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I'd like to review the results of a recent survey I conducted. I'd like to see how one set of answers may/may not have influenced another set of answers.

For example:

If users who answered question #1 on a 1-8 Likert scale with answers from 6-8, does this correlate to how they answered questions 2-8?

Or:

Users who answered false for question 10 did/did not similarly answer questions 11-12.

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Causal influence is more a matter of experimental design than a choice of statistical analysis. If you haven't experimentally manipulated the first set of answers or don't have a randomly assigned control group, you had better have some other, fairly rock-solid rationale for claiming causal influence from correlations. I'm having trouble even thinking of a defensible example. (Comments / edits welcome!)

Anyway, since Likert scale data are ordinal, I'd recommend calculating Kendall's tau to estimate correlations among them. Spearman's rho and the Goodman–Kruskal gamma are common alternatives. For more on those, see:

For a measure of association between binary variables, see the phi coefficient.

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