Kosuke Imai has recently published a great introduction: Quantitative Social Science: An Introduction. Finally a stats data analysis book that has arrived in the present! Yes, we can get away with very little mathematics and still do quantitative analysis. Yes, examples from published work are much more interesting than constructed toy examples. Yes, R can be accessible. Yes, we can talk about causality, measurement, and prediction (even Bayes) before getting to hypothesis testing. Yes, we can work with text and spatial data.
Sociologist. Quantitativist. University of Neuchâtel.
Didier Ruedin 