Crosstabulations: Quick Notes

Describe the table

-table number, independent (explanatory) variable, dependent (response) variable

TI 2-way (x3,x1) presumed independent variable is the column variable (x1) & dependant x3 TII 2-way (x3,x2) another presumed independent variable in column (x2) TIII 3-way (x1(x3,x2)) re examining TII (x2) while holding for original (x1)

Interpret

-one of the rows of column percentages (lowers, highest, or specially relevant row)-percentages as odds (4%, 4/100) to be able to compare odds across columns (times more likely)

Test of significance

Chi-Squared 2 Testing the Null Hypothesis (assym. sig. Value is the associated p value of the test)

Ho: Variables x1,x3 are independent (not associated) in the population from which the sample is drawn.

Assuming conventional level for scientific significance of 95% chance that association is true for the population, the chance of the null hypothesis needs to be less than 5% (the probability produced by the 2 test needs to be p

Interpret Measure of association

Gamma ordinal-ordinal, ordinal-dichotomous nominal (value column of Stat Table) no assoc. weak moderate strong v. strong perfect direction 0 0.2 0.4 0.6 0.8 1 symmetric (if -ve, x1 x3)

suggests a ___ association b/w the variables and x1 explains *100% of the variation in x3.

Logic: a Proportional Reduction of Error PRE statistic, judges the strength of association b/w variables by calculating how much the knowledge of the value of one variable (x1) reduces the error in guessing the value of the other variable (x3)

In the case of involves the guessing of ordinal arrangement of values

= (Ps Pd) / (Ps + Pd) Ps = concordant pairs, Pd = discordant pairs

Elaboration Paradigm 3-way Cross tab

Elaborate a relationship between two variables TII (x3,x2) by introducing a third (x1)

Bivariate analysis examines relationship between independent & dependent variable TII (x3,x2)Multivariate analysis use of third variable (x1) to examine same relationship w/i each sub-samples

-categories of x1 (#cases) define 2+ sub-spaces in the data, partial tables in TIII-in each sub-space x1 is the 'control' variable, held constant

What happens to cell percentages? (Compare multivariate analysis subspaces TIII to bivariate analysis TII)

Five logical possibilities of elaboration paradigm Instance of:

Replication same or very similar c.percentages & differences b/w them in TIII sub-spaces and TIISuppression consistently higher odds ratios in TIII sub-spaces than in TII Specification inconsistent odd ratios in TIII subspaces (1,2,3,4) compared to TII (2.5)

Spurious consistently smaller percentages differences in the row in TIII than TII-thus odd ratios significantly smaller (even approaching 0), defined by control variable ...-rival independent variable (x1)-false association b/w x2 and x3 (relationship 'found' at TII is a spurious relationship) -only appears b/c x1 is a common antecedent to both x2 and x3

Explanation consistently smaller percentages differences in the row in TIII than TII-thus odd ratios significantly smaller (even approaching 0), defined by control variable ...-intervening variable (x1)-dependent on ind. var. x2, independent and determining of variation in dep. Var. x3-'tap' in the causal flow, explanatory power of x2 flows to x3 via x1

Use elaboration to see if bivariate analysis maintains over all statistical significance.

Perform test of significance for each of the sub-spaces, partial tables (2)Ex When controlling for variable x1 the relationship between x3 and x2

-is no longer statistically significant over all, but a partial association remains for a case of x1 -thus variable x1 does not appear to have an impact on weather x2 will affect x3

Perform test of measure of association for each of the partial tables ( or V) -which variable is more important at the bivariate level (TI vs. TII )Ex When controlling for variable x1 the relationship between x3 and x2

-does appear to have an impact on weather x2 will affect x3 an intervening variable -impact of x1 is seen by the various explanatory powers of x2 (TII vs. TIII ), some some