You can find out more on variable selection & statistical analysis procedures related to your research from your university's subscribed journals' articles / theses like ProQuest, EBSCO, Emerald etc. You can also obtain some free academic articles & theses from Google Scholar search albeit some are outdated. Moreover, you can also try out some universities' websites with free theses like this link from Council of Australian University Librarians (CAUL) - last time without login can access, now think you need to create a User ID & password. They have various PhD & some Master theses from different universities in Australia.
http://www.caul.edu.au/register
However, before you embark on the above activity, it is advisable to have your research outline e.g. research problem, research objectives, research questions, conceptual framework / research model and if possible research method. So that you can save time & effort during this literature review by selecting those relevant variables and statistical analysis procedures.
The first and foremost thing for any research to carry out is to define the area of research then possibly the objectives. Once the objectives are defined then the question of variable selection come into picture. Suppose, I wish to study the effect of lead exposure on health of children. This is your general objective. Now, the question is how do you measure your lead exposure? The literature reveiw or help of an expert come handy in such a situation. Obviously, you have to study blood analysis. So blood samples become your first variable. Second, how do you measure effect of lead exposure on health? Now, the question is what are the parameter which are likely to be affected by lead exposure? Expert or litarature review suggest that the growth can be taken as the parameter. Now, the growth can be studied with the help of height , weight and other sexually related variables like age at attainment of menarch in girls or appearance of pubic hair in boys. This obviously define that your subjects should be in the range of 10-14 or 10-15 years age. Now having defined the parameter, the question comes of analysis. So devide the groups in to low exposure and high exposure groups and see the proportion of children attaining the sexualy maturity (menache or appearance of public hair). If it differs you have proved the point.
Take another example that you wish to study the ill effects of alcohol consumptions. Now you have to think what are the possible ill effects of alcohol consumption which comes to your mind. Say, health, money spent, social abuse, crime rate etc. Now for each of this broad term decide the specific variable(s) which you can study. For health, you can choose his frequency of visit to hospital, or duration of period absent from work or more specific health problems like liver cirosis. For money, assess the absolute money spent of alcohol drinking, the proportion of money spent on alcohol drinking or the loan taken by the individuals to fulfill their demand of alcohol consumption. For social abuse, find out from his wife or neighbours how many times he quarrals with them ie., the frequency of fight or the number of times whether went to police station on complains of some crime.
So, start with the area of reasearch, objective definition, variable selection and then appropriate data analysis.
Given any area of research., one can start defining his or her research problem and then proceed to carry out the suitable research.
You have asked two questions in one and both are equally vague. First is variable relevant to address a 'social science' issue; and then 'statistical procedure' to analyse the issue empirically. Now first you have to clearly identify what constitutes your definition of 'social science'. It could be absolutely anything, e.g., income, education, employment, culture, belief, family structure, gender, occupational choice, crime, corruption, and so forth. One added complexity of data in social science is that the variables you are selecting are proxies for what you actually wish to measure. For example, income is a proxy measure for wealth, education is a proxy measure of human capital which is then assumed to have an influence on your ability to undertake income generating activities or make informed choices. Therefore, first get a clear idea of what you want to investigate. Then decide on which indicators best address the issue. The method always comes second as it is dependent on what you have in hand to solve. The starting point will be to consult Human Development Report hosted at UNDP site. Most of those indicators in various tables belong to your 'social science' area. Hope this helps.