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I want to study if atheists/non-believers are having a harder time gaining results from 12-step facilitation treatment for alcohol dependence. My hypothesis is that a higher degree of belief in god/higher power is correlated with a higher degree of sobriety among patients going through a 12-step treatment for alcohol dependence.

I already have all the data I need. A group of around 200 ppl answered a big questionnaire at the beginning of treatment, giving a measure of self evaluated degree of "spiritual acceptance" (combined result from several items). I also have a binary result (sober or not sober) 1.5 years after treatment. So I have an independent variable which is a floating scale and a dependent variable which is binary.

My question is what would be the best strategy for analysis of the data. Since my question is whether atheists are disadvantaged, I'm considering to split the patients in two groups: one group with those who are beyond one standard deviation on the lower end of the spirituality scale and one group with the rest. In other words I would create an arbitrary division and have one "atheist" group and one group with those who are at least somewhat spiritual, then maybe do a chi square test. I'm not sure if this is considered good practice though? Would it be better to do a logistic regression and leave the dependent variable as a floating scale?

Olof
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    See [here](http://stats.stackexchange.com/questions/68834/). Arbitrary cut-offs are to be avoided. – Scortchi - Reinstate Monica Feb 16 '15 at 18:18
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    You should not normally split. [In addition there are several definitional difficulties with conflating non-spirituality with atheism (unless you define spirituality very specifically). If your interest lies in the relationship between effectiveness and spirituality as measured by your instrument, that can be answered without splitting. If it's specifically about atheism you'd need an instrument to address that.] – Glen_b Feb 16 '15 at 21:00
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    (ctd) ... Or at least you'd need a way (other than an arbitrary cut-off) to relate your 'spiritual acceptance' scale to atheism. Presumably if the research is to be applied (i.e. people are to make use of its conclusions in deciding whether a 12-step program makes sense for an atheist), it would be applied to self-identified atheism. Did you ask people to self-identify? [If it isn't to be applied to self-identified atheism, why would you need to split?] – Glen_b Feb 16 '15 at 21:09

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