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I am testing categorical variables for significant relationships, 5 age groups and 3 answer options (yes/no/don't know). Is there a test which will specifically tell me if e.g. age group 1 is significantly more likely to answer 'yes' than age group 2?

I have been using chi-squared but this only tells me if there is a difference in the pattern and not specifically where the difference comes from.

Is looking at indexed values and percentages in the chi-squared table really the only way to find out where the difference came from? I find this method could be fairly inaccurate if a variable has many categories?

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    $\begingroup$ It may be the case that age should not be understood categorically but ordinally, or even continuously (e.g. increasing age increases probability of such-and-such answer). Just a thought. $\endgroup$ – Alexis Nov 5 '14 at 19:03
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    $\begingroup$ These are commonly known as contrasts. After running a regression/ANOVA, one can can test linear combinations of the coefficients (for example, Age 1 vs Age 2, or something more complex such as Age 1 and 2 vs Age 3). However, your case is a bit more complicated since your outcome variable (answer options) is multinomial. $\endgroup$ – Affine Nov 5 '14 at 19:28
  • $\begingroup$ Can contrasts be used for categorical variables? $\endgroup$ – Julia Nov 6 '14 at 8:34
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    $\begingroup$ @Julia: Contrasts are on parameters, so, yes. $\endgroup$ – kjetil b halvorsen Apr 7 '17 at 14:46
  • $\begingroup$ You could look at log-linear models, simply said they try to predict the counts in the cells of you contingency table. But if you google it you will find several links. $\endgroup$ – user83346 Jul 24 '17 at 13:10
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With three answer options, yes/no/don't know, you might look into multinomial logistic regression. Or, maybe, if in your context you can justify an ordering like yes/don't know/no, you can use ordinal logistic regression. If the predictor variable is age, that can be coded as an ordered variable, maybe with only linear and quadratic effects.

If this is more efficient than chi square tests? You could try some simulations to find out ...

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