A statistical model is a formalization of relationships between variables in the form of mathematical equations. A statistical model describes how one or more random variables are related to one or more other variables. The model is statistical as the variables are not deterministically but stochastically related. In mathematical terms, a statistical model is frequently thought of as a pair where is the set of possible observations and the set of possible probability distributions on . It is assumed that there is a distinct element of which generates the observed data. Statistical inference enables us to make statements about which element(s) of this set are likely to be the true one.
Most statistical tests can be described in the form of a statistical model. For example, the Student's t-test for comparing the means of two groups can be formulated as seeing if an estimated parameter in the model is different from 0. Another similarity between tests and models is that there are assumptions involved. Error is assumed to be normally distributed in most models.
Famous quotes containing the word model:
“I had a wonderful job. I worked for a big model agency in Manhattan.... When I got on the subway to go to work, it was like traveling into another world. Oh, the shops were beautiful, we had Bergdorfs, Bendels, Bonwits, DePinna. The women wore hats and gloves. Another world. At home, it was cooking, cleaning, taking care of the kids, going to PTA, Girl Scouts. But when I got into the office, everything was different, I was different.”
—Estelle Shuster (b. c. 1923)