Recall:  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 Establishing Association • 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!” Using/Interpreting Crosstabs • Data arranged in side-by-side frequency distributions • Independent Variable (X) presented across the top of the table – in columns. 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 table 2) Always percentage down within categories of the IV 3) Interpret the relationship by comparing columns across the rows. Diagonals 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 by summarizing: o Magnitude (strength) of the relationship o Direction of the relationship • Magnitude: ranges from 0 (completely unpredictable) to 1 (predictable) Two Cautionary Notes • Direction is not useful wi
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