Statistics and social science

There are a number of distinct uses for statistics in the social sciences. One use is simply to provide a summary description of complicated features in a population.

A second use of statistics is to predict (some) features of a unit or group in a population, given other features of the unit or group. For example, a company may charge lower health insurance rates for people who do not smoke, because smokers have a lower risk of lung cancer. Some companies could also charge lower health insurance rates for people who do not have a heavy cough, because the probability of having lung cancer is lower for such people. Predictions can be made by developing a probabilistic model of the joint distribution of incidence of smoking, lung cancer, and incidence of heavy coughs in the population.

A third use of statistics is to help predict the probable effects of adopting different policies. For example, the government may consider a number of alternative policies for reducing the rate of lung cancer. One policy would ban smoking. Another policy would make everyone who coughs take cough medicine. Both smoking and coughing are predictors of lung cancer. But because smoking is a cause of lung cancer, while coughing is an effect of lung cancer, the first policy seems as if it might achieve the desired effect, while the second does not. In order to answer policy questions we need to know not only how the variables are distributed in the actual population, but also how they are causally related. A causal model specifies the causal relations between features in a population, as well as specifying a probability distribution of the features. Statistical information together with causal information can be used to predict the effects of adopting a certain policy.

A fourth use of statistics is in helping decide which policies should be adopted in order to achieve specific goals. Such decisions are based not only on the probable effects of each policy, but also on assigning different utilities to each possible outcome. This use of statistics is a branch of decision theory.