I am practicing statistics on the gss dataset. I want to study the relationship between people owning guns in the USA and political inclination. Owning guns or not is a nominal variable while political inclination ranges from extremely liberal to extremely conservative.

After some exploratory data analysis I got suspicious that people that are more liberal seem to own more guns. enter image description here How can I test this suspicion? I am aware of $\chi^2$ independence tests, and after conducting one on the data I can say that evidence of the pair of variables not being independent is very high, gun ownership rates depend on political inclinations, while this insight its valuable it says nothing about what I want to test.

I have been investigating Kruskal-wallis, but I am not sure if this is what I want.. Any help is appreciated!

EDIT: Is checking that $\mu_a \leq \mu_b \leq \mu_c \leq \mu_c$ the way to prove this relationship? this surely is a trivial statistics question, can anyone look into it?

  • $\begingroup$ Because it can be so easy to misunderstand how one's software interprets the meaning of a binary encoding, the first thing I would do is verify (by means of inspecting individual records and descriptive summaries) that I am interpreting the "No/Yes" results correctly--and not as the exact opposite of what is really in the database! $\endgroup$ – whuber Oct 10 '14 at 1:37
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    $\begingroup$ Yep the labels are switched in this plot, realized it after posting my question, I didn't bother to reupload the plot tough. Nicely spotted ;) $\endgroup$ – Ramalho Oct 10 '14 at 3:14

With seven ranks on the political affiliation question, I would be tempted to use it as a continuous predictor (1-7, or 0-6) in a logistic regression predicting gun ownership.

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    $\begingroup$ Thanks for the input. Well you could do that, but that would assume that the distance between adjacent political views is the same, namely 1. Why would you suggest a logistic regression? can you explain that line of though further? My experience with logistical regression is that they are powerful for classification. How can I use logistical regressions and make a sound statement that as citizen political range from conservative to liberal gun ownership increases? $\endgroup$ – Ramalho Oct 10 '14 at 0:50
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    $\begingroup$ Classification and explanation are just different interpretations of the same statistical results. If you found a significant (negative) regression coefficient in a logistic regression it would indicate that increased levels of conservativism are associated with decreased levels of gun ownership, which is as much as you can ever say, statistically, with this kind of cross-sectional data. As for the assumption of an interval scale - we often don't work with true interval scales in social sciences, but it's common with likert scales that have enough points (i.e. 7) to use them as such. $\endgroup$ – Sean Murphy Oct 10 '14 at 1:09
  • $\begingroup$ This may be of some help: theanalysisfactor.com/… $\endgroup$ – Sean Murphy Oct 10 '14 at 1:13

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